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Title: History of the inductive sciences, from the earliest to the
       present time

Author: William Whewell

Release Date: August 5, 2022 [eBook #68693]

Language: English

Produced by: Ed Brandon

*** START OF THE PROJECT GUTENBERG EBOOK HISTORY OF THE INDUCTIVE
SCIENCES, FROM THE EARLIEST TO THE PRESENT TIME ***


HISTORY
OF THE
INDUCTIVE SCIENCES.

VOLUME I.


HISTORY
OF THE
INDUCTIVE SCIENCES,
FROM
THE EARLIEST TO THE PRESENT TIME.
BY WILLIAM WHEWELL, D. D.,
MASTER OF TRINITY COLLEGE, CAMBRIDGE.
_THE THIRD EDITION, WITH ADDITIONS._
IN TWO VOLUMES.


VOLUME I.


NEW YORK:
D. APPLETON AND COMPANY,
549 & 551 BROADWAY.
1875.




TO SIR JOHN FREDERICK WILLIAM HERSCHEL,
K.G.H.


MY DEAR HERSCHEL,
IT is with no common pleasure that I take up my pen to dedicate
these volumes to you. They are the result of trains of thought which
have often been the subject of our conversation, and of which the
origin goes back to the period of our early companionship at the
University. And if I had ever wavered in my purpose of combining
such reflections and researches into a whole, I should have derived
a renewed impulse and increased animation from your delightful
Discourse on a kindred subject. For I could not have read it without
finding this portion of philosophy invested with a fresh charm; and
though I might be well aware that I could not aspire to that large
share of popularity which your work so justly gained, I should still
have reflected, that something was due to the subject itself, and
should have hoped that my own aim was so far similar to yours, that
the present work might have a chance of exciting an interest in some
of your readers. That it will interest you, I do not at all hesitate
to believe.

If you were now in England I should stop here: but when a friend is
removed for years to a far distant land, we seem to acquire a right
to speak openly of his good qualities. I cannot, therefore, prevail
upon myself to lay down my pen without alluding to the affectionate
admiration of your moral and social, as well as intellectual
excellencies, which springs up in the hearts of your friends,
whenever you are thought of. They are much delighted to look upon
the halo of deserved fame which plays round your head but still
more, to recollect, {6} as one of them said, that your head is far
from being the best part about you.

May your sojourn in the southern hemisphere be as happy and
successful as its object is noble and worthy of you; and may your
return home be speedy and prosperous, as soon as your purpose is
attained.

Ever, my dear Herschel, yours,

W. WHEWELL.
March 22, 1837.

P.S. So I wrote nearly ten years ago, when you were at the Cape of
Good Hope, employed in your great task of making a complete standard
survey of the nebulæ and double stars visible to man. Now that you
are, as I trust, in a few weeks about to put the crowning stone upon
your edifice by the publication of your "Observations in the
Southern Hemisphere," I cannot refrain from congratulating you upon
having had your life ennobled by the conception and happy execution
of so great a design, and once more offering you my wishes that you
may long enjoy the glory you have so well won.

W. W.
TRINITY COLLEGE, NOV. 22, 1846.



{{7}}
PREFACE
TO THE THIRD EDITION.


IN the Prefaces to the previous Editions of this work, several
remarks were made which it is not necessary now to repeat to the
same extent. That a History of the Sciences, executed as this is,
has some value in the eyes of the Public, is sufficiently proved by
the circulation which it has obtained. I am still able to say that I
have seen no objection urged against the plan of the work, and
scarcely any against the details. The attempt to throw the history
of each science into EPOCHS at which some great and cardinal
discovery was made, and to arrange the subordinate events of each
history as belonging to the PRELUDES and the SEQUELS of such Epochs,
appears to be assented to, as conveniently and fairly exhibiting the
progress of scientific truth. Such a view being assumed, as it was a
constant light and guide to the writer in his task, so will it also,
I think, make the view of the reader far more clear and
comprehensive than it could otherwise be. With regard to the manner
in which this plan has been carried into effect with reference to
particular writers and their researches, as I have said, I have seen
scarcely any objection made. I was aware, as I stated at the outset,
of the difficulty and delicacy of the office which I had undertaken;
but I had various considerations to encourage me to go through it;
and I had a trust, which I {8} have as yet seen nothing to disturb,
that I should be able to speak impartially of the great scientific
men of all ages, even of our own.

I have already said, in the Introduction, that the work aimed at
being, not merely a narration of the facts in the history of
Science, but a basis for the Philosophy of Science. It seemed to me
that our study of the modes of discovering truth ought to be based
upon a survey of the truths which have been discovered. This maxim,
so stated, seems sufficiently self-evident; yet it has, even up to
the present time, been very rarely acted on. Those who discourse
concerning the nature of Truth and the mode of its discovery, still,
commonly, make for themselves examples of truths, which for the most
part are utterly frivolous and unsubstantial (as in most Treatises
on Logic); or else they dig up, over and over, the narrow and
special field of mathematical truth, which certainly cannot, of
itself, exemplify the general mode by which man has attained to the
vast body of certain truth which he now possesses.

Yet it must not be denied that the Ideas which form the basis of
Mathematical Truth are concerned in the formation of Scientific
Truth in general; and discussions concerning these Ideas are by no
means necessarily barren of advantage. But it must be borne in mind
that, besides these Ideas, there are also others, which no less lie
at the root of Scientific Truth; and concerning which there have
been, at various periods, discussions which have had an important
bearing on the progress of Scientific Truth;--such as discussions
concerning the nature and necessary attributes of Matter, of Force,
of Atoms, of Mediums, of Kinds, of Organization. The controversies
which have taken place concerning these have an important place in
the history of Natural Science in {9} its most extended sense. Yet
it appeared convenient to carry on the history of Science, so far as
it depends on Observation, in a line separate from these discussions
concerning Ideas. The account of these discussions and the
consequent controversies, therefore, though it be thoroughly
historical, and, as appears to me, a very curious and interesting
history, is reserved for the other work, the _Philosophy of the
Inductive Sciences_. Such a history has, in truth, its natural place
in the Philosophy of Science; for the Philosophy of Science at the
present day must contain the result and summing up of all the truth
which has been disentangled from error and confusion during these
past controversies.

I have made a few Additions to the present Edition; partly, with a
view of bringing up the history, at least of some of the Sciences,
to the present time,--so far as those larger features of the History
of Science are concerned, with which alone I have here to deal,--and
partly also, especially in the First Volume, in order to rectify and
enlarge some of the earlier portions of the history. Several works
which have recently appeared suggested reconsideration of various
points; and I hoped that my readers might be interested in the
reflections so suggested.

I will add a few sentences from the Preface to the First Edition.

"As will easily be supposed, I have borrowed largely from other
writers, both of the histories of special sciences and of philosophy
in general.[1\P] I have done this without {10} scruple, since the
novelty of my work was intended to consist, not in its superiority
as a collection of facts, but in the point of view in which the
facts were placed. I have, however, in all cases, given references
to my authorities, and there are very few instances in which I have
not verified the references of previous historians, and studied the
original authors. According to the plan which I have pursued, the
history of each science forms a whole in itself, divided into
distinct but connected members, by the _Epochs_ of its successive
advances. If I have satisfied the competent judges in each science
by my selection of such epochs, the scheme of the work must be of
permanent value, however imperfect may be the execution of any of
its portions.

[Note 1\P: Among these, I may mention as works to which I have
peculiar obligations, Tennemann's Geschichte der Philosophie;
Degerando's Histoire Comparée des Systèmes de Philosophie;
Montucla's Histoire des Mathématiques, with Delalande's continuation
of it; Delambre's Astronomie Ancienne, Astronomie du Moyen Age,
Astronomie Moderne, and Astronomie du Dix-huitième Siècle; Bailly's
Histoire d'Astronomie Ancienne, and Histoire d'Astronomie Moderne;
Voiron's Histoire d'Astronomie (published as a continuation of
Bailly), Fischer's Geschichte der Physik, Gmelin's Geschichte der
Chemie, Thomson's History of Chemistry, Sprengel's History of
Medicine, his History of Botany, and in all branches of Natural
History and Physiology, Cuvier's works; in their historical, as in
all other portions, most admirable and instructive.]

"With all these grounds of hope, it is still impossible not to see
that such an undertaking is, in no small degree, arduous, and its
event obscure. But all who venture upon such tasks must gather trust
and encouragement from reflections like those by which their great
forerunner prepared himself for his endeavors;--by recollecting that
they are aiming to advance the best interests and privileges of man;
and that they may expect all the best and wisest of men to join them
in their aspirations and to aid them in their labors.

"'Concerning ourselves we speak not; but as touching the matter
which we have in hand, this we ask;--that men deem it not to be the
setting up of an Opinion, but the performing of a Work; and that
they receive this as a certainty--that we are not laying the
foundations of any sect or doctrine, but of the profit and dignity
of mankind:--Furthermore, {11} that being well disposed to what
shall advantage themselves, and putting off factions and prejudices,
they take common counsel with us, to the end that being by these our
aids and appliances freed and defended from wanderings and
impediments, they may lend their hands also to the labors which
remain to be performed:--And yet, further, that they be of good
hope; neither feign and imagine to themselves this our Reform as
something of infinite dimension and beyond the grasp of mortal man,
when, in truth, it is, of infinite error, the end and true limit;
and is by no means unmindful of the condition of mortality and
humanity, not confiding that such a thing can be carried to its
perfect close in the space of one single day, but assigning it as a
task to a succession of generations.'--BACON--INSTAURATIO MAGNA,
_Præf. ad fin._

"'If there be any man who has it at heart, not merely to take his
stand on what has already been discovered, but to profit by that,
and to go on to something beyond;--not to conquer an adversary by
disputing, but to conquer nature by working;--not to opine probably
and prettily, but to know certainly and demonstrably;--let such, as
being true sons of nature (if they will consent to do so), join
themselves to us; so that, leaving the porch of nature which endless
multitudes have so long trod, we may at last open a way to the inner
courts. And that we may mark the two ways, that old one, and our new
one, by familiar names, we have been wont to call the one the
_Anticipation of the Mind_, the other, the _Interpretation of
Nature_.'--INST. MAG. _Præf. ad Part._ ii.



{{13}}
CONTENTS
OF THE FIRST VOLUME.

                                                                PAGE
~Preface to the Third Edition.                                     7~
~Index of Proper Names.                                           23~
~Index of Technical Terms.                                        33~

INTRODUCTION.                                                      41

BOOK I.

HISTORY OF THE GREEK SCHOOL PHILOSOPHY, WITH REFERENCE TO PHYSICAL
SCIENCE.

CHAPTER I.--PRELUDE TO THE GREEK SCHOOL PHILOSOPHY.

_Sect._ 1. First Attempts of the Speculative Faculty in Physical
Inquiries.                                                         55
_Sect._ 2. Primitive Mistake in Greek Physical Philosophy.         60

CHAPTER II.--THE GREEK SCHOOL PHILOSOPHY.

_Sect._ 1. The General Foundation of the Greek School Philosophy.  63
_Sect._ 2. The Aristotelian Physical Philosophy.                   67
_Sect._ 3. Technical Forms of the Greek Schools.                   73
             1. Technical Forms of the Aristotelian Philosophy.    73
             2.     "        "     "   Platonists.                 75
             3.     "        "     "   Pythagoreans.               77
             4.     "        "     "   Atomists and Others.        78

CHAPTER III.--FAILURE OF THE PHYSICAL PHILOSOPHY OF THE GREEK
SCHOOLS.

_Sect._ 1. Result of the Greek School Philosophy.                  80
_Sect._ 2. Cause of the Failure of the Greek Physical Philosophy.  83
{14}

BOOK II.

HISTORY OF THE PHYSICAL SCIENCES IN ANCIENT GREECE.

Introduction.                                                      95

CHAPTER I.--EARLIEST STAGES OF MECHANICS AND HYDROSTATICS.

_Sect._ 1. Mechanics.                                              96
_Sect._ 2. Hydrostatics.                                           98

CHAPTER II.--EARLIEST STAGES OF OPTICS.                           100

CHAPTER III.--EARLIEST STAGES OF HARMONICS.                       105

BOOK III.

HISTORY OF GREEK ASTRONOMY.

Introduction.                                                     111

CHAPTER I.--EARLIEST STAGES OF ASTRONOMY.

_Sect._ 1. Formation of the Notion of a Year.                     112
_Sect._ 2. Fixation of the Civil Year.                            113
_Sect._ 3. Correction of the Civil Year (Julian Calendar).        117
_Sect._ 4. Attempts at the Fixation of the Month.                 118
_Sect._ 5. Invention of Lunisolar Years.                          120
_Sect._ 6. The Constellations.                                    124
_Sect._ 7. The Planets.                                           126
_Sect._ 8. The Circles of the Sphere.                             128
_Sect._ 9. The Globular Form of the Earth.                        132
_Sect._ 10. The Phases of the Moon.                               134
_Sect._ 11. Eclipses.                                             135
_Sect._ 12. Sequel to the Early Stages of Astronomy.              136

CHAPTER II.--PRELUDE TO THE INDUCTIVE EPOCH OF HIPPARCHUS.        138
{15}

CHAPTER III.--INDUCTIVE EPOCH OF HIPPARCHUS.

_Sect._ 1. Establishment of the Theory of Epicycles and
             Eccentrics.                                          145
_Sect._ 2. Estimate of the Value of the Theory of Eccentrics and
             Epicycles.                                           151
_Sect._ 3. Discovery of the Precession of the Equinoxes.          155

CHAPTER IV.--SEQUEL TO THE INDUCTIVE EPOCH OF HIPPARCHUS.

_Sect._ 1. Researches which verified the Theory.                  157
_Sect._ 2. Researches which did not verify the Theory.            159
_Sect._ 3. Methods of Observation of the Greek Astronomers.       161
_Sect._ 4. Period from Hipparchus to Ptolemy.                     166
_Sect._ 5. Measures of the Earth.                                 169
_Sect._ 6. Ptolemy's Discovery of Evection.                       170
_Sect._ 7. Conclusion of the History of Greek Astronomy.          175
_Sect._ 8. Arabian Astronomy.                                     176

BOOK IV.

HISTORY OF PHYSICAL SCIENCE IN THE MIDDLE AGES.

Introduction.                                                     185

CHAPTER I.--ON THE INDISTINCTNESS OF IDEAS OF THE MIDDLE AGES.

1. Collections of Opinions.                                       187
2. Indistinctness of Ideas in Mechanics.                          188
3.       "             "   shown in Architecture.                 191
4.       "             "   in Astronomy.                          192
5.       "             "   shown by Skeptics.                     192
6. Neglect of Physical Reasoning in Christendom.                  195
7. Question of Antipodes.                                         195
8. Intellectual Condition of the Religious Orders.                197
9. Popular Opinions.                                              199

CHAPTER II.--THE COMMENTATORIAL SPIRIT OF THE MIDDLE AGES.        201

1. Natural Bias to Authority.                                     202
2. Character of Commentators.                                     204
3. Greek Commentators of Aristotle.                               205
{16}
4. Greek Commentators of Plato and Others.                        207
5. Arabian Commentators of Aristotle.                             208

CHAPTER III.--OF THE MYSTICISM OF THE MIDDLE AGES.                211

1. Neoplatonic Theosophy.                                         212
2. Mystical Arithmetic.                                           216
3. Astrology.                                                     218
4. Alchemy.                                                       224
5. Magic.                                                         225

CHAPTER IV.--OF THE DOGMATISM OF THE STATIONARY PERIOD.

1. Origin of the Scholastic Philosophy.                           228
2. Scholastic Dogmas.                                             230
3. Scholastic Physics.                                            235
4. Authority of Aristotle among the Schoolmen.                    236
5. Subjects omitted. Civil Law. Medicine.                         238

CHAPTER V.--PROGRESS OF THE ARTS IN THE MIDDLE AGES.

1. Art and Science.                                               239
2. Arabian Science.                                               242
3. Experimental Philosophy of the Arabians.                       243
4. Roger Bacon.                                                   245
5. Architecture of the Middle Ages.                               246
6. Treatises on Architecture.                                     248

BOOK V.

HISTORY OF FORMAL ASTRONOMY AFTER THE STATIONARY PERIOD.

Introduction.                                                     255

CHAPTER I.--PRELUDE TO THE INDUCTIVE EPOCH OF COPERNICUS.         257

CHAPTER II.--INDUCTION OF COPERNICUS. THE HELIOCENTRIC THEORY
ASSERTED ON FORMAL GROUNDS.                                       262
{17}

CHAPTER III--SEQUEL TO COPERNICUS. THE RECEPTION AND DEVELOPMENT
OF THE COPERNICAN THEORY.

_Sect._ 1. First Reception of the Copernican Theory.              269
_Sect._ 2. Diffusion of the Copernican Theory.                    272
_Sect._ 3. The Heliocentric Theory confirmed by Facts. Galileo's
             Astronomical Discoveries.                            276
_Sect._ 4. The Copernican System opposed on Theological Grounds.  286
_Sect._ 5. The Heliocentric Theory confirmed on Physical
             Considerations. (Prelude to Kepler's Astronomical
             Discoveries.)                                        287

CHAPTER IV.--INDUCTIVE EPOCH OF KEPLER.

_Sect._ 1. Intellectual Character of Kepler.                      290
_Sect._ 2. Kepler's Discovery of his Third Law.                   293
_Sect._ 3. Kepler's Discovery of his First and Second Laws.
             Elliptical Theory of the Planets.                    296

CHAPTER V.--SEQUEL TO THE EPOCH OF KEPLER. RECEPTION, VERIFICATION,
AND EXTENSION OF THE ELLIPTICAL THEORY.

_Sect._ 1. Application of the Elliptical Theory to the Planets.   302
_Sect._ 2.       "       "       "          "      "   Moon.      303
_Sect._ 3. Causes of the further Progress of Astronomy.           305

_THE MECHANICAL SCIENCES._

BOOK VI.

HISTORY OF MECHANICS, INCLUDING FLUID MECHANICS.

Introduction.                                                     311

CHAPTER I.--PRELUDE TO THE EPOCH OF GALILEO.

_Sect._ 1. Prelude to the Science of Statics.                     312
_Sect._ 2. Revival of the Scientific Idea of Pressure.
             --Stevinus.--Equilibrium of Oblique Forces.          316
_Sect._ 3. Prelude to the Science of Dynamics.--Attempts at the
             First Law of Motion.                                 319
{18}

CHAPTER II.--INDUCTIVE EPOCH OF GALILEO.--DISCOVERY OF THE LAWS OF
MOTION IN SIMPLE CASES.

_Sect._ 1. Establishment of the First Law of Motion.              322
_Sect._ 2. Formation and Application of the Motion of Accelerating
             Force. Laws of Falling Bodies.                       324
_Sect._ 3. Establishment of the Second Law of Motion.--Curvilinear
             Motions.                                             330
_Sect._ 4. Generalization of the Laws of Equilibrium.--Principle
             of Virtual Velocities.                               331
_Sect._ 5. Attempts at the Third Law of Motion.--Notion of
             Momentum.                                            334

CHAPTER III.--SEQUEL TO THE EPOCH OF GALILEO.--PERIOD OF
VERIFICATION AND DEDUCTION.                                       340

CHAPTER IV.--DISCOVERY OF THE MECHANICAL PRINCIPLES OF FLUIDS.

_Sect._ 1. Rediscovery of the Laws of Equilibrium of Fluids.      345
_Sect._ 2. Discovery of the Laws of Motion of Fluids.             348

CHAPTER V.--GENERALIZATION OF THE PRINCIPLES OF MECHANICS.

_Sect._ 1. Generalization of the Second Law of Motion.--Central
             Forces.                                              352
_Sect._ 2. Generalization of the Third Law of Motion.--Centre
             of Oscillation.--Huyghens.                           356

CHAPTER VI.--SEQUEL TO THE GENERALIZATION OF THE PRINCIPLES OF
MECHANICS.--PERIOD OF MATHEMATICAL DEDUCTION.--ANALYTICAL
MECHANICS.                                                        362

1. Geometrical Mechanics.--Newton, &c.                            363
2. Analytical Mechanics.--Euler.                                  363
3. Mechanical Problems.                                           364
4. D'Alembert's Principle.                                        365
5. Motion in Resisting Media.--Ballistics.                        365
6. Constellation of Mathematicians.                               366
7. The Problem of Three Bodies.                                   367
8. Mécanique Céleste, &c.                                         371
9. Precession.--Motion of Rigid Bodies.                           374
10. Vibrating Strings.                                            375
11. Equilibrium of Fluids.--Figure of the Earth.--Tides.          376
12. Capillary Action.                                             377
13. Motion of Fluids.                                             378
14. Various General Mechanical Principles.                        380
15. Analytical Generality.--Connection of Statics and Dynamics.   381
{19}

BOOK VII.

HISTORY OF PHYSICAL ASTRONOMY.

CHAPTER I.--PRELUDE TO THE INDUCTIVE EPOCH OF NEWTON.             385

CHAPTER II.--THE INDUCTIVE EPOCH OF NEWTON.--DISCOVERY OF THE
UNIVERSAL GRAVITATION OF MATTER, ACCORDING TO THE LAW OF THE
INVERSE SQUARE OF THE DISTANCE.                                   399

1. Sun's Force on Different Planets.                              399
2. Force in Different Points of an Orbit.                         400
3. Moon's Gravity to the Earth.                                   402
4. Mutual Attraction of all the Celestial Bodies.                 406
5.   "         "         "      Particles of Matter.              411
   Reflections on the Discovery.                                  414
   Character of Newton.                                           416

CHAPTER III.--SEQUEL TO THE EPOCH OF NEWTON.--RECEPTION OF THE
NEWTONIAN THEORY.

_Sect._ 1. General Remarks.                                       420
_Sect._ 2. Reception of the Newtonian Theory in England.          421
_Sect._ 3.     "       "       "         "    Abroad.             429

CHAPTER IV.--SEQUEL TO THE EPOCH OF NEWTON, CONTINUED. VERIFICATION
AND COMPLETION OF THE NEWTONIAN THEORY.

_Sect._ 1. Division of the Subject.                               433
_Sect._ 2. Application of the Newtonian Theory to the Moon.       434
_Sect._ 3.      "         "       "        "          Planets,
             Satellites, and Earth.                               438
_Sect._ 4. Application of the Newtonian Theory to Secular
             Inequalities.                                        444
_Sect._ 5.      "         "       "        "   to the new Planets.446
_Sect._ 6.      "         "       "        "   to Comets.         449
_Sect._ 7.      "         "       "        "   to the Figure of
             the Earth.                                           452
_Sect._ 8. Confirmation of the Newtonian Theory by Experiments on
             Attraction.                                          456
_Sect._ 9. Application of the Newtonian Theory to the Tides.      457

CHAPTER V.--DISCOVERIES ADDED TO THE NEWTONIAN THEORY.

_Sect._ 1. Tables of Astronomical Refraction.                     462
_Sect._ 2. Discovery of the Velocity of Light.--Römer.            463
{20}
_Sect._ 3. Discovery of Aberration.--Bradley.                     464
_Sect._ 4. Discovery of Nutation.                                 465
_Sect._ 5. Discovery of the Laws of Double Stars.--The Two
             Herschels.                                           467

CHAPTER VI.--THE INSTRUMENTS AND AIDS OF ASTRONOMY DURING THE
NEWTONIAN PERIOD.

_Sect._ 1. Instruments.                                           470
_Sect._ 2. Observatories.                                         476
_Sect._ 3. Scientific Societies.                                  478
_Sect._ 4. Patrons of Astronomy.                                  479
_Sect._ 5. Astronomical Expeditions.                              480
_Sect._ 6. Present State of Astronomy.                            481

_ADDITIONS TO THE THIRD EDITION._

INTRODUCTION                                                      489

BOOK I.--THE GREEK SCHOOL PHILOSOPHY.

THE GREEK SCHOOLS.

The Platonic Doctrine of Ideas.                                   491

FAILURE OF THE GREEK PHYSICAL PHILOSOPHY.

Bacon's Remarks on the Greeks.                                    494
Aristotle's Account of the Rainbow.                               495

BOOK II.--THE PHYSICAL SCIENCES IN ANCIENT GREECE.

Plato's Timæus and Republic.                                      497
Hero of Alexandria.                                               501

BOOK III.--THE GREEK ASTRONOMY.

Introduction.                                                     503

EARLIEST STAGES OF ASTRONOMY.

The Globular Form of the Earth.                                   505
The Heliocentric System among the Ancients.                       506
The Eclipse of Thales.                                            508
{21}

BOOK IV.--PHYSICAL SCIENCE IN THE MIDDLE AGES.

General Remarks.                                                  511

PROGRESS IN THE MIDDLE AGES.

Thomas Aquinas.                                                   512
Roger Bacon.                                                      512

BOOK V.--FORMAL ASTRONOMY.

PRELUDE TO COPERNICUS.

Nicolas of Cus.                                                   523

THE COPERNICAN THEORY.

The Moon's Rotation.                                              524
M. Foucault's Experiments.                                        525

SEQUEL TO COPERNICUS.

English Copernicans.                                              526
Giordano Bruno.                                                   530
Did Francis Bacon reject the Copernican Doctrine?                 530
Kepler persecuted.                                                532
The Papal Edicts against the Copernican System repealed.          534

BOOK VI.--MECHANICS.

PRINCIPLES AND PROBLEMS.

Significance of Analytical Mechanics.                             536
Strength of Materials.                                            538
Roofs--Arches--Vaults.                                            541

BOOK VII.--PHYSICAL ASTRONOMY.

PRELUDE TO NEWTON.

The Ancients.                                                     544
Jeremiah Horrox.                                                  545
Newton's Discovery of Gravitation.                                546
{22}

THE PRINCIPIA.

Reception of the _Principia_.                                     548
Is Gravitation proportional to Quantity of Matter?                549

VERIFICATION AND COMPLETION OF THE NEWTONIAN THEORY.

Tables of the Moon and Planets.                                   550
The Discovery of Neptune.                                         554
The Minor Planets.                                                557
Anomalies in the Action of Gravitation.                           560
The Earth's Density.                                              561
Tides.                                                            562
Double Stars.                                                     563

INSTRUMENTS.

Clocks.                                                           565



{{23}}
INDEX OF PROPER NAMES.

The letters _a_, _b_, indicate vol. I., vol. II., respectively.

Abdollatif, _b._ 443.
Aboazen, _a._ 222.
Aboul Wefa, _a._ 180.
Achard, _b._ 174.
Achillini, _b._ 445.
Adam Marsh, _a._ 198.
Adanson, _b._ 404, 405.
Adelbold, _a._ 198.
Adelhard Goth, _a._ 198.
Adet, _b._ 279.
Achilles Tatius, _a._ 127.
Æpinus, _b._ 197, 203, 209.
Agassiz, _b._ 429, 521, 540.
Agatharchus, _b._ 53.
Airy, _a._ 372, 442, 477; _b._ 67, 120.
Albategnius, _a._ 177, 178.
Albertus Magnus, _a._ 229, 237; _b._ 367.
Albumasar, _a._ 222.
Alexander Aphrodisiensis, _a._ 206.
Alexander the Great, _a._ 144.
Alfarabi, _a._ 209.
Alfred, _a._ 198.
Algazel, _a._ 194.
Alhazen, _a._ 243; _b._ 54.
Alis-ben-Isa, _a._ 169.
Alkindi, _a._ 211, 226.
Almansor, _a._ 177.
Almeric, _a._ 236.
Alpetragius, _a._ 179
Alphonso X., _a._ 151, 178.
Amauri, _a._ 236.
Ammonius Saccas, _a._ 206, 212.
Ampère, _b._ 183, 243, 244, 246, 284.
Anaxagoras, _a._ 78; _b._ 53.
Anaximander, _a._ 130, 132, 135.
Anaximenes, _a._ 56.
Anderson, _a._ 342.
Anna Comnena, _a._ 207.
Anselm, _a._ 229.
Arago, _b._ 72, 81, 100, 114, 254.
Aratus, _a._ 167.
Archimedes, _a._ 96, 99, 312, 316.
Arduino, _b._ 514.
Aristarchus, _a._ 137, 259.
Aristyllus, _a._ 144.
Aristophanes, _a._ 120.
Aristotle, _a._ 57, 334; _b._ 24, 58, 361, 412, 417, 420, 438, 444,
455, 583.
Arnold de Villâ Novâ, _a._ 228.
Arriaga, _a._ 335.
Artedi, _b._ 423.
Artephius, _a._ 226.
Aryabatta, _a._ 260.
Arzachel, _a._ 178.
Asclepiades, _b._ 439.
Asclepigenia, _a._ 215.
Aselli, _b._ 453.
Avecibron, _a._ 232.
Averroes, _a._ 194, 210.
Avicenna, _a._ 209.
Avienus, _a._ 169.
Aubriet, _b._ 387.
Audouin, _b._ 483.
Augustine, _a._ 197, 220, 232.
Autolycus, _a._ 130, 131.
Auzout, _a._ 474.

Babbage, Mr. _b._ 254, 555.
Bachman, _b._ 386.
Bacon, Francis, _a._ 278, 383, 412; _b._ 25, 32, 165.
Bacon, Roger, _b._ 55.
Bailly, _a._ 199, 445.
Baliani, _a._ 326, 347.
Banister, _b._ 380.
Barlow, _b._ 67, 223, 245, 254. {24}
Bartholin, _b._ 70.
Barton, _b._ 125.
Bauhin, John, _b._ 381.
Bauhin, Gaspard, _b._ 381.
Beaumont, Elie de, _b._ 527, 532, 533, 539, 583, 588.
Beccaria, _b._ 199.
Beccher, _b._ 268.
Bede, _a._ 198, 232.
Bell, Sir Charles, _b._ 463.
Bélon, _b._ 421, 476.
Benedetti, _a._ 314, 321, 324, 336.
Bentley, _a._ 422, 424.
Berard, _b._ 154.
Bergman, _b._ 266, 281, 321.
Bernard of Chartres, _a._ 229.
Bernoulli, Daniel, _a._ 375, 378, 379, 380, 430; _b._ 32, 37, 39.
Bernoulli, James, _a._ 358.
Bernoulli, James, the younger, _b._ 42.
Bernoulli, John, _a._ 359, 361, 363, 366, 375, 393, 430; _b._ 32.
Bernoulli, John, the younger, _b._ 32.
Berthollet, _b._ 267, 278, 281.
Berzelius, _b._ 284, 289, 304, 335, 347, 348.
Bessel, _a._ 272.
Betancourt, _b._ 173.
Beudant, _b._ 348.
Bichat, _b._ 463.
Bidone, _a._ 350.
Biela, _a._ 452.
Biker, _b._ 174.
Biot, _b._ 75, 76, 81, 223, 249.
Black, _b._ 160, 272, 281.
Blair, _b._ 67.
Bloch, _b._ 425.
Blondel, _a._ 342.
Bock, _b._ 371.
Boëthius, _a._ 197, 208.
Boileau, _a._ 390.
Bonaparte, _b._ 241, 296.
Bonaventura, _a._ 233.
Bontius, _b._ 422.
Borelli, _a._ 323, 387, 393, 405, 406.
Bossut, _a._ 350.
Boué, Ami, _b._ 523.
Bouguer, _a._ 377.
Bouillet, _b._ 166.
Bourdon, _b._ 461.
Bournon, _b._ 326.
Bouvard, _a._ 443.
Boyle, _a._ 395; _b._ 80, 163, 263.
Boze, _b._ 198.
Bradley, _a._ 438, 441, 456, 463, 465.
Brander, _b._ 508, 516.
Brassavola, _b._ 368.
Brewster, Sir David, _b._ 65, 75, 81, 113, 119, 123, 331, 332.
Briggs, _a._ 276.
Brisbane, Sir Thomas, _a._ 478.
Brocchi, _b._ 519, 576, 589.
Brochant de Villiers, _b._ 527, 532.
Broderip, _b._ 562.
Brongniart, Alexandre, _b._ 516, 530.
Brongniart, Adolphe, _b._ 539.
Brook, Taylor, _a._ 359, 375; _b._ 31.
Brooke, Mr., _b._ 325.
Brougham, Lord, _b._ 80, 112.
Brown, Robert, _b._ 409, 474.
Brunfels, _b._ 368.
Bruno, Giordano, _a._ 272.
Buat, _a._ 350.
Buch, Leopold von, _b._ 523, 527, 539, 557.
Buckland, Dr., _b._ 534.
Budæus, _a._ 74.
Buffon, _b._ 317, 460, 476.
Bullfinger, _a._ 361.
Bullialdus, _a._ 172, 397.
Burckhardt, _a._ 442, 448.
Burg, _b._ 443.
Burkard, _b._ 459.
Burnet, _b._ 559, 584.

Cabanis, _b._ 489.
Cæsalpinus, _b._ 316, 371, 373.
Calceolarius, _b._ 508.
Calippus, _a._ 123, 140.
Callisthenes, _a._ 144.
Camerarius, Joachim, _b._ 372.
Camerarius, Rudolph Jacob, _b._ 458, 459.
Campanella, _a._ 224, 237.
Campani, _a._ 474.
Camper, _b._ 476.
Canton, _b._ 197, 198, 219.
Capelli, _a._ 435.
Cappeller, _b._ 318. {25}
Cardan, _a._ 313, 319, 330, 335.
Carlini, _a._ 456.
Carne, _b._ 538.
Caroline, Queen, _a._ 422.
Carpa, _b._ 445.
Casræus, _a._ 326.
Cassini, Dominic, _a._ 454, 462, 479; _b._ 33.
Cassini, J., _a._ 439, 463.
Castelli, _a._ 340, 342, 346, 348.
Catelan, _a._ 358.
Cavallieri, _a._ 430.
Cavendish, _a._ 456; _b._ 204, 273, 278.
Cauchy, _a._ 379; _b._ 43, 127.
Caus, Solomon de, _a._ 332.
Cesare Cesariano, _a._ 249.
Chalid ben Abdolmalic, _a._ 169.
Chatelet, Marquise du, _a._ 361.
Chaussier, _b._ 463.
Chladni, _b._ 40, 41.
Christie, _b._ 254.
Christina, _a._ 390.
Chrompré, _b._ 304.
Cicero, _a._ 119.
Cigna, _a._ 376; _b._ 202.
Clairaut, _a._ 367, 377, 410, 437, 451, 454; _b._ 67.
Clarke, _a._ 361, 424.
Cleomedes, _a._ 161, 167.
Clusius, _b._ 378.
Cobo, _b._ 379.
Colombe, Ludovico delle, _a._ 346.
Colombus, Realdus, _b._ 446, 450.
Columna, Fabius, _b._ 381.
Commandinus, _a._ 316.
Comparetti, _b._ 79.
Condamine, _a._ 453.
Constantine of Africa, _b._ 367.
Conti, Abbé de, _a._ 360.
Conybeare, _b._ 519, 525.
Copernicus, _a._ 257.
Cosmas Indicopleustes, _a._ 196.
Cotes, _a._ 366, 425.
Coulomb, _b._ 204, 207, 209, 221.
Crabtree, _a._ 276, 302, 304.
Cramer, _b._ 35.
Cronstedt, _b._ 341.
**Cruickshank, _b._ 240.
Cumming, Prof., _b._ 252.
Cunæus, _b._ 196.
Cuvier, _b._ 421, 422, 466, 478, 481, 487, 492, 516, 517, 520, 522.

D'Alembert, _a._ 361, 365, 367, 372, 374, 376, 378, 446; _b._ 33, 37.
D'Alibard, _b._ 198.
Dalton, Dr. John, _b_. 157, 169, 174, 285 &c., 288, &c.
Daniell, _b._ 178, 554.
Dante, _a._ 200.
D'Arcy, _a._ 380.
Davy, _b._ 291, 293, 295, 301.
Daubenton, _b._ 476.
Daubeny, Dr., _b._ 550.
Daussy, _a._ 459.
De Candolle, Prof., _b._ 408, 473.
Dechen, M. von, _b._ 533.
Defrance, _b._ 516, 518.
Degerando, _a._ 194, 228.
De la Beche, Sir H., _b._ 519.
Delambre, _a._ 442, 447.
De la Rive, Prof., _b._ 187.
Delisle, _a._ 431.
De Luc, _b._ 167, 177.
Démeste, _b._ 319.
Democritus, _a._ 78; _b._ 360.
Derham, _b._ 165.
Desaguliers, _b._ 193.
Descartes, _a._ 323, 328, 338, 343, 354, 387, 423; _b._ 56, 59, 220.
Des Hayes, _b._ 519.
Desmarest, _b._ 512, 515.
Dexippus, _a._ 208.
Digges, _a._ 331.
Dillenius, _b._ 402.
Diogenes Laërtius, _a._ 187.
Dioscorides, _b._ 364, 367.
Dollond, _a._475; _b._ 67.
Dominis, Antonio de, _b._ 59.
Dubois, _b._ 445.
Dufay, _b._ 194, &c., 201.
Du Four, _b._ 79.
Dufrénoy, _b._ 527, 532.
Dulong, _b._ 150, 187.
Duns Scotus, _a._ 233, 237.
Dunthorne, _a._ 435.
Dupuis, _a._ 125.
Durret, _a._ 288. {26}
Dutens, _a._ 82.
Duvernay, _b._ 475.

Ebn Iounis, _a._ 177.
Encke, _a._ 451, 467, 483.
Eratosthenes, _a._ 158.
Ericsen, _b._ 167.
Eristratus _b._ 453.
Etienne, _b._ 445.
Evelyn, _a._ 422.
Euclid, _a._ 100, 101, 131, 132.
Eudoxus, _a._ 140, 143.
Euler, _a._ 363, 367, 370, 377, 380, 437; _b._ 32, 40.
Eusebius, _a._ 195.
Eustachius, _b._ 445, 453.
Eustratus, _a._ 207.

Fabricius, _a._ 207.
Fabricius of Acquapendente, _b._ 456.
Fabricius, David, _a._ 300.
Fallopius, _b._ 445.
Faraday, Dr., _b._ 245, 254, 291, 292, 296, 302.
Fermat, _a._ 341, 353.
Fitton, Dr., _b._ 524.
Flacourt, _b._ 379.
Flamsteed, _a._ 304, 409, 410, 419, 427, 435.
Fleischer, _b._ 57.
Fontaine, _a._ 372.
Fontenelle, _a._ 439; _b._ 265, 509.
Forbes, Prof. James, _b._ 155.
Forster, Rev. Charles, _a._ 243.
Fourcroy, _b._ 278, 281.
Fourier, _b._ 141, 147, 152, 180.
Fowler, _b._ 242.
Fracastoro, _b._ 507.
Francis I. (king of France), _a._ 237.
Franklin, _b._ 195, 197, 202.
Fraunhofer, _a._ 472, 475; _b._ 68, 98. 128.
Frederic II., Emperor, _a._ 236.
Fresnel, _b._ 72, 92, 96, 102, 114, 115, 179.
Fries, _b._ 418.
Frontinus, _a._ 250.
Fuchs, _b._ 334, 369.
Fuchsel, _b._ 513.

Gærtner, _b._ 404.
Galen, _b._ 440, 443, 444, 445, 462, 464.
Galileo, _a._ 276, 319, 322, 324, &c., 336, 342, 345.
Gall, _b._ 463, 465.
Galvani, _b._ 238, 240.
Gambart, _a._ 451.
Gascoigne, _a._ 470.
Gassendi, _a._ 288, 341, 390, 392; _b._ 33.
Gauss, _a._ 372, 448.
Gay-Lussac, _b._ 158, 169, 179, 283, 290.
Geber, _a._ 178, 224.
Gellibrand, _b._ 219.
Geminus, _a._ 118, 143, 166.
Generelli, Cirillo, _b._ 587.
Geoffroy (botanist), _b._ 459.
Geoffroy (chemist), _b._ 265.
Geoffroy Saint-Hilaire, _b._ 477, 480, 483.
George Pachymerus, _a._ 207.
Gerbert, _a._ 198.
Germain, Mlle. Sophie, _b._ 43.
Germanicus, _a._ 168.
Gessner, _b._ 316, 372, 508.
Ghini, _b._ 376.
Gibbon, _a._ 242.
Gilbert, _a._ 274, 394; _b._ 192, 217, 219, 224.
Giordano Bruno, _a._ 272, 273.
Girard, _a._ 350.
Girtanner, _b._ 169.
Giseke, _b._ 398.
Glisson, _b._ 466.
Gmelin, _b._ 348.
Godefroy of St. Victor, _a._ 231.
Goldfuss, _b._ 519.
Göppert, _b._ 578.
Göthe, _b._ 63, 469, 473.
Gough, _b._ 171.
Graham, _a._ 471; _b._ 219.
Grammatici, _b._ 435.
Grazia, Vincenzio di, _a._ 346.
Greenough, _b._ 527.
Gregory, David, _a._ 426, 435.
Gregory VII., Pope, _a._ 227.
Gregory IX., Pope, _a._ 237.
Gren, _b._ 174.
Grew, _b._ 457, 475.
Grey, _b._ 194.
Grignon, _b._ 319.
Grimaldi, _a._ 341; _b._ 60, 79. {27}
Grotthuss, _b._ 304.
Guericke, Otto, _b._ 33, 193.
Guettard, _b._ 510.
Gulielmini, _b._ 317.
Guyton de Morveau, _b._ 278, 281.

Hachette, _b._ 350.
Hadley, _a._ 474.
Haidinger, _b._ 330.
Halicon, _a._ 150.
Haller, _b._ 401, 466.
Halley, _a._ 354, 355, 396, 398, 421, 426, 435, 443, 450, 454, 480;
_b._ 225.
Haly, _a._ 222.
Hamilton, Sir W. (mathem.), _b._ 124, 130.
Hampden, Dr., _a._ 228.
Hansen, _a._ 372, 374.
Hansteen, _b._ 219.
Harding, _a._ 448.
Harris, Mr. Snow, _b._ 209.
Harrison, _a._ 473.
Hartsoecker, _a._ 474.
Harvey, _b._ 446, 449, 456.
Hausmann, _b._ 329.
Haüy, _b._ 320, &c., 325, 342.
Hawkesbee, _b._ 193, 195.
Hegel, _a._ 415.
Helmont, _b._ 262.
Henckel, _b._ 318.
Henslow, Professor, _b._ 474.
Heraclitus, _a._ 56.
Herman, Paul, _b._ 379.
Hermann, Contractus, _a._ 198.
Hermann, James, _a._ 359, 362, 363; _b._ 386, 387.
Hermolaus Barbarus, _a._ 75.
Hernandez, _b._ 379.
Herodotus, _a._ 57; _b._ 361, 506.
Herophilus, _b._ 441.
Herrenschneider, _b._ 145.
Herschel, Sir John, _a._ 467; _b._ 67, 81, 254, 333, 555, 559.
Herschel, Sir William, _a._ 446; _b._ 80.
Hevelius, _a._ 450, 471, 480.
Higgins, _b._ 287.
Hill, _b._ 319, 403.
Hipparchus, _a._ 144.
Hippasus, _a._ 107.
Hippocrates, _b._ 438.
Hoff, K. E. A. von, _b._ 545, 550.
Hoffmann, _b._ 527.
Home, _b._ 518.
Homer, _b._ 438.
Hooke, _a._ 324, 353, 354, 387, 395, 396, 401, 406; _b._ 29, 41, 62,
77, 79, 85.
Hopkins, Mr. W., _b._ 40, 557.
Horrox, _a._ 276, 303, 395.
Hoskins, _a._ 355.
Howard, Mr. Luke, _b._ 179.
Hudson, _b._ 403.
Hugo of St. Victor, _a._ 231.
Humboldt, Alexander von, _b._ 219, 523, 538, 549.
Humboldt, Wilhelm von, _b._ 240.
Hunter, John, _b._ 476.
Hutton (fossilist), _b._ 519.
Hutton (geologist), _a._ 456; _b._ 515, 584.
Huyghens, _a._ 337, 343, 353, 357, 377, 387, 412; _b._ 33, 62, 70,
86, 87.
Hyginus, _a._ 168.

Iamblichus, _a._ 214.
Ideler, _a._ 113.
Ivory, _a._ 372.

Jacob of Edessa, _a._ 209.
Jameson, Professor, _b._ 338, 514.
Job, _a._ 124.
John of Damascus, _a._ 206.
John Philoponus, _a._ 206.
John of Salisbury, _a._ 232, 234.
John Scot Erigena, _a._ 229.
Jordanus Nemorarius, _a._ 314, 331.
Joseph, _a._ 226.
Julian, _a._ 215.
Jung, Joachim, _b._ 384.
Jussieu, Adrien de, _b._ 407.
Jussieu, Antoine Laurent de, _b._ 406.
Jussieu, Bernard de, _b._ 406.

Kæmpfer, _b._ 379.
Kant, _b._ 490.
Kazwiri, _b._ 583.
Keckerman, _a._ 235.
Keill, _a._ 367, 426; _b._ 264.
Kelland, Mr. Philip, _b._ 127, 130. {28}
Kempelen, _b._ 47.
Kepler, _a._ 263, 271, 290, 353, 383, &c., 415, 462; _b._ 55, 56.
Kircher, _a._ 218.
Kirwan, _b._ 274, 278.
Klaproth, _b._ 279.
Klingenstierna, _a._ 475; _b._ 67.
Knaut, Christopher, _b._ 386.
Knaut, Christian, _b._ 386.
König, _b._ 519.
Krafft, _b._ 142, 225.
Kratzenstein, _b._ 166.
Kriege, _b._ 380.

Lacaille, _a._ 442, 454.
Lactantius, _a._ 195.
Lagrange, _a._ 367, 369, 375, 381, 444; _b._ 35, 37, 39.
Lamé, _b._ 129.
La Hire, _a._ 439, 463.
Lalande, _a._ 440, 447.
Lamarck, _b._ 408, 478, 518.
Lambert, _b._ 40, 142, 221.
Landen, _a._ 375.
Lansberg, _a._ 288, 302, 303.
Laplace, _a._ 370, &c., 444, 457; _b._ 36, 140, 147, 184.
Lasus, _a._ 107.
Latreille, _b._ 485.
Lavoisier, _b._ 274, 275, 276, &c., 280.
Laughton, _a._ 424.
Launoy, _a._ 236.
Laurencet, _b._ 484.
Lawrence, _b._ 565.
Lecchi, _a._ 350.
Leeuwenhoek, _b._ 457, 460.
Legendre, _b._ 223.
L'Hôpital, _a._ 358.
Leibnitz, _a._ 360, 391.
Le Monnier, _a._ 435, 437, 463.
Leonardo da Vinci, _a._ 251, 318; _b._ 507, 586.
Leonicenus, _b._ 368.
Le Roi, _b._ 167, 178.
Leslie, _b._ 145, 151, 181.
Levy, _b._ 331.
Leucippus, _a._ 78, 84.
Lexell, _a._ 447, 452.
Lhwyd, _b._ 508.
Libri, _b._ 151.
Lindenau, _a._ 440.
Lindley, _b._ 474, 519.
Linnæus, _b._ 318, 388, 423.
Linus, _b._ 61.
Lister, _b._ 509, 511.
Littrow, _a._ 477.
Lloyd, Professor, _b._ 125, 130.
Lobel, _b._ 381, 408.
Locke, _a._ 422.
Longomontanus, _a._ 297, 302.
Louville, _a._ 431, 439.
Lubbock, _a._ 372, 373, 459.
Lucan, _a._ 190.
Lucas, _b._ 62.
Lyell, _b._ 500, 529, 545, 560, 562, 590.

Macleay, _b._ 418.
Magini, _a._ 270.
Mairan, _a._ 361.
Malpighi, _b._ 456.
Malus, _b._ 71, 74.
Manilius, _a._ 168.
Maraldi, _a._439; _b._ 79.
Marcet, _b._ 187.
Margrave, _b._ 422.
Marinus (anatomist), _b._ 462.
Marinus (Neoplatonist), _a._ 215.
Marriotte, _a._ 343.
Marsilius Ficinus, _a._ 238.
Martianus Capella, _a._ 259.
Martyn, T., _b._ 402.
Mæstlin, _a._ 271, 287.
Matthioli, _b._ 381.
Maupertuis, _a._ 367, 431, 453.
Mayer, Tobias, _a._ 165; _b._ 146, 206, 221.
Mayo, Herbert, _b._ 464.
Mayow, _b._ 277.
Mazeas, _b._ 80, 199.
MacCullagh, Professor, _b._ 123, 130.
Meckel, _b._ 486.
Melloni, _b._ 154.
Menelaus, _a._ 167.
Mersenne, _a._ 328, 342, 347, 390; _b._ 28.
Messa, _b._ 445.
Meton, _a._ 121.
Meyranx, _b._ 484.
Michael Scot, _a._ 226.
Michell, _b._ 511. {29}
Michelotti, _a._ 350.
Miller, Professor, _b._ 331.
Milton, _a._ 200, 275, 340.
Mitscherlich, _b._ 334.
Mohs, _b._ 326, 329, 345, &c., 349, 351.
Mondino, _b._ 445.
Monge, _b._ 274.
Monnet, _b._ 510.
Monnier, _b._ 197.
Monteiro, _b._ 331.
Montfaucon, _b._ 196.
Morin, _a._ 288.
Morison, _b._ 383.
Moro, Lazzaro, _b._ 587.
Morveau, Guyton de, _b._ 278, 281.
Mosotti, _b._ 211.
Munro, _b._ 476.
Murchison, Sir Roderic, _b._ 530.
Muschenbroek, _b._ 166.

Napier, _a._ 276, 306.
Naudæus, _a._ 226.
Naumann, _b._ 331, 352.
Newton, _a._ 343, 349, 353, 355, 363, 399, &c., 420, 432, 463; _b._
33, 39, 59, 70, 73, 77, 88, 142, 450.
Nicephorus Blemmydes, _a._ 207.
Nicholas de Cusa, _a._ 261.
Nicomachus, _a._ 104.
Nigidius Figulus, _a._ 219.
Nobili, _b._ 154.
Nollet, _b._ 196.
Nordenskiöld, _b._ 350.
Norman, _b._ 218.
Norton, _a._ 331.
Numa, _a._ 118, 261.

Odoardi, _b._ 513, 515.
Oersted, Professor, _b._ 243.
Œyenhausen, _b._ 533.
Oken, Professor, _b._ 477.
Olbers, _a._ 448.
Orpheus, _a._ 214.
Osiander, _a._ 268.
Ott, _b._ 145.
Otto Guericke, _b._ 193, 195.
Ovid, _b._ 506.

Pabst von Ohain, _b._ 341.
Packe, _b._ 509.
Pallas, _b._ 476, 513.
Papin, _b._ 173.
Pappus, _a._ 188.
Paracelsus, _a._ 226; _b._ 262.
Pardies, _b._ 61.
Pascal, _a._ 346.
Paulus III., Pope, _a._ 267.
Pecquet, _b._ 453.
Pepys, _a._ 422.
Perrier, _a._ 348.
Peter of Apono, _a._ 226.
Peter Bungo, _a._ 217.
Peter Damien, _a._ 231.
Peter the Lombard, _a._ 231.
Peter de Vineis, _a._ 237.
Petit, _b._ 149, 187.
Petrarch, _a._ 237.
Philip, Dr. Wilson, _b._ 454.
Phillips, William, _b._ 325, 343, 525.
Philolaus, _a._ 259.
Photius, _a._ 208.
Piazzi, _a._ 447, 485.
Picard, _a._ 404, 464, 470; _b._ 33.
Piccolomini, _a._ 336.
Pictet, _b._ 168.
Picus of Mirandula, _a._ 226, 238.
Plana, _a._ 372.
Playfair, _a._ 423.
Pliny, _a._ 150, 187, 219; _b._ 316, 359, 364.
Plotinus, _a._ 207, 213.
Plunier, _b._ 380.
Plutarch, _a._ 77, 187.
Poisson, _a._ 372, 377; _b._ 40, 43, 182, 208, 222.
Polemarchus, _a._ 141, 142.
Poncelet, _a._ 350.
Pond, _a._ 477.
Pontanus, Jovianus, _b._ 458.
Pontécoulant, _a._ 372.
Pope, _a._ 427.
Porphyry, _a._ 205, 207.
Posidonius, _a._ 169.
Potter, Mr. Richard, _b._ 126, 130.
Powell, Prof., _b._ 128, 130, 154.
Prevost, Pierre, _b._ 143.
Prevost, Constant, _b._ 589.
Prichard, Dr., _b._ 500, 565. {30}
Priestley, _b._ 271, 273, 279.
Proclus, _a._ 204, 207, 214, 217, 222.
Prony, _a._ 350; _b._ 174.
Proust, _b._ 267.
Prout, Dr., _b._ 289, 454.
Psellus, _a._ 208.
Ptolemy _a._ 149, &c.; _b._ 26
Ptolemy Euergetes, _a._ 155.
Purbach, _a._ 299.
Pythagoras, _a._ **65, 78, 127, 217.
Pytheas, _a._ 162.

Quetelet, M., _b._ 130.

Raleigh, _b._ 378.
Ramsden, _a._ 471.
Ramus, _a._ 237, 301.
Raspe, _b._ 514, 516.
Ray, _b._ 384, 422.
Raymund Lully, _a._ 226.
Reaumur, _b._ 509.
Recchi, _b._ 379.
Redi, _b._ 475.
Reichenbach, _a._ 472.
Reinhold, _a._ 269.
Rennie, Mr. George, _a._ 350.
Rheede, _b._ 379.
Rheticus, _a._ 266, 269.
Riccioli, _a._ 288, 341.
Richman, _b._ 142, 199.
Richter, _b._ 286.
Riffault, _b._ 304.
Riolan, _b._ 448.
Rivinus, _b._ 386.
Rivius, _a._ 250, 326.
Robert Grostête, _a._ 198, 226.
Robert of Lorraine, _a._ 198.
Robert Marsh, _a._ 199.
Roberval, _b._ 33.
Robins, _a._ 342.
Robinson, Dr., _a._ 477.
Robison, _a._ 169. 173, 206.
Roger Bacon, _a._ 199, 226, 244.
Rohault, _a._ 391, 423.
Romé de Lisle, _b._ 318, 319, 320, 324, 328.
Römer, _a._ 464, 480; _b._ 33.
Rondelet, _b._ 421.
Roscoe, _b._ 409.
Ross, Sir John, _b._ 219.
Rothman, _a._ 264.
Rouelle, _b._ 512, 515.
Rousseau, _b._ 401.
Rudberg, _b._ 127.
Ruellius, _b._ 368.
Rufus, _b._ 441.
Rumphe, _b._ 379.

Saluces, _a._ 376.
Salusbury, _a._ 276.
Salviani, _b._ 421
Santbach, _a._ 325.
Santorini, _b._ 462.
Saron, _a._ 446.
Savart, _b._ 40, 44, 245.
Savile, _a._ 205.
Saussure, _b._ 177, 513.
Sauveur, _b._ 30, 37.
Scheele, _b._ 271.
Schelling, _b._ 63.
Schlottheim, _b._ 514, 519.
Schmidt, _b._ 557.
Schomberg, Cardinal, _a._ 267.
Schweigger, _b._ 251.
Schwerd, _b._ 125.
Scilla, _b._ 508.
Scot, Michael, _b._ 367.
Scrope, Mr. Poulett, _b._ 550.
Sedgwick, Professor, _b._ 533, 538.
Sedillot, M., _a._ 179.
Seebeck, Dr., _b._ 75, 81, 252.
Segner, _a._ 375.
Seneca, _a._ 168, 259, 346.
Sergius, _a._ 209.
Servetus, _b._ 446.
Sextus Empiricus, _a._ 193.
S'Gravesande, _a._ 361.
Sharpe, _b._ 174.
Sherard, _b._ 379.
Simon of Genoa, _b._ 367.
Simplicius, _a._ 204, 206.
Sloane, _b._ 380.
Smith, Mr. Archibald, _b._ 130.
Smith, Sir James Edward, _b._ 403.
Smith, William, _b._ 515, 521.
Snell, _b._ 56, 57.
Socrates, _b._ 442.
Solomon, _a._ 227**; _b._ 361. {31}
Sorge, _b._ 38.
Sosigenes, _a._ 118, 168.
Southern, _b._ 174.
Sowerby, _b._ 519.
Spallanzani, _b._ 454.
Spix, _b._ 477.
Sprengel, _b._ 473.
Stahl, _b._ 268.
Stancari, _b._ 29.
Steno, _b._ 317, 507, 512.
Stephanus, _b._ 445.
Stevinus, _a._ 317, 336, 345, 357.
Stillingfleet, _b._ 403.
Stobæus, _a._ 208.
Stokes, Mr. C. _b._ 578.
Strabo, _a._ 203; _b._ 363, 587.
Strachey, _b._ 511.
Stukeley, _b._ 511.
Svanberg, _b._ 149.
Surian, _b._ 380.
Sylvester II. (Pope), _a._ 198, 227.
Sylvius, _b._ 263, 445, 446.
Symmer, _b._ 202.
Syncellus, _a._ 117.
Synesius, _a._ 166.

Tacitus, _a._ 220.
Tartalea, _b._ 315, 321, 325.
Tartini, _b._ 38.
Taylor, Brook, _a._ 359, 375; _b._ 31.
Tchong-Kang, _a._ 135, 162.
Telaugé, _a._ 217.
Tennemann, _a._ 228.
Thales, _a._ 56, 57, 63, 130.
Thebit, _a._ 226.
Thenard, _b._ 283.
Theodore Metochytes, _a._ 207.
Theodosius, _a._ 168.
Theophrastus, _a._ 205; _b._ 360, 362, 363, 370.
Thomas Aquinas, _a._ 226, 232, 237.
Thomson, Dr., _b._ 288, 289.
Tiberius, _a._ 220.
Timocharis, _a._ 144.
Torricelli, _a._ 336, 340, 347, 349.
Tournefort, _b._ 386, 458.
Tostatus, _a._ 197.
Totaril, Cardinal, _a._ 237.
Tragus, _b._ 368.
Trithemius, _a._ 228.
Troughton, _a._ 471.
Turner, _b._ 289.
Tycho Brahe, _a._ 297, 302; _b._ 55, 56.

Ubaldi, _a._ 313.
Ulugh Beigh, _a._ 178.
Ungern-Sternberg, Count, _b._ 550.
Uranus, _a._ 209.
Ure, Dr., _b._ 174.
Usteri, _b._ 473.

Vaillant, Sebastian, _b._ 459.
Vallisneri, _b._ 508.
Van Helmont, _b._ 262.
Varignon, _a._ 344; _b._ 454.
Varolius, _b._ 463.
Varro, Michael, _a._ 314, 319, 326, 332.
Vesalius, _b._ 444, 445, 462.
Vicq d'Azyr, _b._ 463, 476.
Vieussens, _b._ 463.
Vincent, _a._ 355.
Vincent of Beauvais, _b._ 367.
Vinci, Leonardo da, _a._ 251, 318; _b._ 507.
Virgil (bishop of Salzburg), _a._ 197.
Virgil (a necromancer), _a._ 227.
Vitello, _b._ 56.
Vitruvius, _a._ 249, 251; _b._ 25.
Viviani, _a._ 337, 340.
Voet, _a._ 390.
Voigt, _b._ 473.
Volta, _b._ 238, 240.
Voltaire, _a._ 361, 431.
Voltz, _b._ 533.
Von Kleist, _b._ 196.

Wallerius, _b._ 319.
Wallis, _a._ 276, 341, 343, 387, 395; _b._ 37.
Walmesley, _a._ 440.
Warburton, _a._ 427.
Ward, Seth, _a._ 276, 396.
Wargentin, _a._ 441.
Watson, _b._ 195, 196, 202.
Weber, Ernest and William, _b._ 43.
Weiss, Prof., _b._ 326, 327.
Wells, _b._ 170, 177, 242.
Wenzel, _b._ 286. {32}
Werner, _b._ 318, 337, 341, 514, 520, 521, 528, 584.
Wheatstone, _b._ 44.
Wheler, _b._ 379.
Whewell, _a._ 459; _b._ 330.
Whiston, _a._ 424.
Wilcke, _b._ 161, 198, 204.
Wilkins (Bishop), _a._ 275, 332, 395.
William of Hirsaugen, _a._ 198.
Willis, Rev. Robert, _a._ 246; _b._ 40, 47.
Willis, Thomas, _b._ 462, 463, 465.
Willoughby, _b._ 422, 423.
Wolf, Caspar Frederick, _b._ 472.
Wolff, _a._ 361; _b._ 165.
Wollaston, _b._ 68, 70, 71, 81, 288, 325.
Woodward, _b._ 508, 511, 584.
Wren, _a._ 276, 343, 395; _b._ 421.
Wright, _a._ 435.

Xanthus, _b._ 360.

Yates, _b._ 219.
Young, Thomas, _a._ 350; _b._ 43, 92, &c., 111, 112.

Zabarella, _a._ 235.
Zach, _a._ 448.
Ziegler, _b._ 174.
Zimmerman, _b._ 557.



{{33}}
INDEX OF TECHNICAL TERMS.


Aberration, _a._ 464.
Absolute and relative, _a._ 69.
Accelerating force, _a._ 326.
Achromatism, _b._ 66.
Acid, _b._ 263.
Acoustics, _b._ 24.
Acronycal rising and setting, _a._ 131.
Action and reaction, _a._ 343.
Acuation, _b._ 319.
Acumination, _b._ 319.
Acute harmonics, _b._ 37.
Ætiology, _b._ 499.
Affinity (in Chemistry), _b._ 265.
    "    (in Natural History), _b._ 418.
Agitation, Centre of, _a._ 357.
Alidad, _a._ 184.
Alineations, _a._ 158, 161.
Alkali, _b._ 262.
Almacantars, _a._ **181.
Almagest, _a._ 170.
Almanac, _a._ **181.
Alphonsine tables, _a._ 178.
Alternation (of formations), _b._ 538.
Amphoteric silicides, _b._ 352.
Analogy (in Natural History), _b._ 418.
Analysis (chemical), _b._ 262.
    "    (polar, of light), _b._ 80.
Angle of cleavage, _b._ 322.
    "    incidence, _b._ 53.
    "    reflection, _b._ 53.
Animal electricity, _b._ 238.
Anïon, _b._ 298.
Annus, _a._ 113.
Anode, _b._ 298.
Anomaly, _a._ 139, 141.
Antarctic circle, _a._ 131.
Antichthon, _a._ 82.
Anticlinal line, _b._ 537.
Antipodes, _a._ 196.
Apogee, _a._ 146.
Apotelesmatic astrology, _a._ 222.
Apothecæ, _b._ 366.
Appropriate ideas, _a._ 87.
Arctic circle, _a._ 131.
Armed magnets, _b._ 220.
Armil, _a._ 163.
Art and science, _a._ 239.
Articulata, _b._ 478.
Artificial magnets, _b._ 220.
Ascendant, _a._ 222.
Astrolabe, _a._ 164.
Atmology, _b._ 137, 163.
Atom, _a._ 78.
Atomic theory, _b._ 285.
Axes of symmetry (of crystals), _b._ 327.
Axis (of a mountain chain), _b._ 537.
Azimuth, _a._ **181.
Azot, _b._ 276.

Ballistics, _a._ 365.
Bases (of salts), _b._264.
Basset (of strata), _b._ 512.
Beats, _b._ 29.

Calippic period, _a._ 123.
Caloric, _b._ 143.
Canicular period, _a._ 118.
Canon, _a._ 147.
Capillary action, _a._ 377.
Carbonic acid gas, _b._ 276
Carolinian tables, _a._ 304.
Catasterisms, _a._ 158.
Categories, _a._ 206.
Cathïon, _b._ 298.
Cathode, _b._ 298.
Catïon, _b._ 298.
Causes, Material, formal, efficient, final, _a._ 73. {34}
Centrifugal force, _a._ 330.
Cerebral system, _b._ 463.
Chemical attraction, _b._ 264.
Chyle, _b._ 453.
Chyme, _b._ 453.
Circles of the sphere, _a._ 128.
Circular polarization, _b._ 82, 119.
    "    progression (in Natural History), _b._ 418.
Civil year, _a._ 117.
Climate, _b._ 146.
Coexistent vibrations, _a._ 376.
Colures, _a._ 131.
Conditions of existence (of animals), _b._ 483, 492.
Conducibility, _b._ 143.
Conductibility, _b._ 143.
Conduction, _b._ 139.
Conductivity, _b._ 143.
Conductors, _b._ 194.
Conical refraction, _b._ 124.
Conservation of areas, _a._ 380.
Consistence (in Thermotics), _b._ 160.
Constellations, _a._ 124.
Constituent temperature, _b._ 170.
Contact-theory of the Voltaic pile, _b._ 295.
Cor (of plants), _b._ 374.
Cosmical rising and setting, _a._ 131.
Cotidal lines, _a._ 460.
Craters of elevation, _b._ 556.

Dæmon, _a._ 214.
D'Alembert's principle, _a._ 365.
Day, _a._ 112.
Decussation of nerves, _b._ 462.
Deduction, _a._ 48.
Deferent, _a._ 175.
Definite proportions (in Chemistry), _b._ 285.
Delta, _b._ 546.
Dephlogisticated air, _b._ 273.
Depolarization, _b._ 80.
    "          of heat, _b._ 155.
Depolarizing axes, _b._ 81.
Descriptive phrase (in Botany), _b._ 393.
Dew, _b._ 177.
Dichotomized, _a._ 137.
Diffraction, _b._ 79.
Dimorphism, _b._ 336.
Dioptra, _a._ 165.
Dipolarization, _b._ 80, 82.
Direct motion of planets, _a._ 138.
Discontinuous functions, _b._ 36.
Dispensatoria, _b._ 366.
Dispersion (of light), _b._ 126.
Doctrine of the sphere, _a._ 130.
Dogmatic school (of medicine), _b._ 439.
Double refraction, _b._ 69.

Eccentric, _a._ 145.
Echineis, _a._ 190.
Eclipses, _a._ 135.
Effective forces, _a._ 359.
Elective attraction, _b._ 265.
Electrical current, _b._ 242.
Electricity, _b._ 192.
Electrics, _b._ 194.
Electrical tension, _b._ 242.
Electro-dynamical, _b._ 246.
Electrodes, _b._ 298.
Electrolytes, _b._ 298.
Electro-magnetism, _b._ 243.
Elements (chemical), _b._ 309.
Elliptical polarization, _b._ 122, 123.
Empiric school (of medicine), _b._ 439.
Empyrean, _a._ 82.
Enneads, _a._ 213.
Entelechy, _a._ 74.
Eocene, _b._ 529.
Epicycles, _a._ 140, 145
Epochs, _a._ 46.
Equant, _a._ 175.
Equation of time, _a._ 159.
Equator, _a._ 130.
Equinoctial points, _a._ 131.
Escarpment, _b._ 537.
Evection, _a._ 171, 172.
Exchanges of heat, Theory of, _b._ 143.

Facts and ideas, _a._ 43.
Faults (in strata), _b._ 537.
Final causes, _b._ 442, 492.
Finite intervals (hypothesis of), _b._ 126.
First law of motion, _a._ 322.
Fits of easy transmission, _b._ 77, 89.
Fixed air, _b._ 272.
Fixity of the stars, _a._ 158. {35}
Formal optics, _b._ 52.
Franklinism, _b._ 202.
Fresnel's rhomb, _b._ 105.
Fringes of shadows, _b._ 79, 125.
Fuga vacui, _a._ 347.
Full months, _a._ 122.
Function (in Physiology), _b._ 435.

Galvanism, _b._ 239.
Galvanometer, _b._ 251.
Ganglionic system, _b._ 463.
Ganglions, _b._ 463.
Generalization, _a._ 46.
Geocentric theory, _a._ 258.
Gnomon, _a._ 162.
Gnomonic, _a._ 137.
Golden number, _a._ 123.
Grave harmonics, _b._ 38.
Gravitate, _a._ 406.

Habitations (of plants), _b._ 562.
Hæcceity, _a._ 233.
Hakemite tables, _a._ 177.
Halogenes, _b._ 308.
Haloide, _b._ 352.
Harmonics, Acute, _b._ 37.
    "      Grave, _b._ 38.
Heat, _b._ 139.
  "   Latent, _b._ 160.
Heccædecaëteris, _a._ 121.
Height of a homogeneous atmosphere, _b._ 34.
Heliacal rising and setting, _a._ 131.
Heliocentric theory, _a._ 258.
Hemisphere of Berosus, _a._ 162.
Hollow months, _a._ 122.
Homoiomeria, _a._ 78.
Horizon, _a._ 131.
Horoscope, _a._ 222.
Horror of a vacuum, _a._ 346.
Houses (in Astrology), _a._ 222.
Hydracids, _b._ 283.
Hygrometer, _b._ 177.
Hygrometry, _b._ 138.
Hypostatical principles, _b._ 262.

Iatro-chemists, _b._ 263.
Ideas of the Platonists, _a._ 75.
Ilchanic tables, _a._ 178.
Impressed forces, _a._ 359.
Inclined plane, _a._ 313.
Induction (electric), _b._ 197.
    "     (logical), _a._ 43.
Inductive, _a._ 42.
    "      charts, _a._ 47.
    "      epochs, _a._ 46.
Inflammable air, _b._ 273.
Influences, _a._ 219.
Intercalation, _a._ 118.
Interferences, _b._ 86, 93.
Ionic school, _a._ 56.
Isomorphism, _b._ 334.
Isothermal lines, _b._ 146, 538.
Italic school, _a._ 56.

Joints (in rocks), _b._ 537.
Judicial astrology, _a._ 222.
Julian calendar, _a._ 118.

Lacteals, _b._ 453.
Latent heat, _b._ 160.
Laws of motion, first, _a._ 322.
  "        "    second, _a._ 330.
  "        "    third, _a._ 334.
Leap year, _a._ 118.
Leyden phial, _b._ 196.
Librations (of planets), _a._ 297.
Libration of Jupiter's Satellites, _a._ 441.
Limb of an instrument, _a._ 162.
Longitudinal vibrations, _b._ 44.
Lunisolar year, _a._ 120.
Lymphatics, _b._ 453.

Magnetic elements, _b._ 222.
     "   equator, _b._ 219.
Magnetism, _b._ 217.
Magneto-electric induction, _b._ 256.
Matter and form, _a._ 73.
Mean temperature, _b._ 146.
Mechanical mixture of gases, _b._ 172.
Mechanico-chemical sciences, _b._ 191.
Meiocene, _b._ 529.
Meridian line, _a._ 164.
Metals, _b._ 306, 307.
Meteorology, _b._ 138.
Meteors, _a._ 86.
Methodic school (of medicine), _b._ 439. {36}
Metonic cycle, _a._ 122.
Mineral alkali, _b._ 264.
Mineralogical axis, _b._ 537.
Minutes, _a._ 163.
Miocene, _b._ 529.
Mollusca, _b._ 478.
Moment of inertia, _a._ 356.
Momentum, _a._ 337, 338.
Moon's libration, _a._ 375.
Morphology, _b._ 469, 474.
Movable polarization, _b._ 105.
Multiple proportions (in Chemistry), _b._ 285.
Music of the spheres, _a._ 82.
Mysticism, _a._ 209, 211.

Nadir, _a._ **182.
Nebular hypothesis, _b._ 501.
Neoplatonists, _a._ 207.
Neutral axes, _b._ 81.
Neutralization (in Chemistry), _b._ 263.
Newton's rings, _b._ 77, 124.
   "     scale of color, _b._ 77.
Nitrous air, _b._ 273.
Nomenclature, _b._ 389.
Nominalists, _a._ 238.
Non-electrics, _b._ 194.
Numbers of the Pythagoreans, _a._ 82, 216.
Nutation, _a._ 465.
Nycthemer, _a._ 159.

Octaëteris, _a._ 121.
Octants, _a._ 180.
Oolite, _b._ 529.
Optics, _b._ 51, &c.
Organical sciences, _b._ 435.
Organic molecules, _b._ 460.
Organization, _b._ 435.
Oscillation, Centre of, _a._ 356.
Outcrop (of strata), _b._ 512.
Oxide, _b._ 282.
Oxyd, _b._ 282.
Oxygen, _b._ 276.

Palæontology, _b._ 519.
Palætiological sciences, _b._ 499.
Parallactic instrument, _a._ 165.
Parallax, _a._ 159.
Percussion, Centre of, _a._ 357.
Perfectihabia, _a._ 75.
Perigee, _a._ 146.
Perijove, _a._ 446.
Periodical colors, _b._ 93.
Phases of the moon, _a._ 134.
Philolaic tables, _a._ 304.
Phlogisticated air, _b._ 273.
Phlogiston, _b._ 268.
Phthongometer, _b._ 47.
Physical optics, _b._ 52.
Piston, _a._ 346.
Plagihedral faces, _b._ 82.
Plane of maximum areas, _b._ 380.
Pleiocene, _b._ 529.
Plesiomorphous, _b._ 335.
Plumb line, _a._ 164.
Pneumatic trough, _b._ 273.
Poikilite, _b._ 530.
Polar decompositions, _b._ 293.
Polarization, _b._ 72, 74.
     "        Circular, _b._ 82, 119.
     "        Elliptical, _b._ 122, 124.
     "        Movable, _b._ 105.
     "        Plane, _b._ 120.
     "        of heat, _b._ 153.
Poles (voltaic), _b._ 298.
  "   of maximum cold, _b._ 146.
Potential levers, _a._ 318.
Power and act, _a._ 74.
Precession of the equinoxes, _a._ 155.
Predicables, _a._ 205.
Predicaments, _a._ 206.
Preludes of epochs, _a._ 46.
Primary rocks, _b._ 513.
Primitive rocks, _b._ 513.
Primum calidum, _a._ 77.
Principal plane (of a rhomb), _b._ 73.
Principle of least action, _a._ 380.
Prosthapheresis, _a._ 146.
Provinces (of plants and animals), _b._ 562.
Prutenic tables, _a._ 270.
Pulses, _b._ 33.
Pyrites, _b._ 352.

Quadrant, _a._ 164
Quadrivium, _a._ 199.
Quiddity, _a._ 234. {37}
Quinary division (in Natural History), _b._ 418.
Quintessence, _a._ 73.

Radiata, _b._ 478.
Radiation, _b._ 139.
Rays, _b._ 58.
Realists, _a._ 238.
Refraction, _b._ 54.
     "      of heat, _b._ 155.
Remora, _a._ 190.
Resinous electricity, _b._ 195.
Rete mirabile, _b._ 463.
Retrograde motion of planets, _a._ 139.
Roman calendar, _a._ 123.
Rotatory vibrations, _b._ 44.
Rudolphine tables, _a._ 270, 302.

Saros, _a._ 136.
Scholastic philosophy, _a._ 230.
School philosophy, _a._ 50.
Science, _a._ 42.
Secondary rocks, _b._ 513.
    "     mechanical sciences, _b._ 23.
Second law of motion, _a._ 330.
Seconds, _a._ 163.
Secular inequalities, _a._ 370.
Segregation, _b._ 558.
Seminal contagion, _b._ 459.
    "   proportions, _a._ 79.
Sequels of epochs, _a._ 47.
Silicides, _b._ 352.
Silurian rocks, _b._ 530.
Simples, _b._ 367.
Sine, _a._ 181.
Solar heat, _b._ 145.
Solstitial points, _a._ 131.
Solution of water in air, _b._ 166.
Sothic period, _a._ 118.
Spagiric art, _b._ 262.
Specific heat, _b._ 159.
Sphere, _a._ 130.
Spontaneous generation, _b._ 457.
Statical electricity, _b._ 208.
Stationary periods, _a._ 48.
    "      planets, _a._ 139.
Stations (of plants), _b._ 562.
Sympathetic sounds, _b._ 37.
Systematic Botany, _b._ 357.
Systematic Zoology, _b._ 412.
Systems of crystallization, _b._ 328.

Tables, Solar, (of Ptolemy), _a._ 146.
    "   Hakemite, _a._ 177.
    "   Toletan, _a._ 177.
    "   Ilchanic, _a._ 178.
    "   Alphonsine, _a._ 178.
    "   Prutenic, _a._ 270.
    "   Rudolphine, _a._ 302.
    "   Perpetual (of Lansberg), _a._ 302.
    "   Philolaic, _a._ 304.
    "   Carolinian, _a._ 304.
Tangential vibrations, _b._ 45.
Tautochronous curves, _a._ 372.
Technical terms, _b._ 389.
Temperament, _b._ 47.
Temperature, _b._ 139.
Terminology, _b._ 389.
Tertiary rocks, _b._ 513.
Tetractys, _a._ 77.
Theory of analogues, _b._ 483.
Thermomultiplier, _b._ 154.
Thermotics, _b._ 137.
Thick plates. Colors of, _b._ 79.
Thin plates. Colors of, _b._ 77.
Third law of motion, _a._ 334.
Three principles (in Chemistry), _b._ 261.
Toletan tables, _a._ 177.
Transition rocks, _b._ 530.
Transverse vibrations, _b._ 44, 93, 101.
Travertin, _b._ 546.
Trepidation of the fixed stars, _a._ 179.
Trigonometry, _a._ 167.
Trivial names, _b._ 392.
Trivium, _a._ 199.
Tropics, _a._ 131.
Truncation (of crystals), _b._ 319.
Type (in Comparative Anatomy), _b._ 476.

Uniform force, _a._ 327.
Unity of Composition (in Comparative Anatomy), _b._ 483.
Unity of plan (in Comparative Anatomy), _b._ 483.

Variation of the moon, _a._ 179, 303. {38}
Vegetable alkali, _b._ 264.
Vertebrata, _b._ 478.
Vibrations, _b._ 44.
Vicarious elements, _b._ 334.
    "     solicitations, _a._ 359.
Virtual velocities, _a._ 333.
Vitreous electricity, _b._ 195.
Volatile alkali, _b._ 264.
Volta-electrometer, _b._ 299.
Voltaic electricity, _b._ 239.
    "   pile, _b._ 239.
Volumes, Theory of, _b._ 290.
Voluntary, violent, and natural motion, _a._ 319.
Vortices, _a._ 388.

Week, _a._ 127.

Year, _a._ 112.

Zenith, _a._ 181.
Zodiac, _a._ 131.
Zones, _a._ 136.



{{39}}
A
HISTORY
OF THE
INDUCTIVE SCIENCES.

INTRODUCTION.


"A just story of learning, containing the antiquities and originals
of KNOWLEDGES, and their sects; their inventions, their diverse
administrations and managings; their flourishings, their
oppositions, decays, depressions, oblivions, removes; with the
causes and occasions of them, and all other events concerning
learning, throughout all ages of the world; I may truly affirm to be
wanting.

"The use and end of which work I do not so much design for
curiosity, or satisfaction of those that are the lovers of learning:
but chiefly for a more serious and grave purpose; which is this, in
few words--that it will make learned men more wise in the use and
administration of learning."
BACON, _Advancement of Learning_, book ii.



{{41}}
INTRODUCTION.


IT is my purpose to write the History of some of the most important
of the Physical Sciences, from the earliest to the most recent
periods. I shall thus have to trace some of the most remarkable
branches of human knowledge, from their first germ to their growth
into a vast and varied assemblage of undisputed truths; from the
acute, but fruitless, essays of the early Greek Philosophy, to the
comprehensive systems, and demonstrated generalizations, which
compose such sciences as the Mechanics, Astronomy, and Chemistry, of
modern times.

The completeness of historical view which belongs to such a design,
consists, not in accumulating all the details of the cultivation of
each science, but in marking the larger features of its formation.
The historian must endeavor to point out how each of the important
advances was made, by which the sciences have reached their present
position; and when and by whom each of the valuable truths was
obtained, of which the aggregate now constitutes a costly treasure.

Such a task, if fitly executed, must have a well-founded interest
for all those who look at the existing condition of human knowledge
with complacency and admiration. The present generation finds itself
the heir of a vast patrimony of science; and it must needs concern
us to know the steps by which these possessions were acquired, and
the documents by which they are secured to us and our heirs forever.
Our species, from the time of its creation, has been travelling
onwards in pursuit of truth; and now that we have reached a lofty
and commanding position, with the broad light of day around us, it
must be grateful to look back on the line of our vast progress;--to
review the journey, begun in early twilight amid primeval wilds; for
a long time continued with slow advance and obscure prospects; and
gradually and in later days followed along more open and lightsome
paths, in a wide and fertile region. The historian of science, from
early periods to the present times, may hope for favor on the score
of the mere subject of his narrative, and in virtue of the curiosity
which the men {42} of the present day may naturally feel respecting
the events and persons of his story.

But such a survey may possess also an interest of another kind; it
may be instructive as well as agreeable; it may bring before the
reader the present form and extent, the future hopes and prospects
of science, as well as its past progress. The eminence on which we
stand may enable us to see the land of promise, as well as the
wilderness through which we have passed. The examination of the
steps by which our ancestors acquired our intellectual estate, may
make us acquainted with our expectations as well as our
possessions;--may not only remind us of what we have, but may teach
us how to improve and increase our store. It will be universally
expected that a History of Inductive Science should point out to us
a philosophical distribution of the existing body of knowledge, and
afford us some indication of the most promising mode of directing
our future efforts to add to its extent and completeness.

To deduce such lessons from the past history of human knowledge, was
the intention which originally gave rise to the present work. Nor is
this portion of the design in any measure abandoned; but its
execution, if it take place, must be attempted in a separate and
future treatise, _On the Philosophy of the Inductive Sciences_. An
essay of this kind may, I trust, from the progress already made in
it, be laid before the public at no long interval after the present
history.[1\1]

[Note 1\1: The _Philosophy of the Inductive Sciences_ was published
shortly after the present work.]

Though, therefore, many of the principles and maxims of such a work
will disclose themselves with more or less of distinctness in the
course of the history on which we are about to enter, the systematic
and complete exposition of such principles must be reserved for this
other treatise. My attempts and reflections have led me to the
opinion, that justice cannot be done to the subject without such a
division of it.

To this future work, then, I must refer the reader who is disposed
to require, at the outset, a precise explanation of the terms which
occur in my title. It is not possible, without entering into this
philosophy, to explain adequately how science which is INDUCTIVE
differs from that which is not so; or why some portions of
_knowledge_ may properly be selected from the general mass and
termed SCIENCE. It will be sufficient at present to say, that the
sciences of which we have {43} here to treat, are those which are
commonly known as the _Physical Sciences_; and that by _Induction_
is to be understood that process of collecting general truths from
the examination of particular facts, by which such sciences have
been formed.

There are, however, two or three remarks, of which the application
will occur so frequently, and will tend so much to give us a clearer
view of some of the subjects which occur in our history, that I will
state them now in a brief and general manner.

_Facts and Ideas_.[2\1]--In the first place then, I remark, that, to
the formation of science, two things are requisite;--Facts and
Ideas; observation of Things without, and an inward effort of
Thought; or, in other words, Sense and Reason. Neither of these
elements, by itself can constitute substantial general knowledge.
The impressions of sense, unconnected by some rational and
speculative principle, can only end in a practical acquaintance with
individual objects; the operations of the rational faculties, on the
other hand, if allowed to go on without a constant reference to
external things, can lead only to empty abstraction and barren
ingenuity. Real speculative knowledge demands the combination of the
two ingredients;--right reason, and facts to reason upon. It has
been well said, that true knowledge is the interpretation of nature;
and therefore it requires both the interpreting mind, and nature for
its subject; both the document, and the ingenuity to read it aright.
Thus invention, acuteness, and connection of thought, are necessary
on the one hand, for the progress of philosophical knowledge; and on
the other hand, the precise and steady application of these
faculties to facts well known and clearly conceived. It is easy to
point out instances in which science has failed to advance, in
consequence of the absence of one or other of these requisites;
indeed, by far the greater part of the course of the world, the
history of most times and most countries, exhibits a condition thus
stationary with respect to knowledge. The facts, the impressions on
the senses, on which the first successful attempts at physical
knowledge proceeded, were as well known long before the time when
they were thus turned to account, as at that period. The motions of
the stars, and the effects of weight, were familiar to man before
the rise of the Greek Astronomy and Mechanics: but the "diviner
mind" was still absent; the act of thought had not been exerted, by
which these facts were bound together under the form of laws and
principles. And even at {44} this day, the tribes of uncivilized and
half-civilized man, over the whole face of the earth, have before
their eyes a vast body of facts, of exactly the same nature as those
with which Europe has built the stately fabric of her physical
philosophy; but, in almost every other part of the earth, the
process of the intellect by which these facts become science, is
unknown. The scientific faculty does not work. The scattered stones
are there, but the builder's hand is wanting. And again, we have no
lack of proof that mere activity of thought is equally inefficient
in producing real knowledge. Almost the whole of the career of the
Greek schools of philosophy; of the schoolmen of Europe in the
middle ages; of the Arabian and Indian philosophers; shows us that
we may have extreme ingenuity and subtlety, invention and
connection, demonstration and method; and yet that out of these
germs, no physical science may be developed. We may obtain, by such
means, Logic and Metaphysics, and even Geometry and Algebra; but out
of such materials we shall never form Mechanics and Optics,
Chemistry and Physiology. How impossible the formation of these
sciences is without a constant and careful reference to observation
and experiment;--how rapid and prosperous their progress may be when
they draw from such sources the materials on which the mind of the
philosopher employs itself;--the history of those branches of
knowledge for the last three hundred years abundantly teaches us.

[Note 2\1: For the _Antithesis of Facts and Ideas_, see the
_Philosophy_, book i. ch. 1, 2, 4, 5.]

Accordingly, the existence of clear Ideas applied to distinct Facts
will be discernible in the History of Science, whenever any marked
advance takes place. And, in tracing the progress of the various
provinces of knowledge which come under our survey, it will be
important for us to see that, at all such epochs, such a combination
has occurred; that whenever any material step in general knowledge
has been made,--whenever any philosophical discovery arrests our
attention,--some man or men come before us, who have possessed, in
an eminent degree, a clearness of the ideas which belong to the
subject in question, and who have applied such ideas in a vigorous
and distinct manner to ascertained facts and exact observations. We
shall never proceed through any considerable range of our narrative,
without having occasion to remind the reader of this reflection.

_Successive Steps in Science_.[3\1]--But there is another remark
which we must also make. Such sciences as we have here to do with
are, {45} commonly, not formed by a single act;--they are not
completed by the discovery of one great principle. On the contrary,
they consist in a long-continued advance; a series of changes; a
repeated progress from one principle to another, different and often
apparently contradictory. Now, it is important to remember that this
contradiction is apparent only. The principles which constituted the
triumph of the preceding stages of the science, may appear to be
subverted and ejected by the later discoveries, but in fact they are
(so far as they were true) taken up in the subsequent doctrines and
included in them. They continue to be an essential part of the
science. The earlier truths are not expelled but absorbed, not
contradicted but extended; and the history of each science, which
may thus appear like a succession of revolutions, is, in reality, a
series of developments. In the intellectual, as in the material
world,

  Omnia mutantur nil interit . . . . .
  Nec manet ut fuerat nec formas servat easdem,
  Sed tamen ipsa eadem est.

  All changes, naught is lost; the forms are changed,
  And that which has been is not what it was,
  Yet that which has been is.

Nothing which was done was useless or unessential, though it ceases
to be conspicuous and primary.

[Note 3\1: Concerning _Successive Generalizations in Science_ see
the _Philosophy_, book i. ch. 2, sect. 11.]

Thus the final form of each science contains the substance of each
of its preceding modifications; and all that was at any antecedent
period discovered and established, ministers to the ultimate
development of its proper branch of knowledge. Such previous
doctrines may require to be made precise and definite, to have their
superfluous and arbitrary portions expunged, to be expressed in new
language, to be taken up into the body of science by various
processes;--but they do not on such accounts cease to be true
doctrines, or to form a portion of the essential constituents of our
knowledge.

_Terms record Discoveries_.[4\1]--The modes in which the earlier
truths of science are preserved in its later forms, are indeed
various. From being asserted at first as strange discoveries, such
truths come at last to be implied as almost self-evident axioms.
They are recorded by some familiar maxim, or perhaps by some new
word or phrase, which becomes part of the current language of the
philosophical world; and thus asserts a principle, while it appears
merely to indicate a transient {46} notion;--preserves as well as
expresses a truth;--and, like a medal of gold, is a treasure as well
as a token. We shall frequently have to notice the manner in which
great discoveries thus stamp their impress upon the terms of a
science; and, like great political revolutions, are recorded by the
change of the current coin which has accompanied them.

[Note 4\1: Concerning _Technical Terms_, see _Philosophy_, book i.
ch. 3.]

_Generalization_.--The great changes which thus take place in the
history of science, the revolutions of the intellectual world, have,
as a usual and leading character, this, that they are steps of
_generalization_; transitions from particular truths to others of a
wider extent, in which the former are included. This progress of
knowledge, from individual facts to universal laws,--from particular
propositions to general ones,--and from these to others still more
general, with reference to which the former generalizations are
particular,--is so far familiar to men's minds, that, without here
entering into further explanation, its nature will be understood
sufficiently to prepare the reader to recognize the exemplifications
of such a process, which he will find at every step of our advance.

_Inductive Epochs; Preludes; Sequels_.--In our history, it is the
_progress_ of knowledge only which we have to attend to. This is the
main action of our drama; and all the events which do not bear upon
this, though they may relate to the cultivation and the cultivators
of philosophy, are not a necessary part of our theme. Our narrative
will therefore consist mainly of successive steps of generalization,
such as have just been mentioned. But among these, we shall find
some of eminent and decisive importance, which have more peculiarly
influenced the fortunes of physical philosophy, and to which we may
consider the rest as subordinate and auxiliary. These primary
movements, when the Inductive process, by which science is formed,
has been exercised in a more energetic and powerful manner, may be
distinguished as the _Inductive Epochs_ of scientific history; and
they deserve our more express and pointed notice. They are, for the
most part, marked by the great discoveries and the great
philosophical names which all civilized nations have agreed in
admiring. But, when we examine more clearly the history of such
discoveries, we find that these epochs have not occurred suddenly
and without preparation. They have been preceded by a period, which
we may call their _Prelude_ during which the ideas and facts on
which they turned were called into action;--were gradually evolved
into clearness and connection, permanency and certainty; till at
last the discovery which marks the epoch, seized and fixed forever
the truth which had till then been obscurely and {47} doubtfully
discerned. And again, when this step has been made by the principal
discoverers, there may generally be observed another period, which
we may call the _Sequel_ of the Epoch, during which the discovery
has acquired a more perfect certainty and a more complete
development among the leaders of the advance; has been diffused to
the wider throng of the secondary cultivators of such knowledge, and
traced into its distant consequences. This is a work, always of time
and labor, often of difficulty and conflict. To distribute the
History of science into such Epochs, with their Preludes and
Sequels, if successfully attempted, must needs make the series and
connections of its occurrences more distinct and intelligible. Such
periods form resting-places, where we pause till the dust of the
confused march is laid, and the prospect of the path is clear.

_Inductive Charts_.[5\1]--Since the advance of science consists in
collecting by induction true general laws from particular facts, and
in combining several such laws into one higher generalization, in
which they still retain their truth; we might form a Chart, or
Table, of the progress of each science, by setting down the
particular facts which have thus been combined, so as to form
general truths, and by marking the further union of these general
truths into others more comprehensive. The Table of the progress of
any science would thus resemble the Map of a River, in which the
waters from separate sources unite and make rivulets, which again
meet with rivulets from other fountains, and thus go on forming by
their junction trunks of a higher and higher order. The
representation of the state of a science in this form, would
necessarily exhibit all the principal doctrines of the science; for
each general truth contains the particular truths from which it was
derived, and may be followed backwards till we have these before us
in their separate state. And the last and most advanced
generalization would have, in such a scheme, its proper place and
the evidence of its validity. Hence such an _Inductive Table_ of
each science would afford a criterion of the correctness of our
distribution of the inductive Epochs, by its coincidence with the
views of the best judges, as to the substantial contents of the
science in question. By forming, therefore, such Inductive Tables of
the principal sciences of which I have here to speak, and by
regulating by these tables, my views of the history of the sciences,
I conceive that I have secured the distribution of my {48} history
from material error; for no merely arbitrary division of the events
could satisfy such conditions. But though I have constructed such
charts to direct the course of the present history, I shall not
insert them in the work, reserving them for the illustration of the
philosophy of the subject; for to this they more properly belong,
being a part of the _Logic of Induction_.

[Note 5\1: Inductive charts of the History of Astronomy and of
Optics, such as are here referred to, are given in the _Philosophy_,
book xi. ch. 6.]

_Stationary Periods_.--By the lines of such maps the real advance of
science is depicted, and nothing else. But there are several
occurrences of other kinds, too interesting and too instructive to
be altogether omitted. In order to understand the conditions of the
progress of knowledge, we must attend, in some measure, to the
failures as well as the successes by which such attempts have been
attended. When we reflect during how small a portion of the whole
history of human speculations, science has really been, in any
marked degree, progressive, we must needs feel some curiosity to
know what was doing in these _stationary_ periods; what field could
be found which admitted of so wide a deviation, or at least so
protracted a wandering. It is highly necessary to our purpose, to
describe the baffled enterprises as well as the achievements of
human speculation.

_Deduction_.--During a great part of such stationary periods, we
shall find that the process which we have spoken of as essential to
the formation of real science, the conjunction of clear Ideas with
distinct Facts, was interrupted; and, in such cases, men dealt with
ideas alone. They employed themselves in reasoning from principles,
and they arranged, and classified, and analyzed their ideas, so as
to make their reasonings satisfy the requisitions of our rational
faculties. This process of drawing conclusions from our principles,
by rigorous and unimpeachable trains of demonstration, is termed
_Deduction_. In its due place, it is a highly important part of
every science; but it has no value when the fundamental principles,
on which the whole of the demonstration rests, have not first been
obtained by the induction of facts, so as to supply the materials of
substantial truth. Without such materials, a series of
demonstrations resembles physical science only as a shadow resembles
a real object. To give a real significance to our propositions,
Induction must provide what Deduction cannot supply. From a pictured
hook we can hang only a pictured chain.

_Distinction of common Notions and Scientific Ideas_.[6\1]--When the
{49} notions with which men are conversant in the common course of
practical life, which give meaning to their familiar language, and
employment to their hourly thoughts, are compared with the Ideas on
which exact science is founded, we find that the two classes of
intellectual operations have much that is common and much that is
different. Without here attempting fully to explain this relation
(which, indeed, is one of the hardest problems of our philosophy),
we may observe that they have this in common, that both are acquired
by acts of the mind exercised in connecting external impressions,
and may be employed in conducting a train of reasoning; or, speaking
loosely (for we cannot here pursue the subject so as to arrive at
philosophical exactness), we may say, that all notions and ideas are
obtained by an _inductive_, and may be used in a _deductive_
process. But scientific Ideas and common Notions differ in this,
that the former are precise and stable, the latter vague and
variable; the former are possessed with clear insight, and employed
in a sense rigorously limited, and always identically the same; the
latter have grown up in the mind from a thousand dim and diverse
suggestions, and the obscurity and incongruity which belong to their
origin hang about all their applications. Scientific Ideas can often
be adequately exhibited for all the purposes of reasoning, by means
of Definitions and Axioms; all attempts to reason by means of
Definitions from common Notions, lead to empty forms or entire
confusion.

[Note 6\1: Scientific Ideas depend upon certain _Fundamental Ideas_,
which are enumerated in the _Philosophy_, book i. ch. 8.]

Such common Notions are sufficient for the common practical conduct
of human life: but man is not a practical creature merely; he has
within him a _speculative_ tendency, a pleasure in the contemplation
of ideal relations, a love of knowledge as knowledge. It is this
speculative tendency which brings to light the difference of common
Notions and scientific Ideas, of which we have spoken. The mind
analyzes such Notions, reasons upon them, combines and connects
them; for it feels assured that intellectual things ought to be able
to bear such handling. Even practical knowledge, we see clearly, is
not possible without the use of the reason; and the speculative
reason is only the reason satisfying itself of its own consistency.
The speculative faculty cannot be controlled from acting. The mind
cannot but claim a right to speculate concerning all its own acts
and creations; yet, when it exercises this right upon its common
practical notions, we find that it runs into barren abstractions and
ever-recurring cycles of subtlety. Such Notions are like waters
naturally stagnant; however much we urge and agitate them, they only
revolve in stationary {50} whirlpools. But the mind is capable of
acquiring scientific Ideas, which are better fitted to undergo
discussion and impulsion. When our speculations are duly fed from
the springheads of Observation, and frequently drawn off into the
region of Applied Science, we may have a living stream of consistent
and progressive knowledge. That science may be both real as to its
import, and logical as to its form, the examples of many existing
sciences sufficiently prove.

_School Philosophy_.--So long, however, as attempts are made to form
sciences, without such a verification and realization of their
fundamental ideas, there is, in the natural series of speculation,
no self-correcting principle. A philosophy constructed on notions
obscure, vague, and unsubstantial, and held in spite of the want of
correspondence between its doctrines and the actual train of
physical events, may long subsist, and occupy men's minds. Such a
philosophy must depend for its permanence upon the pleasure which
men feel in tracing the operations of their own and other men's
minds, and in reducing them to logical consistency and systematical
arrangement.

In these cases the main subjects of attention are not external
objects, but speculations previously delivered; the object is not to
interpret nature, but man's mind. The opinions of the Masters are
the facts which the Disciples endeavor to reduce to unity, or to
follow into consequences. A series of speculators who pursue such a
course, may properly be termed a _School_, and their philosophy a
_School Philosophy_; whether their agreement in such a mode of
seeking knowledge arise from personal communication and tradition,
or be merely the result of a community of intellectual character and
propensity. The two great periods of School Philosophy (it will be
recollected that we are here directing our attention mainly to
physical science) were that of the Greeks and that of the Middle
Ages;--the period of the first waking of science, and that of its
midday slumber.

What has been said thus briefly and imperfectly, would require great
detail and much explanation, to give it its full significance and
authority. But it seemed proper to state so much in this place, in
order to render more intelligible and more instructive, at the first
aspect, the view of the attempted or effected progress of science.

It is, perhaps, a disadvantage inevitably attending an undertaking
like the present, that it must set out with statements so abstract;
and must present them without their adequate development and proof.
Such an Introduction, both in its character and its scale of
execution, may be compared to the geographical sketch of a country,
with which {51} the historian of its fortunes often begins his
narration. So much of Metaphysics is as necessary to us as such a
portion of Geography is to the Historian of an Empire; and what has
hitherto been said, is intended as a slight outline of the Geography
of that Intellectual World, of which we have here to study the
History.

The name which we have given to this History--A HISTORY OF THE
INDUCTIVE SCIENCES--has the fault of seeming to exclude from the
rank of Inductive Sciences those which are not included in the
History; as Ethnology and Glossology, Political Economy, Psychology.
This exclusion I by no means wish to imply; but I could find no
other way of compendiously describing my subject, which was intended
to comprehend those Sciences in which, by the observation of facts
and the use of reason, systems of doctrine have been established
which are universally received as truths among thoughtful men; and
which may therefore be studied as examples of the manner in which
truth is to be discovered. Perhaps a more exact description of the
work would have been, _A History of the principal Sciences hitherto
established by Induction_. I may add that I do not include in the
phrase "Inductive Sciences," the branches of Pure Mathematics
(Geometry, Arithmetic, Algebra, and the like), because, as I have
elsewhere stated (_Phil. Ind. Sc._, book ii. c. 1), these are not
_Inductive_ but _Deductive_ Sciences. They do not infer true
theories from observed facts, and more general from more limited
laws: but they trace the conditions of all theory, the properties of
space and number; and deduce results from ideas without the aid of
experience. The History of these Sciences is briefly given in
Chapters 13 and 14 of the Second Book of the _Philosophy_ just
referred to.


I may further add that the other work to which I refer, the
_Philosophy of the Inductive Sciences_, is in a great measure
historical, no less than the present _History_. That work contains
the history of the Sciences so far as it depends on _Ideas_; the
present work contains the history so far as it depends upon
_Observation_. The two works resulted simultaneously from the same
examination of the principal writers on science in all ages, and may
serve to supplement each other.



{{53}}
BOOK I.

HISTORY
OF THE
GREEK SCHOOL PHILOSOPHY,
WITH REFERENCE TO
PHYSICAL SCIENCE.


  Τίς γὰρ ἀρχὰ δέξατο ναυτιλίας;
  Τίς δὲ κίνδυνος κρατεροῖς ἀδάμαντος δῆσεν ἄλοις;
  . . . . . . Ἐπεὶ δ' ἐμβόλου
  Κρέμασαν ἀγκύρας ὕπερθεν
  Χρυσέαν χείρεσσι λαβὼν φιάλαν
  Ἀρχὸς ἐν πρύμνᾳ πατέρ Οὐρανιδᾶν
  Ἐγχεικέραυνον Ζῆνα, καὶ ὠκυπόρους
  Κυμάτων ῥίπας, ἀνέμων τ' ἐκάλει,
  Ἀματά τ' εὔφρονα, καὶ
  Φιλίαν νόστοιο μοῖραν.
         PINDAR. _Pyth._ iv. 124, 349.


  Whence came their voyage? them what peril held
  With adamantine rivets firmly bound?
    *     *     *     *     *     *
    But soon as on the vessel's bow
      The anchor was hung up,
    Then took the Leader on the prow
      In hands a golden cup,
    And on great Father Jove did call,
    And on the Winds and Waters all,
      Swept by the hurrying blast;
    And on the Nights, and Ocean Ways,
    And on the fair auspicious Days,
      And loved return at last.



{{55}}
BOOK I.


HISTORY OF THE GREEK SCHOOL PHILOSOPHY, WITH REFERENCE TO PHYSICAL
SCIENCE.




CHAPTER I.

PRELUDE TO THE GREEK SCHOOL PHILOSOPHY.


_Sect._ 1.--_First Attempts of the Speculative Faculty in Physical
Inquiries._

AT an early period of history there appeared in men a propensity to
pursue speculative inquiries concerning the various parts and
properties of the material world. What they saw excited them to
meditate, to conjecture, and to reason: they endeavored to account for
natural events, to trace their causes, to reduce them to their
principles. This habit of mind, or, at least that modification of it
which we have here to consider, seems to have been first unfolded
among the Greeks. And during that obscure introductory interval which
elapsed while the speculative tendencies of men were as yet hardly
disentangled from the practical, those who were most eminent in such
inquiries were distinguished by the same term of praise which is
applied to sagacity in matters of action, and were called _wise_
men--σοφοὶ. But when it came to be clearly felt by such persons that
their endeavors were suggested by the love of knowledge, a motive
different from the motives which lead to the wisdom of active life, a
name was adopted of a more appropriate, as well as of a more modest
signification, and they were termed _philosophers_, or lovers of
wisdom. This appellation is said[7\1] to have been first assumed by
Pythagoras. Yet he, in Herodotus, instead of having this title, is
called a powerful _sophist_--Ἑλλήνων οὐ τῷ ἀσθενεστάτῳ σοφιστῇ
Πυθαγόρῃ;[8\1] the historian using this word, as it would seem,
without intending to imply that misuse of reason which the term
afterwards came to denote. The historians of literature {56} placed
Pythagoras at the origin of the Italic School, one of the two main
lines of succession of the early Greek philosophers: but the other,
the Ionic School, which more peculiarly demands our attention, in
consequence of its character and subsequent progress, is deduced from
Thales, who preceded the age of _Philosophy_, and was one of the
_sophi_, or "wise men of Greece."

[Note 7\1: Cic. Tusc. v. 3.]

[Note 8\1: Herod. iv. 95.]

The Ionic School was succeeded in Greece by several others; and the
subjects which occupied the attention of these schools became very
extensive. In fact, the first attempts were, to form systems which
should explain the laws and causes of the material universe; and to
these were soon added all the great questions which our moral
condition and faculties suggest. The physical philosophy of these
schools is especially deserving of our study, as exhibiting the
character and fortunes of the most memorable attempt at universal
knowledge which has ever been made. It is highly instructive to
trace the principles of this undertaking; for the course pursued was
certainly one of the most natural and tempting which can be
imagined; the essay was made by a nation unequalled in fine mental
endowments, at the period of its greatest activity and vigor; and
yet it must be allowed (for, at least so far as physical science is
concerned, none will contest this), to have been entirely
unsuccessful. We cannot consider otherwise than as an utter failure,
an endeavor to discover the causes of things, of which the most
complete results are the Aristotelian physical treatises; and which,
after reaching the point which these treatises mark, left the human
mind to remain stationary, at any rate on all such subjects, for
nearly two thousand years.

The early philosophers of Greece entered upon the work of physical
speculation in a manner which showed the vigor and confidence of the
questioning spirit, as yet untamed by labors and reverses. It was
for later ages to learn that man must acquire, slowly and patiently,
letter by letter, the alphabet in which nature writes her answers to
such inquiries. The first students wished to divine, at a single
glance, the whole import of her book. They endeavored to discover
the origin and principle of the universe; according to Thales,
_water_ was the origin of all things, according to Anaximenes,
_air_; and Heraclitus considered _fire_ as the essential principle
of the universe. It has been conjectured, with great plausibility,
that this tendency to give to their Philosophy the form of a
Cosmogony, was owing to the influence of the poetical Cosmogonies
and Theogonies which had been produced and admired at a still
earlier age. Indeed,  such wide and ambitious {57} doctrines as
those which have been mentioned, were better suited to the dim
magnificence of poetry, than to the purpose of a philosophy which
was to bear the sharp scrutiny of reason. When we speak of the
_principles_ of things, the term, even now, is very ambiguous and
indefinite in its import, but how much more was that the case in the
first attempts to use such abstractions! The term which is commonly
used in this sense (ἀρχὴ), signified at first _the beginning_; and
in its early philosophical applications implied some obscure mixed
reference to the mechanical, chemical, organic, and historical
causes of the visible state of things, besides the theological views
which at this period were only just beginning to be separated from
the physical. Hence we are not to be surprised if the sources from
which the opinions of this period appear to be derived are rather
vague suggestions and casual analogies, than any reasons which will
bear examination. Aristotle conjectures, with considerable
probability, that the doctrine of Thales, according to which water
was the universal element, resulted from the manifest importance of
moisture in the support of animal and vegetable life.[9\1] But such
precarious analyses of these obscure and loose dogmas of early
antiquity are of small consequence to our object.

[Note 9\1: Metaph. i. 3.]

In more limited and more definite examples of inquiry concerning the
causes of natural appearances, and in the attempts made to satisfy
men's curiosity in such cases, we appear to discern a more genuine
prelude to the true spirit of physical inquiry. One of the most
remarkable instances of this kind is to be found in the speculations
which Herodotus records, relative to the cause of the floods of the
Nile. "Concerning the nature of this river," says the father of
history,[10\1] "I was not able to learn any thing, either from the
priests or from any one besides, though I questioned them very
pressingly. For the Nile is flooded for a hundred days, beginning
with the summer solstice; and after this time it diminishes, and is,
during the whole winter, very small. And on this head I was not able
to obtain any thing satisfactory from any one of the Egyptians, when
I asked what is the power by which the Nile is in its nature the
reverse of other rivers."

[Note 10\1: Herod. ii. 19.]

We may see, I think, in the historian's account, that the Grecian
mind felt a craving to discover the reasons of things which other
nations did not feel. The Egyptians, it appears, had no theory, and
felt no want of a theory. Not so the Greeks; they had their reasons
to render, though they were not such as satisfied Herodotus. "Some
{58} of the Greeks," he says, "who wish to be considered great
philosophers (Ἑλλήνων τινες ἐπισήμοι βουλόμενοι γενέσθαι σοφίην),
have propounded three ways of accounting for these floods. Two of
them," he adds, "I do not think worthy of record, except just so far
as to mention them." But as these are some of the earliest Greek
essays in physical philosophy, it will be worth while, even at this
day, to preserve the brief notice he has given of them, and his own
reasonings upon the same subject.

"One of these opinions holds that the Etesian winds [which blew from
the north] are the cause of these floods, by preventing the Nile
from flowing into the sea." Against this the historian reasons very
simply and sensibly. "Very often when the Etesian winds do not blow,
the Nile is flooded nevertheless. And moreover, if the Etesian winds
were the cause, all other rivers, which have their course opposite
to these winds, ought to undergo the same changes as the Nile; which
the rivers of Syria and Libya so circumstanced do not."

"The next opinion is still more unscientific (ἀνεπιστημονεστέρη),
and is, in truth, marvellous for its folly. This holds that the
ocean flows all round the earth, and that the Nile comes out of the
ocean, and by that means produces its effects." "Now," says the
historian, "the man who talks about this ocean-river, goes into the
region of fable, where it is not easy to demonstrate that he is
wrong. I know of no such river. But I suppose that Homer and some of
the earlier poets invented this fiction and introduced it into their
poetry."

He then proceeds to a third account, which to a modern reasoner
would appear not at all unphilosophical in itself, but which he,
nevertheless, rejects in a manner no less decided than the others.
"The third opinion, though much the most plausible, is still more
wrong than the others; for it asserts an impossibility, namely, that
the Nile proceeds from the melting of the snow. Now the Nile flows
out of Libya, and through Ethiopia, which are very hot countries,
and thus comes into Egypt, which is a colder region. How then can it
proceed from snow?" He then offers several other reasons "to show,"
as he says, "to any one capable of reasoning on such subjects (ἀνδρί
γε λογίζεσθαι τοιούτων πέρι οἵῳ τε ἔοντι), that the assertion cannot
be true. The winds which blow from the southern regions are hot; the
inhabitants are black; the swallows and kites (ἰκτῖνοι) stay in the
country the whole year; the cranes fly the colds of Scythia, and
seek their warm winter-quarters there; which would not be if it
snowed ever so little." He adds another reason, founded apparently
upon {59} some limited empirical maxim of weather-wisdom taken from
the climate of Greece. "Libya," he said, "has neither rain nor ice,
and therefore no snow; _for_, in five days after a fall of snow
there must be a fall of rain; so that if it snowed in those regions
it must rain too." I need not observe that Herodotus was not aware
of the difference between the climate of high mountains and plains
in a torrid region; but it is impossible not to be struck both with
the activity and the coherency of thought displayed by the Greek
mind in this primitive physical inquiry.

But I must not omit the hypothesis which Herodotus himself proposes,
after rejecting those which have been already given. It does not
appear to me easy to catch his exact meaning, but the statement will
still be curious. "If," he says, "one who has condemned opinions
previously promulgated may put forward his own opinion concerning so
obscure a matter, I will state why it seems to me that the Nile is
flooded in summer." This opinion he propounds at first with an
oracular brevity, which it is difficult to suppose that he did not
intend to be impressive. "In winter the sun is carried by the seasons
away from his former course, and goes to the upper parts of Libya. And
_there, in short, is the whole account;_ for that region to which this
divinity (the sun) is nearest, must naturally be most scant of water,
and the river-sources of that country must be dried up."

But the lively and garrulous Ionian immediately relaxes from this
apparent reserve. "To explain the matter more at length," he
proceeds, "it is thus. The sun when he traverses the upper parts of
Libya, does what he commonly does in summer;--he _draws_ the water
to him (ἕλκει ἐπ' ἑωϋτὸν τὸ ὕδωρ), and having thus drawn it, he
pushes it to the upper regions (of the air probably), and then the
winds take it and disperse it till they dissolve in moisture. And
thus the winds which blow from those countries, Libs and Notus, are
the most moist of all winds. Now when the winter relaxes and the sun
returns to the north, he still draws water from all the rivers, but
they are increased by showers and rain torrents so that they are in
flood till the summer comes; and then, the rain falling and the sun
still drawing them, they become small. But the Nile, not being fed
by rains, yet being drawn by the sun, is, alone of all rivers, much
more scanty in the winter than in the summer. For in summer it is
drawn like all other rivers, but in winter it alone has its supplies
shut up. And in this way, I have been led to think the sun is the
cause of the occurrence in question." We may remark that the
historian here appears to {60} ascribe the inequality of the Nile at
different seasons to the influence of the sun upon its springs
alone, the other cause of change, the rains being here excluded; and
that, on this supposition, the same relative effects would be
produced whether the sun increase the sources in winter by melting
the snows, or diminish them in summer by what he calls _drawing_
them upwards.

This specimen of the early efforts of the Greeks in physical
speculations, appears to me to speak strongly for the opinion that
their philosophy on such subjects was the native growth of the Greek
mind, and owed nothing to the supposed lore of Egypt and the East;
an opinion which has been adopted with regard to the Greek
Philosophy in general by the most competent judges on a full survey
of the evidence.[11\1] Indeed, we have no evidence whatever that, at
any period, the African or Asiatic nations (with the exception
perhaps of the Indians) ever felt this importunate curiosity with
regard to the definite application of the idea of cause and effect
to visible phenomena; or drew so strong a line between a fabulous
legend and a reason rendered; or attempted to ascend to a natural
cause by classing together phenomena of the same kind. We may be
well excused, therefore, for believing that they could not impart to
the Greeks what they themselves did not possess; and so far as our
survey goes, physical philosophy has its origin, apparently
spontaneous and independent, in the active and acute intellect of
Greece.

[Note 11\1: Thirlwall, _Hist. Gr._, ii. 130; and, as there quoted,
Ritter, _Geschichte der Philosophie_, i. 159-173.]


_Sect._ 2.--_Primitive Mistake in Greek Physical Philosophy._

WE now proceed to examine with what success the Greeks followed the
track into which they had thus struck. And here we are obliged to
confess that they very soon turned aside from the right road to
truth, and deviated into a vast field of error, in which they and
their successors have wandered almost to the present time. It is not
necessary here to inquire why those faculties which appear to be
bestowed upon us for the discovery of truth, were permitted by
Providence to fail so signally in answering that purpose; whether,
like the powers by which we seek our happiness, they involve a
responsibility on our part, and may be defeated by rejecting the
guidance of a higher faculty; or whether these endowments, though
they did not {61} immediately lead man to profound physical
knowledge, answered some nobler and better purpose in his
constitution and government. The fact undoubtedly was, that the
physical philosophy of the Greeks soon became trifling and
worthless; and it is proper to point out, as precisely as we can, in
what the fundamental mistake consisted.

To explain this, we may in the first place return for a moment to
Herodotus's account of the cause of the floods of the Nile.

The reader will probably have observed a remarkable phrase used by
Herodotus, in his own explanation of these inundations. He says that
the sun _draws_, or attracts, the water; a metaphorical term,
obviously intended to denote some more general and abstract
conception than that of the visible operation which the word
primarily signifies. This abstract notion of "drawing" is, in the
historian, as we see, very vague and loose; it might, with equal
propriety, be explained to mean what we now understand by mechanical
or by chemical attraction, or pressure, or evaporation. And in like
manner, all the first attempts to comprehend the operations of
nature, led to the introduction of abstract conceptions, often
vague, indeed, but not, therefore, unmeaning; such as _motion_ and
_velocity_, _force_ and _pressure_, _impetus_ and _momentum_ (ῥοπὴ).
And the next step in philosophizing, necessarily was to endeavor to
make these vague abstractions more clear and fixed, so that the
logical faculty should be able to employ them securely and
coherently. But there were two ways of making this attempt; the one,
by examining the words only, and the thoughts which they call up;
the other, by attending to the facts and things which bring these
abstract terms into use. The latter, the method of _real_ inquiry,
was the way to success; but the Greeks followed the former, the
_verbal_ or _notional_ course, and failed.

If Herodotus, when the notion of the sun's attracting the waters of
rivers had entered into his mind, had gone on to instruct himself,
by attention to facts, in what manner this notion could be made more
definite, while it still remained applicable to all the knowledge
which could be obtained, he would have made some progress towards a
true solution of his problem. If, for instance, he had tried to
ascertain whether this Attraction which the sun exerted upon the
waters of rivers, depended on his influence at their fountains only,
or was exerted over their whole course, and over waters which were
not parts of rivers, he would have been led to reject his
hypothesis; for he would have found, by observations sufficiently
obvious, that the sun's Attraction, as shown in such cases, is a
tendency to lessen all expanded and {62} open collections of
moisture, whether flowing from a spring or not; and it would then be
seen that this influence, operating on the whole surface of the
Nile, must diminish it as well as other rivers, in summer, and
therefore could not be the cause of its overflow. He would thus have
corrected his first loose conjecture by a real study of nature, and
might, in the course of his meditations, have been led to available
notions of Evaporation, or other natural actions. And, in like
manner, in other cases, the rude attempts at explanation, which the
first exercise of the speculative faculty produced, might have been
gradually concentrated and refined, so as to fall in, both with the
requisitions of reason and the testimony of sense.

But this was not the direction which the Greek speculators took. On
the contrary; as soon as they had introduced into their philosophy
any abstract and general conceptions, they proceeded to scrutinize
these by the internal light of the mind alone, without any longer
looking abroad into the world of sense. They took for granted that
philosophy must result from the relations of those notions which are
involved in the common use of language, and they proceeded to seek
their philosophical doctrines by studying such notions. They ought
to have reformed and fixed their usual conceptions by Observation;
they only analyzed and expanded them by Reflection: they ought to
have sought by trial, among the Notions which passed through their
minds, some one which admitted of exact application to Facts; they
selected arbitrarily, and, consequently, erroneously, the Notions
according to which Facts should be assembled and arranged: they
ought to have collected clear Fundamental Ideas from the world of
things by _inductive_ acts of thought; they only derived results by
_Deduction_ from one or other of their familiar Conceptions.[12\1]

[Note 12\1: The course by which the Sciences were formed, and which
is here referred to as that which the Greeks did _not_ follow, is
described in detail in the _Philosophy_, book xi., _Of the
Construction of Science_.]

When this false direction had been extensively adopted by the Greek
philosophers, we may treat of it as the method of their _Schools_.
Under that title we must give a further account of it. {63}




CHAPTER II.

THE GREEK SCHOOL PHILOSOPHY.


_Sect._ 1.--_The general Foundation of the Greek School Philosophy._

THE physical philosophy of the Greek Schools was formed by looking
at the material world through the medium of that common language
which men employ to answer the common occasions of life; and by
adopting, arbitrarily, as the grounds of comparison of facts, and of
inference from them, notions more abstract and large than those with
which men are practically familiar, but not less vague and obscure.
Such a philosophy, however much it might be systematized, by
classifying and analyzing the conceptions which it involves, could
not overcome the vices of its fundamental principle. But before
speaking of these defects, we must give some indications of its
character.

The propensity to seek for principles in the common usages of
language may be discerned at a very early period. Thus we have an
example of it in a saying which is reported of Thales, the founder
of Greek philosophy.[13\1] When he was asked, "What is the
_greatest_ thing?" he replied, "_Place_; for all other things are
_in_ the world, but the world is _in_ it." In Aristotle we have the
consummation of this mode of speculation. The usual point from which
he starts in his inquiries is, that we say thus or thus in common
language. Thus, when he has to discuss the question, whether there
be, in any part of the universe, a Void, or space in which there is
nothing, he inquires first in how many senses we say that one thing
is _in_ another. He enumerates many of these;[14\1] we say the part
is in the whole, as the finger is _in_ the hand; again we say, the
species is in the genus, as man is included _in_ animal; again, the
government of Greece is _in_ the king; and various other senses are
described or exemplified, but of all these _the most proper_ is when
we say a thing is _in_ a vessel, and generally, _in place_. He next
examines what _place_ is, and comes to this conclusion, that "if
about a body there be another body including it, it is in place, and
if not, not." A body _moves_ when it changes its place; but {64} he
adds, that if water be in a vessel, the vessel being at rest, the
parts of the water may still move, for they are included by each
other; so that while the whole does not change its place, the parts
may change their places in a circular order. Proceeding then to the
question of a _void_, he, as usual, examines the different senses in
which the term is used, and adopts, as the most proper, _place
without matter_; with no useful result, as we shall soon see.

[Note 13\1: Plut. _Conv. Sept. Sap._ Diog. Laert. i. 35.]

[Note 14\1: Physic. Ausc. iv. 3.]

Again,[15\1] in a question concerning mechanical action, he says,
"When a man moves a stone by pushing it with a stick, _we say_ both
that the man moves the stone, and that the stick moves the stone,
but the latter _more properly_."

[Note 15\1: Physic. Ausc. viii. 5.]

Again, we find the Greek philosophers applying themselves to extract
their dogmas from the most general and abstract notions which they
could detect; for example,--from the conception of the Universe as
One or as Many things. They tried to determine how far we may, or
must, combine with these conceptions that of a whole, of parts, of
number, of limits, of place, of beginning or end, of full or void,
of rest or motion, of cause and effect, and the like. The analysis
of such conceptions with such a view, occupies, for instance, almost
the whole of Aristotle's _Treatise on the Heavens_.

The Dialogue of Plato, which is entitled _Parmenides_, appears at
first as if its object were to show the futility of this method of
philosophizing; for the philosopher whose name it bears, is
represented as arguing with an Athenian named Aristotle,[16\1] and,
by a process of metaphysical analysis, reducing him at least to this
conclusion, "that whether _One_ exist, or do not exist, it follows
that both it and other things, with reference to themselves and to
each other, all and in all respects, both are and are not, both
appear and appear not." Yet the method of Plato, so far as concerns
truths of that kind with which we are here concerned, was little
more efficacious than that of his rival. It consists mainly, as may
be seen in several of the dialogues, and especially in the _Timæus_,
in the application of notions as loose as those of the Peripatetics;
for example, the conceptions of the Good, the Beautiful, the
Perfect; and these are rendered still more arbitrary, by assuming an
acquaintance with the views of the Creator of the universe. The
philosopher is thus led to maxims which agree with those {65} of the
Aristotelians, that there can be no void, that things seek their own
place, and the like.[17\1]

[Note 16\1: This Aristotle is not the Stagirite, who was forty-five
years younger than Plato, but one of the "thirty tyrants," as they
were called.]

[Note 17\1: Timæus, p. 80.]

Another mode of reasoning, very widely applied in these attempts,
was the doctrine of contrarieties, in which it was assumed, that
adjectives or substantives which are in common language, or in some
abstract mode of conception, opposed to each other, must point at
some fundamental antithesis in nature, which it is important to
study. Thus Aristotle[18\1] says, that the Pythagoreans, from the
contrasts which number suggests, collected ten principles,--Limited
and Unlimited, Odd and Even, One and Many, Right and Left, Male and
Female, Rest and Motion, Straight and Curved, Light and Darkness,
Good and Evil, Square and Oblong. We shall see hereafter, that
Aristotle himself deduced the doctrine of Four Elements, and other
dogmas, by oppositions of the same kind.

[Note 18\1: Metaph. 1. 5.]

The physical speculator of the present day will learn without
surprise, that such a mode of discussion as this, led to no truths
of real or permanent value. The whole mass of the Greek philosophy,
therefore, shrinks into an almost imperceptible compass, when viewed
with reference to the progress of physical knowledge. Still the
general character of this system, and its fortunes from the time of
its founders to the overthrow of their authority, are not without
their instruction, and, it may be hoped, not without their interest.
I proceed, therefore, to give some account of these doctrines in
their most fully developed and permanently received form, that in
which they were presented by Aristotle.


_Sect._ 2.--_The Aristotelian Physical Philosophy._

THE principal physical treatises of Aristotle are, the eight Books
of "Physical Lectures," the four Books "Of the Heavens," the two
Books "Of Production and Destruction:" for the Book "Of the World"
is now universally acknowledged to be spurious; and the
"Meteorologies," though full of physical explanations of natural
phenomena, does not exhibit the doctrines and reasonings of the
school in so general a form; the same may be said of the "Mechanical
Problems." The treatises on the various subjects of Natural History,
"On Animals," "On the Parts of Animals," "On Plants," "On
Physiognomonics," "On Colors," "On Sound," contain an extraordinary
{66} accumulation of facts, and manifest a wonderful power of
systematizing; but are not works which expound principles, and
therefore do not require to be here considered.

The Physical Lectures are possibly the work concerning which a
well-known anecdote is related by Simplicius, a Greek commentator of
the sixth century, as well as by Plutarch. It is said, that
Alexander the Great wrote to his former tutor to this effect; "You
have not done well in publishing these lectures; for how shall we,
your pupils, excel other men, if you make that public to all, which
we learnt from you?" To this Aristotle is said to have replied: "My
Lectures are published and not published; they will be intelligible
to those who heard them, and to none besides." This may very easily
be a story invented and circulated among those who found the work
beyond their comprehension; and it cannot be denied, that to make
out the meaning and reasoning of every part, would be a task very
laborious and difficult, if not impossible. But we may follow the
import of a large portion of the Physical Lectures with sufficient
clearness to apprehend the character and principles of the
reasoning; and this is what I shall endeavor to do.

The author's introductory statement of his view of the nature of
philosophy falls in very closely with what has been said, that he
takes his facts and generalizations as they are implied in the
structure of language. "We must in all cases proceed," he says,
"from what is known to what is unknown." This will not be denied;
but we can hardly follow him in his inference. He adds, "We must
proceed, therefore, from universal to particular. And something of
this," he pursues, "may be seen in language; for names signify
things in a general and indefinite manner, as _circle_, and by
defining we unfold them into particulars." He illustrates this by
saying, "thus children at first call all men _father_, and all women
_mother_, but afterwards distinguish."

In accordance with this view, he endeavors to settle several of the
great questions concerning the universe, which had been started
among subtle and speculative men, by unfolding the meaning of the
words and phrases which are applied to the most general notions of
things and relations. We have already noticed this method. A few
examples will illustrate it further:--Whether there was or was not a
_void_, or place without matter, had already been debated among
rival sects of philosophers. The antagonist arguments were briefly
these:--There must be a void, because a body cannot move into a
space except it is {67} empty, and therefore without a void there
could be no motion:--and, on the other hand, there is no void, for
the intervals between bodies are filled with air, and air is
something. These opinions had even been supported by reference to
experiment. On the one hand, Anaxagoras and his school had shown,
that air, when confined, resisted compression, by squeezing a blown
bladder, and pressing down an inverted vessel in the water; on the
other hand, it was alleged that a vessel full of fine ashes held as
much water as if the ashes were not there, which could only be
explained by supposing void spaces among the ashes. Aristotle
decides that there is no void, on such arguments as this:[19\1]--In
a void there could be no difference of up and down; for as in
nothing there are no differences, so there are none in a privation
or negation; but a void is merely a privation or negation of matter;
therefore, in a void, bodies could not move up and down, which it is
in their nature to do. It is easily seen that such a mode of
reasoning, elevates the familiar forms of language and the
intellectual connections of terms, to a supremacy over facts; making
truth depend upon whether terms are or are not privative, and
whether we say that bodies fall _naturally_. In such a philosophy
every new result of observation would be compelled to conform to the
usual combinations of phrases, as these had become associated by the
modes of apprehension previously familiar.

[Note 19\1: Physic. Ausc. iv. 7, p. 215.]

It is not intended here to intimate that the common modes of
apprehension, which are the basis of common language, are limited
and casual. They imply, on the contrary, universal and necessary
conditions of our perceptions and conceptions; thus all things are
necessarily apprehended as existing in Time and Space, and as
connected by relations of Cause and Effect; and so far as the
Aristotelian philosophy reasons from these assumptions, it has a
real foundation, though even in this case the conclusions are often
insecure. We have an example of this reasoning in the eighth
Book,[20\1] where he proves that there never was a time in which
change and motion did not exist; "For if all things were at rest,
the first motion must have been produced by some change in some of
these things; that is, there must have been a change before the
first change;" and again, "How can _before_ and _after_ apply when
time is not? or how can time be when motion is not? If," he adds,
"time is a numeration of motion, and if time be eternal, motion must
be eternal." But he sometimes {68} introduces principles of a more
arbitrary character; and besides the general relations of thought,
takes for granted the inventions of previous speculators; such, for
instance, as the then commonly received opinions concerning the
frame of the world. From the assertion that motion is eternal,
proved in the manner just stated, Aristotle proceeds by a curious
train of reasoning, to identify this eternal motion with the diurnal
motion of the heavens. "There must," he says, "be something which is
the First Mover:"[21\1] this follows from the relation of causes and
effects. Again, "Motion must go on constantly, and, therefore, must
be either continuous or successive. Now what is continuous is more
properly said to take place _constantly_, than what is successive.
Also the continuous is better; but we always suppose that which is
better to take place in nature, if it be possible. The motion of the
First Mover will, therefore, be continuous, if such an eternal
motion be possible." We here see the vague judgment of _better_ and
_worse_ introduced, as that of _natural_ and _unnatural_ was before,
into physical reasonings.

[Note 20\1: Ib. viii. 1, p. 258.]

[Note 21\1: Physic. Ausc. viii. 6. p. 258.]

I proceed with Aristotle's argument.[22\1] "We have now, therefore,
to show that there may be an infinite single, continuous motion, and
that this is circular." This is, in fact, proved, as may readily be
conceived, from the consideration that a body may go on perpetually
revolving uniformly in a circle. And thus we have a demonstration,
on the principles of this philosophy, that there is and must be a
First Mover, revolving eternally with a uniform circular motion.

[Note 22\1: Ib. viii. 8.]

Though this kind of philosophy may appear too trifling to deserve
being dwelt upon, it is important for our purpose so far as to
exemplify it, that we may afterwards advance, confident that we have
done it no injustice.

I will now pass from the doctrines relating to the motions of the
heavens, to those which concern the material elements of the
universe. And here it may be remarked that the tendency (of which we
are here tracing the development) to extract speculative opinions
from the relations of words, must be very natural to man; for the
very widely accepted doctrine of the Four Elements which appears to
be founded on the opposition of the adjectives _hot_ and _cold_,
_wet_ and _dry_, is much older than Aristotle, and was probably one
of the earliest of philosophical dogmas. The great master of this
philosophy, however, puts the opinion in a more systematic manner
than his predecessors. {69}

"We seek," he says,[23\1] "the principles of sensible things, that
is, of tangible bodies. We must take, therefore, not all the
contrarieties of quality, but those only which have reference to the
touch. Thus black and white, sweet and bitter, do not differ as
tangible qualities, and therefore must be rejected from our
consideration.

[Note 23\1: De Gen. et Corrupt. ii. 2.]

"Now the contrarieties of quality which refer to the touch are
these: hot, cold; dry, wet; heavy, light; hard, soft; unctuous,
meagre; rough, smooth; dense, rare." He then proceeds to reject all
but the four first of these, for various reasons; heavy and light,
because they are not active and passive qualities; the others,
because they are combinations of the four first, which therefore he
infers to be the four elementary qualities.

"[24\1] Now in four things there are six combinations of two; but the
combinations of two opposites, as hot and cold, must be rejected; we
have, therefore, four elementary combinations, which agree with the
four apparently elementary bodies. Fire is hot and dry; air is hot and
wet (for steam is air); water is cold and wet, earth is cold and dry."

[Note 24\1: Ib. iii. 8.]

It may be remarked that this disposition to assume that some common
elementary quality must exist in the cases in which we habitually
apply a common adjective, as it began before the reign of the
Aristotelian philosophy, so also survived its influence. Not to
mention other cases, it would be difficult to free Bacon's
_Inquisitio in naturam calidi_, "Examination of the nature of heat,"
from the charge of confounding together very different classes of
phenomena under the cover of the word _hot_.

The correction of these opinions concerning the elementary
composition of bodies belongs to an advanced period in the history
of physical knowledge, even after the revival of its progress. But
there are some of the Aristotelian doctrines which particularly
deserve our attention, from the prominent share they had in the very
first beginnings of that revival; I mean the doctrines concerning
motion.

These are still founded upon the same mode of reasoning from
adjectives; but in this case, the result follows, not only from the
opposition of the words, but also from the distinction of their
being _absolutely_ or _relatively_ true. "Former writers," says
Aristotle, "have considered heavy and light _relatively_ only,
taking cases, where both things have weight, but one is lighter than
the other; and they imagined that, in {70} this way, they defined
what was _absolutely_ (ἁπλῶς) heavy and light." We now know that
things which rise by their lightness do so only because they are
pressed upwards by heavier surrounding bodies; and this assumption
of absolute levity, which is evidently gratuitous, or rather merely
nominal, entirely vitiated the whole of the succeeding reasoning.
The inference was, that fire must be absolutely light, since it
tends to take its place above the other three elements; earth
absolutely heavy, since it tends to take its place below fire, air,
and water. The philosopher argued also, with great acuteness, that
air, which tends to take its place below fire and above water, must
do so _by its nature_, and not in virtue of any combination of heavy
and light elements. "For if air were composed of the parts which
give fire its levity, joined with other parts which produce gravity,
we might assume a quantity of air so large, that it should be
lighter than a small quantity of fire, having more of the light
parts." It thus follows that each of the four elements tends to its
own place, fire being the highest, air the next, water the next, and
earth the lowest.

The whole of this train of errors arises from fallacies which have a
verbal origin;--from considering light as opposite to heavy; and
from considering levity as a quality of a body, instead of regarding
it as the effect of surrounding bodies.

It is worth while to notice that a difficulty which often
embarrasses persons on their entrance upon physical
speculations,--the difficulty of conceiving that up and down are
different directions in different places,--had been completely got
over by Aristotle and the Greek philosophers. They were steadily
convinced of the roundness of the earth, and saw that this truth led
to the conclusion that all heavy bodies tend in converging
directions to the centre. And, they added, as the heavy tends to the
centre, the light tends to the exterior, "for Exterior is opposite
to Centre as heavy is to light."[25\1]

[Note 25\1: De Cœlo, iv. 4.]

The tendencies of bodies downwards and upwards, their weight, their
fall, their floating or sinking, were thus accounted for in a manner
which, however unsound, satisfied the greater part of the
speculative world till the time of Galileo and Stevinus, though
Archimedes in the mean time published the true theory of floating
bodies, which is very different from that above stated. Other parts
of the doctrines of motion were delivered by the Stagirite in the
same spirit and with the same success. The motion of a body which is
thrown along the {71} ground diminishes and finally ceases; the
motion of a body which falls from a height goes on becoming quicker
and quicker; this was accounted for on the usual principle of
opposition, by saying that the former is a _violent_, the latter a
_natural_ motion. And the later writers of this school expressed the
characters of such motions in verse. The rule of natural motion
was[26\1]
  Principium tepeat, medium cum fine calebit.
  Cool at the first, it warm and warmer glows.
And of violent motion, the law was--
  Principium fervet, medium calet, ultima friget.
  Hot at the first, then barely warm, then cold.

[Note 26\1: Alsted. Encyc. tom. i. p. 687.]

It appears to have been considered by Aristotle a difficult problem
to explain why a stone thrown from the hand continues to move for
some time, and then stops. If the hand was the cause of the motion,
how could the stone move at all when left to itself? if not, why
does it ever stop? And he answers this difficulty by saying,[27\1]
"that there is a motion communicated to the air, the successive
parts of which urge the stone onwards; and that each part of this
medium continues to act for some while after it has been acted on,
and the motion ceases when it comes to a particle which cannot act
after it has ceased to be acted on." It will be readily seen that
the whole of this difficulty, concerning a body which moves forward
and is retarded till it stops, arises from ascribing the
retardation, not to the real cause, the surrounding resistances, but
to the body itself.

[Note 27\1: Phys. Ausc. viii. 10.]

One of the doctrines which was the subject of the warmest discussion
between the defenders and opposers of Aristotle, at the revival of
physical knowledge, was that in which he asserts,[28\1] "That body
is heavier than another which in an equal bulk moves downward
quicker." The opinion maintained by the **Aristotelians at the time of
Galileo was, that bodies fall quicker exactly in proportion to their
weight. The master himself asserts this in express terms, and
reasons upon it.[29\1] Yet in another passage he appears to
distinguish between weight and actual motion downwards.[30\1] "In
physics, we call bodies heavy and light from their _power_ of
motion; but these names are not applied to their actual operations
(ἐνέργειαις) except any one thinks {72} _momentum_ (ῥοπὴ) to be a
word of both applications. But heavy and light are, as it were, the
_embers_ or _sparks_ of motion, and therefore proper to be treated
of here."

[Note 28\1: De Cœlo, iv. 1, p. 308.]

[Note 29\1: Ib. iii. 2.]

[Note 30\1: Ib. iv. 1, p. 307.]

The distinction just alluded to, between Power or Faculty of Action,
and actual Operation or Energy, is one very frequently referred to
by Aristotle; and though not by any means useless, may easily be so
used as to lead to mere verbal refinements instead of substantial
knowledge.

The Aristotelian distinction of Causes has not any very immediate
bearing upon the parts of physics of which we have here mainly
spoken; but it was so extensively accepted, and so long retained,
that it may be proper to notice it.[31\1] "One kind of Cause is the
matter of which any thing is made, as bronze of a statue, and silver
of a vial; another is the form and pattern, as the Cause of an
octave is the ratio of two to one; again, there is the Cause which
is the origin of the production, as the father of the child; and
again, there is the End, or that for the sake of which any thing is
done, as health is the cause of walking." These four kinds of Cause,
the _material_, the _formal_, the _efficient_, and the _final_, were
long leading points in all speculative inquiries; and our familiar
forms of speech still retain traces of the influence of this
division.

[Note 31\1: Phys. ii. 3.]

It is my object here to present to the reader in an intelligible
shape, the principles and mode of reasoning of the Aristotelian
philosophy, not its results. If this were not the case, it would be
easy to excite a smile by insulating some of the passages which are
most remote from modern notions. I will only mention, as specimens,
two such passages, both very remarkable.

In the beginning of the book "On the Heavens," he proves[32\1] the
world to be _perfect_, by reasoning of the following kind: "The
bodies of which the world is composed are solids, and therefore have
three dimensions: now three is the most perfect number; it is the
first of numbers, for of _one_ we do not speak as a number; of _two_
we say _both_; but _three_ is the first number of which we say
_all_; moreover, it has a beginning, a middle, and an end."

[Note 32\1: De Cœlo, i. 1.]

The reader will still perceive the verbal foundations of opinions
thus supported.

"The simple elements must have simple motions, and thus fire and air
have their natural motions upwards, and water and earth have {73}
their natural motions downwards; but besides these motions, there is
motion in a circle, which is unnatural to these elements, but which
is a more perfect motion than the other, because a circle is a
perfect line, and a straight line is not; and there must be
something to which this motion is natural. From this it is evident,"
he adds, with obvious animation, "that there is some essence of body
different from those of the four elements, more divine than those,
and superior to them. If things which move in a circle move contrary
to nature, it is marvellous, or rather absurd, that this, the
unnatural motion, should alone be continuous and eternal; for
unnatural motions decay speedily. And so, from all this, we must
collect, that besides the four elements which we have here and about
us, there is another removed far off, and the more excellent in
proportion as it is more distant from us." This fifth element was
the "_quinta essentia_," of after writers, of which we have a trace
in our modern literature, in the word _quintessence_.


_Sect._ 3.--_Technical Forms of the Greek Schools._

WE have hitherto considered only the principle of the Greek Physics;
which was, as we have seen, to deduce its doctrines by an analysis
of the notions which common language involves. But though the
Grecian philosopher began by studying words in their common
meanings, he soon found himself led to fix upon some special shades
or applications of these meanings as the permanent and standard
notion, which they were to express; that is, he made his language
_technical_. The invention and establishment of technical terms is
an important step in any philosophy, true or false; we must,
therefore, say a few words on this process, as exemplified in the
ancient systems.

1. _Technical Forms of the Aristotelian Philosophy._--We have
already had occasion to cite some of the distinctions introduced by
Aristotle, which may be considered as technical; for instance, the
classification of Causes as _material_, _formal_, _efficient_, and
_final_; and the opposition of Qualities as _absolute_ and
_relative_. A few more of the most important examples may suffice.
An analysis of objects into _Matter_ and _Form_, when metaphorically
extended from visible objects to things conceived in the most
general manner, became an habitual hypothesis of the Aristotelian
school. Indeed this metaphor is even yet one of the most significant
of those which we can employ, to suggest one of the most comprehensive
and fundamental antitheses with which philosophy has to do;--the
opposition of sense and reason, of {74} impressions and laws. In this
application, the German philosophers have, up to the present time,
rested upon this distinction a great part of the weight of their
systems; as when Kant says, that Space and Time are the _Forms of
Sensation_. Even in our own language, we retain a trace of the
influence of this Aristotelian notion, in the word _Information_, when
used for that knowledge which may be conceived as moulding the mind
into a definite shape, instead of leaving it a mere mass of
unimpressed susceptibility.

Another favorite Aristotelian antithesis is that of _Power_ and
_Act_ (δύναμις, ἐνέργεια). This distinction is made the basis of
most of the physical philosophy of the school; being, however,
generally introduced with a peculiar limitation. Thus, Light is
defined to be "the Act of what is lucid, as being lucid. And if," it
is added, "the lucid be so in power but not in act, we have
darkness." The reason of the limitation, "as being lucid," is, that
a lucid body may act in other ways; thus a torch may move as well as
shine, but its moving is not its act _as being a lucid_ body.

Aristotle appears to be well satisfied with this explanation, for he
goes on to say, "Thus light is not Fire, nor any body whatever, or
the emanation of any body (for that would be a kind of body), but it
is the presence of something like Fire in the body; it is, however,
impossible that two bodies should exist in the same place, so that
it is not a body;" and this reasoning appears to leave him more
satisfied with his doctrine, that Light is an _Energy_ or _Act_.

But we have a more distinctly technical form given to this notion.
Aristotle introduced a word formed by himself to express the act
which is thus opposed to inactive power: this is the celebrated word
ἐντελέχεια. Thus the noted definition of Motion in the third book of
the Physics,[33\1] is that it is "the _Entelechy_, or Act, of a
movable body in respect of being movable;" and the definition of the
Soul is[34\1] that it is "the _Entelechy_ of a natural body which
has life by reason of its power." This word has been variously
translated by the followers of Aristotle, and some of them have
declared it untranslatable. _Act_ and _Action_ are held to be
inadequate substitutes; the _very act_, _ipse cursus actionis_, is
employed by some; _primus actus_ is employed by many, but another
school use _primus actus_ of a non-operating form. Budæus uses
_efficacia_. Cicero[35\1] translates it "quasi quandam continuatam
motionem, et perennem;" but this paraphrase, though it may {75} fall
in with the description of the soul, which is the subject with which
Cicero is concerned, does not appear to agree with the general
applications of the term. Hermolaus Barbarus is said to have been so
much oppressed with this difficulty of translation, that he
consulted the evil spirit by night, entreating to be supplied with a
more common and familiar substitute for this word: the mocking
fiend, however, suggested only a word equally obscure, and the
translator, discontented with this, invented for himself the word
_perfectihabia_.

[Note 33\1: Phys. iii. 1.]

[Note 34\1: De Animâ, ii. 1.]

[Note 35\1: Tusc. i. 10.]

We need not here notice the endless apparatus of technicalities
which was, in later days, introduced into the Aristotelian
philosophy; but we may remark, that their long continuance and
extensive use show us how powerful technical phraseology is, for the
perpetuation either of truth or error. The Aristotelian terms, and
the metaphysical views which they tend to preserve, are not yet
extinct among us. In a very recent age of our literature it was
thought a worthy employment by some of the greatest writers of the
day, to attempt to expel this system of technicalities by ridicule.

"Crambe regretted extremely that _substantial forms_, a race of
harmless beings, which had lasted for many years, and afforded a
comfortable subsistence to many poor philosophers, should now be
hunted down like so many wolves, without a possibility of retreat.
He considered that it had gone much harder with them than with
_essences_, which had retired from the schools into the
apothecaries' shops, where some of them had been advanced to the
degree of _quintessences_.**"[36\1]

[Note 36\1: Martinus Scriblerus, cap. vii.]

We must now say a few words on the technical terms which others of
the Greek philosophical sects introduced.

2. _Technical Forms of the Platonists._--The other sects of the Greek
philosophy, as well as the Aristotelians, invented and adopted
technical terms, and thus gave fixity to their tenets and consistency
to their traditionary systems; of these I will mention a few.

A technical expression of a contemporary school has acquired perhaps
greater celebrity than any of the terms of Aristotle. I mean the
_Ideas_ of Plato. The account which Aristotle gives of the origin of
these will serve to explain their nature.[37\1] "Plato," says he,
"who, in his youth, was in habits of communication first with
Cratylus and the Heraclitean opinions, which represent all the
objects of sense as being in a perpetual flux, so that concerning
these no science nor certain {76} knowledge can exist, entertained
the same opinions at a later period also. When, afterwards, Socrates
treated of moral subjects, and gave no attention to physics, but, in
the subjects which he did discuss, arrived at universal truths, and
before any man, turned his thoughts to definitions, Plato adopted
similar doctrines on this subject also; and construed them in this
way, that these truths and definitions must be applicable to
something else, and not to sensible things: for it was impossible,
he conceived, that there should be a general common definition of
any sensible object, since such were always in a state of change.
The things, then, which were the subjects of universal truths he
called _Ideas_; and held that objects of sense had their names
according to Ideas and after them; so that things participated in
that Idea which had the same name as was applied to them."

[Note 37\1: Arist. Metaph. i. 6. The same account is repeated, and
the subject discussed, Metaph. xii. 4.]

In agreement with this, we find the opinions suggested in the
_Parmenides_ of Plato, the dialogue which is considered by many to
contain the most decided exposition of the doctrine of Ideas. In
this dialogue, Parmenides is made to say to Socrates, then a young
man,[38\1] "O Socrates, philosophy has not yet claimed you for her
own, as, in my judgment, she will claim you, and you will not
dishonor her. As yet, like a young man as you are, you look to the
opinions of men. But tell me this: it appears to you, as you say,
that there are certain _Kinds_ or _Ideas_ (εἰδὴ) of which things
partake and receive applications according to that of which they
partake: thus those things which partake of _Likeness_ are called
_like_; those things which partake of _Greatness_ are called
_great_; those things which partake of _Beauty_ and _Justice_ are
called _beautiful_ and _just_." To this Socrates assents. And in
another part of the dialogue he shows that these Ideas are not
included in our common knowledge, from whence he infers that they
are objects of the Divine mind.

[Note 38\1: Parmenid. p. 131.]

In the Phædo the same opinion is maintained, and is summed up in
this way, by a reporter of the last conversation of Socrates,[39\1]
εἶναι τι ἕκαστον τῶν εἰδῶν, καὶ τούτων τ' ἄλλα μεταλαμβάνοντα αὐτῶν
τούτων τὴν ἐπωνυμίαν ἴσχειν; "that each _Kind_ has an existence, and
that other things partake of these Kinds, and are called according
to the Kind of which they partake."

[Note 39\1: Phædo, p. 102.]

The inference drawn from this view was, that in order to obtain true
and certain knowledge, men must elevate themselves, as much as
possible, to these Ideas of the qualities which they have to
consider: {77} and as things were thus called after the Ideas, the
Ideas had a priority and pre-eminence assigned them. The _Idea_ of
Good, Beautiful, and Wise was the "First Good," the "First
Beautiful," the "First Wise." This dignity and distinction were
ultimately carried to a large extent. Those Ideas were described as
eternal and self-subsisting, forming an "Intelligible World," full
of the models or archetypes of created things. But it is not to our
purpose here to consider the Platonic Ideas in their theological
bearings. In physics they were applied in the same form as in
morals. The _primum calidum_, _primum frigidum_ were those Ideas of
fundamental Principles by participation of which, all things were
hot or cold.

This school did not much employ itself in the development of its
principles as applied to physical inquiries: but we are not without
examples of such speculations. Plutarch's Treatise Περὶ τοῦ Πρώτου
Ψυχροῦ, "On the First Cold," may be cited as one. It is in reality a
discussion of a question which has been agitated in modern times
also;--whether cold be a positive quality or a mere privation. "Is
there, O Favorinus," he begins, "a First Power and Essence of the
Cold, as Fire is of the Hot; by a certain presence and participation
of which all other things are cold: or is rather coldness a
privation of heat, as darkness is of light, and rest of motion?"

3. _Technical Forms of the Pythagoreans._--The _Numbers_ of the
Pythagoreans, when propounded as the explanation of physical
phenomena, as they were, are still more obscure than the Ideas of
the Platonists. There were, indeed, considerable resemblances in the
way in which these two kinds of notions were spoken of. Plato called
his Ideas _unities_, _monads_; and as, according to him, Ideas, so,
according to the Pythagoreans, Numbers, were the causes of things
being what they are.[40\1] But there was this difference, that
things shared the nature of the Platonic Ideas "by participation,"
while they shared the nature of Pythagorean Numbers "by imitation."
Moreover, the Pythagoreans followed their notion out into much
greater development than any other school, investing particular
numbers with extraordinary attributes, and applying them by very
strange and forced analogies. Thus the number Four, to which they
gave the name of _Tetractys_, was held to be the most perfect
number, and was conceived to correspond to the human soul, in some
way which appears to be very imperfectly understood by the
commentators of this philosophy. {78}

[Note: 40\1: Arist. Metaph. i. 6.]

It has been observed by a distinguished modern scholar,[41\1] that
the place which Pythagoras ascribed to his numbers is intelligible
only by supposing that he confounded, first a numerical unit with a
geometrical point, and then this with a material atom. But this
criticism appears to place systems of physical philosophy under
requisitions too severe. If all the essential properties and
attributes of things were fully represented by the relations of
number, the philosophy which supplied such an explanation of the
universe, might well be excused from explaining also that existence
of objects which is distinct from the existence of all their
qualities and properties. The Pythagorean love of numerical
speculations might have been combined with the doctrine of atoms,
and the combination might have led to results well worth notice. But
so far as we are aware, no such combination was attempted in the
ancient schools of philosophy; and perhaps we of the present day are
only just beginning to perceive, through the disclosures of
chemistry and crystallography, the importance of such a line of
inquiry.

[Note 41\1: Thirlwall's _Hist. Gr._ ii. 142.]

4. _Technical Forms of the Atomists and Others._--The atomic
doctrine, of which we have just spoken, was one of the most definite
of the physical doctrines of the ancients, and was applied with most
perseverance and knowledge to the explanation of phenomena. Though,
therefore, it led to no success of any consequence in ancient times,
it served to transmit, through a long series of ages, a habit of
really physical inquiry; and, on this account, has been thought
worthy of an historical disquisition by Bacon.[42\1]

[Note 42\1: Parmenidis et Telesii et præcipue Democriti Philosophia,
&c., Works, vol. ix. 317.]

The technical term, _Atom_, marks sufficiently the nature of the
opinion. According to this theory, the world consists of a
collection of simple particles, of one kind of matter, and of
indivisible smallness (as the name indicates), and by the various
configurations and motions of these particles, all kinds of matter
and all material phenomena are produced.

To this, the Atomic Doctrine of Leucippus and Democritus, was
opposed the _Homoiomeria_ of Anaxagoras; that is, the opinion that
material things consist of particles which are homogeneous in each
kind of body, but various in different kinds: thus for example,
since by food the flesh and blood and bones of man increase, the
author of this doctrine held that there are in food particles of
flesh, and blood, {79} and bone. As the former tenet points to the
corpuscular theories of modern times, so the latter may be
considered as a dim glimpse of the idea of chemical analysis. The
Stoics also, who were, especially at a later period, inclined to
materialist views, had their technical modes of speaking on such
subjects. They asserted that matter contained in itself tendencies
or dispositions to certain forms, which dispositions they called
λόγοι **σπερματικοὶ, _seminal proportions_, or _seminal reasons_.

Whatever of sound view, or right direction, there might be in the
notions which suggested these and other technical expressions, was,
in all the schools of philosophy (so far as physics was concerned)
quenched and overlaid by the predominance of trifling and barren
speculations; and by the love of subtilizing and commenting upon the
works of earlier writers, instead of attempting to interpret the
book of nature. Hence these technical terms served to give fixity
and permanence to the traditional dogmas of the sect, but led to no
progress of knowledge.

The advances which were made in physical science proceeded, not from
these schools of philosophy (if we except, perhaps, the obligations
of the science of Harmonics to the Pythagoreans), but from reasoners
who followed an independent path. The sequel of the ambitious hopes,
the vast schemes, the confident undertakings of the philosophers of
ancient Greece, was an entire failure in the physical knowledge of
which it is our business to trace the history. Yet we are not, on
that account, to think slightingly of these early speculators. They
were men of extraordinary acuteness, invention, and range of
thought; and, above all, they had the merit of first completely
unfolding the speculative faculty--of starting in that keen and
vigorous chase of knowledge out of which all the subsequent culture
and improvement of man's intellectual stores have arisen. The sages
of early Greece form the heroic age of science. Like the first
navigators in their own mythology, they boldly ventured their
untried bark in a distant and arduous voyage, urged on by the hopes
of a supernatural success; and though they missed the imaginary
golden prize which they sought, they unlocked the gates of distant
regions, and opened the seas to the keels of the thousands of
adventurers who, in succeeding times, sailed to and fro, to the
indefinite increase of the mental treasures of mankind.

But inasmuch as their attempts, in one sense, and at first, failed,
we must proceed to offer some account of this failure, and of its
nature and causes. {80}




CHAPTER III.

FAILURE OF THE PHYSICAL PHILOSOPHY OF THE GREEK SCHOOLS.


_Sect._ 1.--_Result of the Greek School Philosophy_.

THE methods and forms of philosophizing which we have described as
employed by the Greek Schools, failed altogether in their
application to physics. No discovery of general laws, no explanation
of special phenomena, rewarded the acuteness and boldness of these
early students of nature. Astronomy, which made considerable
progress during the existence of the sects of Greek philosophers,
gained perhaps something by the authority with which Plato taught
the supremacy and universality of mathematical rule and order; and
the truths of Harmonics, which had probably given rise to the
Pythagorean passion for numbers, were cultivated with much care by
that school. But after these first impulses, the sciences owed
nothing to the philosophical sects; and the vast and complex
accumulations and apparatus of the Stagirite do not appear to have
led to any theoretical physical truths.

This assertion hardly requires proof, since in the existing body of
science there are no doctrines for which we are indebted to the
Aristotelian School. Real truths, when once established, remain to
the end of time a part of the mental treasure of man, and may be
discerned through all the additions of later days. But we can point
out no physical doctrine now received, of which we trace the
anticipation in Aristotle, in the way in which we see the Copernican
system anticipated by Aristarchus, the resolution of the heavenly
appearances into circular motions suggested by Plato, and the
numerical relations of musical intervals ascribed to Pythagoras. But
it may be worth while to look at this matter more closely.

Among the works of Aristotle are thirty-eight chapters of
"Problems," which may serve to exemplify the progress he had really
made in the reduction of phenomena to laws and causes. Of these
Problems, a large proportion are physiological, and these I here
pass by, as not illustrative of the state of physical knowledge. But
those which are properly physical are, for the most part, questions
concerning such {81} facts and difficulties as it is the peculiar
business of theory to explain. Now it may be truly said, that in
scarcely any one instance are the answers, which Aristotle gives to
his questions, of any value. For the most part, indeed, he propounds
his answer with a degree of hesitation or vacillation which of
itself shows the absence of all scientific distinctness of thought;
and the opinions so offered never appear to involve any settled or
general principle.

We may take, as examples of this, the problems of the simplest kind,
where the principles lay nearest at hand--the mechanical ones.
"Why," he asks,[43\1] "do small forces move great weights by means
of a lever, when they have thus to move the lever added to the
weight? Is it," he suggests, "because a greater radius moves
faster?" "Why does a small wedge split great weights?[44\1] Is it
because the wedge is composed of two opposite levers?" "Why,[45\1]
when a man rises from a chair, does he bend his leg and his body to
acute angles with his thigh? Is it because a right angle is
connected with equality and rest?" "Why[46\1] can a man throw a
stone further with a sling than with his hand? Is it that when he
throws with his hand he moves the stone from rest, but when he uses
the sling he throws it already in motion?" "Why,[47\1] if a circle
be thrown on the ground, does it first describe a straight line and
then a spiral, as it falls? Is it that the air first presses equally
on the two sides and supports it, and afterwards presses on one side
more?" "Why[48\1] is it difficult to distinguish a musical note from
the octave above? Is it that proportion stands in the place of
equality?" It must be allowed that these are very vague and
worthless surmises; for even if we were, as some commentators have
done, to interpret some of them so as to agree with sound
philosophy, we should still be unable to point out, in this author's
works, any clear or permanent apprehension of the general principles
which such an interpretation implies.

[Note 43\1: Mech. Prob. 4.]

[Note 44\1: Ib. 18.]

[Note 45\1: Ib. 31.]

[Note 46\1: Ib. 13.]

[Note 47\1: Περὶ Ἄψυχα. 11.]

[Note 48\1: Περὶ Ἁρμον. 14.]

Thus the Aristotelian physics cannot be considered as otherwise than
a complete failure. It collected no general laws from facts; and
consequently, when it tried to explain facts, it had no principles
which were of any avail.

The same may be said of the physical speculations of the other
schools of philosophy. They arrived at no doctrines from which they
could deduce, by sound reasoning, such facts as they saw; though
they {82} often venture so far to trust their principles as to infer
from them propositions beyond the domain of sense. Thus, the
principle that each element seeks _its own place_, led to the
doctrine that, the place of fire being the highest, there is, above
the air, a Sphere of Fire--of which doctrine the word _Empyrean_,
used by our poets, still conveys a reminiscence. The Pythagorean
tenet that ten is a perfect number,[49\1] led some persons to assume
that the heavenly bodies are in number ten; and as nine only were
known to them, they asserted that there was an _antichthon_, or
_counter-earth_, on the other side of the sun, invisible to us.
Their opinions respecting numerical ratios, led to various other
speculations concerning the distances and positions of the heavenly
bodies: and as they had, in other cases, found a connection between
proportions of distance and musical notes, they assumed, on this
suggestion, _the music of the spheres_.

[Note 49\1: Arist. Metaph. i. 5.]

Although we shall look in vain in the physical philosophy of the
Greek Schools for any results more valuable than those just
mentioned, we shall not be surprised to find, recollecting how much
an admiration for classical antiquity has possessed the minds of
men, that some writers estimate their claims much more highly than
they are stated here. Among such writers we may notice Dutens, who,
in 1766, published his "Origin of the Discoveries attributed to the
Moderns; in which it is shown that our most celebrated Philosophers
have received the greatest part of their knowledge from the Works of
the Ancients." The thesis of this work is attempted to be proved, as
we might expect, by very large interpretations of the general
phrases used by the ancients. Thus, when Timæus, in Plato's
dialogue, says of the Creator of the world,[50\1] "that he infused
into it two powers, the origins of motions, both of that of the same
thing and of that of different things;" Dutens[51\1] finds in this a
clear indication of the projectile and attractive forces of modern
science. And in some of the common declamation of the Pythagoreans
and Platonists concerning the general prevalence of numerical
relations in the universe, he discovers their acquaintance with the
law of the inverse square of the distance by which gravitation is
regulated, though he allows[52\1] that it required all the
penetration of Newton and his followers to detect this law in the
scanty fragments by which it is transmitted.

[Note 50\1: Tim. 96.]

[Note 51\1: 3d ed. p. 83.]

[Note 52\1: Ib. p. 88.]

Argument of this kind is palpably insufficient to cover the failure
of the Greek attempts at a general physical philosophy; or rather we
{83} may say, that such arguments, since they are as good as can be
brought in favor of such an opinion, show more clearly how entire
the failure was. I proceed now to endeavor to point out its causes.


_Sect._ 2.--_Cause of the Failure of the Greek Physical Philosophy._

THE cause of the failure of so many of the attempts of the Greeks to
construct physical science is so important, that we must endeavor to
bring it into view here; though the full development of such
subjects belongs rather to the Philosophy of Induction. The subject
must, at present, be treated very briefly.

I will first notice some errors which may naturally occur to the
reader's mind, as possible causes of failure, but which, we shall be
able to show, were not the real reasons in this case.

The cause of failure was _not the neglect of facts_. It is often
said that the Greeks disregarded experience, and spun their
philosophy out of their own thoughts alone; and this is supposed by
many to be their essential error. It is, no doubt, true, that the
disregard of experience is a phrase which may be so interpreted as
to express almost any defect of philosophical method; since
coincidence with experience is requisite to the truth of all theory.
But if we fix a more precise sense on our terms, I conceive it may
be shown that the Greek philosophy did, in its opinions, recognize
the necessity and paramount value of observations; did, in its
origin, proceed upon observed facts; and did employ itself to no
small extent in classifying and arranging phenomena. We must
endeavor to illustrate these assertions, because it is important to
show that these steps alone do not necessarily lead to science.

1. The acknowledgment of experience as the main ground of physical
knowledge is so generally understood to be a distinguishing feature
of later times, that it may excite surprise to find that Aristotle,
and other ancient philosophers, not only asserted in the most
pointed manner that all our knowledge must begin from experience,
but also stated in language much resembling the habitual phraseology
of the most modern schools of philosophizing, that particular facts
must be _collected_; that from these, general principles must be
obtained by _induction_; and that these principles, when of the most
general kind, are _axioms_. A few passages will show this.

"The way[53\1] must be the same," says Aristotle, in speaking of the
rules of reasoning, "with respect to philosophy, as it is with
respect to {84} any art or science whatever; we must collect the
facts, and the things to which the facts happen, in each subject,
and provide as large a supply of these as possible." He then
proceeds to say that "we are not to look at once at all this
collected mass, but to consider small and definite portions" . . .
"And thus it is the office of observation to supply principles in
each subject; for instance, astronomical observation supplies the
principles of astronomical science. For the phenomena being properly
assumed, the astronomical demonstrations were from these discovered.
And the same applies to every art and science. So that if we take
the facts (τὰ ὑπάρχοντα) belonging to each subject, it is _our_ task
to mark out clearly the course of the demonstrations. For if _in our
natural history_ (κατὰ τὴν ἱστορίαν) we have omitted nothing of the
facts and properties which belong to the subject, we shall learn
what we can demonstrate and what we cannot."

[Note 53\1: Anal. Prior. i. 30.]

These facts, τὰ ὑπάρχοντα, he, at other times, includes in the term
_sensation_. Thus, he says,[54\1] "It is obvious that if any
sensation is wanting, there must be also some knowledge wanting
which we are thus prevented from having, since we arrive at
knowledge either by induction or by demonstration. Demonstration
proceeds from universal propositions, Induction from particulars.
But we cannot have universal theoretical propositions except from
induction; and we cannot make inductions without having sensation;
for sensation has to do with particulars."

[Note 54\1: Anal. Post. i. 18.]

In another place,[55\1] after stating that principles must be prior
to, and better known than conclusions, he distinguishes such
principles into absolutely prior, and prior relative to us: "The
prior principles, relative to us, are those which are nearer to the
sensation; but the principles absolutely prior are those which are
more remote from the sensation. The most general principles are the
more remote, the more particular are nearer. The general principles
which are necessary to knowledge are _axioms_."

[Note 55\1: Ib. i. 2.]

We may add to these passages, that in which he gives an account of
the way in which Leucippus was led to the doctrine of atoms. After
describing the opinions of some earlier philosophers, he says,[56\1]
"Thus, proceeding in violation of sensation, and disregarding it,
because, as they held, they must follow reason, some came to the
conclusion that the universe was one, and infinite, and at rest. As
it appeared, however, that though this ought to be by reasoning, it
{85} would go near to madness to hold such opinions in practice (for
no one was ever so mad as to think fire and ice to be one),
Leucippus, therefore, pursued a line of reasoning which was in
accordance with sensation, and which was not irreconcilable with the
production and decay, the motion and multitude of things." It is
obvious that the school to which Leucippus belonged (the Eclectic)
must have been, at least in its origin, strongly impressed with the
necessity of bringing its theories into harmony with the observed
course of nature.

[Note 56\1: De Gen. et Cor. i. 8.]

2. Nor was this recognition of the fundamental value of experience a
mere profession. The Greek philosophy did, in its beginning, proceed
upon observation. Indeed it is obvious that the principles which it
adopted were, in the first place, assumed in order to account for
some classes of facts, however imperfectly they might answer their
purpose. The principle of things seeking their own places, was
invented in order to account for the falling and floating of bodies.
Again, Aristotle says, that heat is that which brings together
things of the same kind, cold is that which brings together things
whether of the same or of different kinds: it is plain that in this
instance he intended by his principle to explain some obvious facts,
as the freezing of moist substances, and the separation of
heterogeneous things by fusion; for, as he adds, if fire brings
together things which are akin, it will separate those which are not
akin. It would be easy to illustrate the remark further, but its
truth is evident from the nature of the case; for no principles
could be accepted for a moment, which were the result of an
arbitrary caprice of the mind, and which were not in some measure
plausible, and apparently confirmed by facts.

But the works of Aristotle show, in another way, how unjust it would
be to accuse him of disregarding facts. Many large treatises of his
consist almost entirely of collections of facts, as for instance,
those "On Colors," "On Sounds," and the collection of Problems to
which we have already referred; to say nothing of the numerous
collection of facts bearing on natural history and physiology, which
form a great portion of his works, and are even now treasuries of
information. A moment's reflection will convince us that the
physical sciences of our own times, for example. Mechanics and
Hydrostatics, are founded almost entirely upon facts with which the
ancients were as familiar as we are. The defect of their philosophy,
therefore, wherever it may lie, consists neither in the speculative
depreciation of the value of facts, nor in the practical neglect of
their use.

3. Nor again, should we hit upon the truth, if we were to say that
{86} Aristotle, and other ancient philosophers, did indeed collect
facts; but that they took no steps in classifying and comparing
them; and that thus they failed to obtain from them any general
knowledge. For, in reality, the treatises of Aristotle which we have
mentioned, are as remarkable for the power of classifying and
systematizing which they exhibit, as for the industry shown in the
accumulation. But it is not classification of facts merely which can
lead us to knowledge, except we adopt that special arrangement,
which, in each case, brings into view the principles of the subject.
We may easily show how unprofitable an arbitrary or random
classification is, however orderly and systematic it may be.

For instance, for a long period all unusual fiery appearances in the
sky were classed together as _meteors_. Comets, shooting-stars, and
globes of fire, and the aurora borealis in all its forms, were thus
grouped together, and classifications of considerable extent and
minuteness were proposed with reference to these objects. But this
classification was of a mixed and arbitrary kind. Figure, color,
motion, duration, were all combined as characters, and the
imagination lent its aid, transforming these striking appearances
into fiery swords and spears, bears and dragons, armies and
chariots. The facts so classified were, notwithstanding, worthless;
and would not have been one jot the less so, had they and their
classes been ten times as numerous as they were. No rule or law that
would stand the test of observation was or could be thus discovered.
Such classifications have, therefore, long been neglected and
forgotten. Even the ancient descriptions of these objects of
curiosity are unintelligible, or unworthy of trust, because the
spectators had no steady conception of the usual order of such
phenomena. For, however much we may fear to be misled by
preconceived opinions, the caprices of imagination distort our
impressions far more than the anticipations of reason. In this case
men had, indeed we may say with regard to many of these meteors,
they still have, no science: not for want of facts, nor even for
want of classification of facts; but because the classification was
one in which no real principle was contained.

4. Since, as we have said before, two things are requisite to
science,--Facts and Ideas; and since, as we have seen. Facts were
not wanting in the physical speculations of the ancients, we are
naturally led to ask, Were they then deficient in Ideas? Was there a
want among them of mental activity, and logical connection of
thought? But it is so obvious that the answer to this inquiry must
be in the negative, that we need not dwell upon it. No one who knows
any thing of the {87} history of the ancient Greek mind, can
question, that in acuteness, in ingenuity, in the power of close and
distinct reasoning, they have never been surpassed. The common
opinion, which considers the defect of their philosophical character
to reside rather in the exclusive activity of such qualities, than
in the absence of them, is at least so far just.

5. We come back again, therefore, to the question, What was the
radical and fatal defect in the physical speculations of the Greek
philosophical schools?

To this I answer: The defect was, that though they had in their
possession Facts and Ideas, _the Ideas were not distinct and
appropriate to the Facts_.

The peculiar characteristics of scientific ideas, which I have
endeavored to express by speaking of them as _distinct_ and
_appropriate to the facts_, must be more fully and formally set
forth, when we come to the philosophy of the subject. In the mean
time, the reader will probably have no difficulty in conceiving
that, for each class of Facts, there is some special set of Ideas,
by means of which the facts can be included in general scientific
truths; and that these Ideas, which may thus be termed
_appropriate_, must be possessed with entire distinctness and
clearness, in order that they may be successfully applied. It was
the want of Ideas having this reference to material phenomena, which
rendered the ancient philosophers, with very few exceptions,
helpless and unsuccessful speculators on physical subjects.

This must be illustrated by one or two examples. One of the facts
which Aristotle endeavors to explain is this; that when the sun's
light passes through a hole, whatever be the form of the hole, the
bright image, if formed at any considerable distance from the hole,
is round, instead of imitating the figure of the hole, as shadows
resemble their objects in form. We shall easily perceive this
appearance to be a necessary consequence of the circular figure of
the sun, if we conceive light to be diffused from the luminary by
means of straight rays proceeding from every point of the sun's disk
and passing through every point within the boundary of the hole. By
attending to the consequences of this mode of conception, it will be
seen that each point of the hole will be the vertex of a double cone
of rays which has the sun's disk for its base on one side and an
image of the sun on the other; and the figure of the image of the
hole will be determined by supposing a series of equal bright
circles, images of the sun, to be placed along the boundary of an
image equal to the hole itself. The figure of the image thus
determined will partake of the form of the hole, and {88} of the
circular form of the sun's image: but these circular images become
larger and larger as they are further from the hole, while the
central image of the hole remains always of the original size; and
thus at a considerable distance from the hole, the trace of the
hole's form is nearly obliterated, and the image is nearly a perfect
circle. Instead of this distinct conception of a cone of rays which
has the sun's disk for its basis, Aristotle has the following loose
conjecture.[57\1] "Is it because light is emitted in a conical form;
and of a cone, the base is a circle; so that on whatever the rays of
the sun fall, they appear more circular?" And thus though he applies
the notion of rays to this problem, he possesses this notion so
_indistinctly_ that his explanation is of no value. He does not
introduce into his explanation the consideration of the sun's
circular figure, and is thus prevented from giving a true account of
this very simple optical phenomenon.

[Note 57\1: Problem. 15, ὁσα μαθηματίκης, &c.]

6. Again, to pass to a more extensive failure: why was it that
Aristotle, knowing the property of the lever, and many other
mechanical truths, was unable to form them into a science of
mechanics, as Archimedes afterwards did?

The reason was, that, instead of considering rest and motion
directly, and distinctly, with reference to the Idea of Cause, that
is Force, he wandered in search of reasons among other ideas and
notions, which could not be brought into steady connection with the
facts;--the ideas of properties of circles, of proportions of
velocities,--the notions of "strange" and "common," of "natural" and
"unnatural." Thus, in the Proem to his Mechanical Problems, after
stating some of the difficulties which he has to attack, he says,
"Of all such cases, the circle contains the principle of the cause.
And this is what might be looked for; for it is nothing absurd, if
something _wonderful_ is derived from something more wonderful
still. Now the most wonderful thing is, that opposites should be
combined; and the circle is constituted of such combinations of
opposites. For it is constructed by a stationary point and a moving
line, which are contrary to each other in nature; and hence we may
the less be surprised at the resulting contrarieties. And in the
first place, the circumference of the circle, though a line without
breadth, has opposite qualities; for it is both _convex_ and
_concave_. In the next place, it has, at the same time, opposite
motions, for it moves forward and backward at the same time. For the
circumference, setting out from any point, comes to the same point
again, so {89} that by a continuous progression, the last point
becomes the first. So that, as was before stated, it is not
surprising that the circle should be the principle of all wonderful
properties."

Aristotle afterwards proceeds to explain more specially how he
applies the properties of the circle in this case. "The reason," he
says, in his fourth Problem, "why a force, acting at a greater
distance from the fulcrum, moves a weight more easily, is, that it
describes a greater circle." He had already asserted that when a
body at the end of a lever is put in motion, it may be considered as
having two motions; one in the direction of the tangent, and one in
the direction of the radius; the former motion is, he says,
_according to nature_, the latter, _contrary to nature_. Now in the
smaller circle, the motion, contrary to nature, is more considerable
than it is in the larger circle. "Therefore," he adds, "the mover or
weight at the larger arm will be transferred further by the same
force than the weight moved, which is at the extremity of the
shorter arm."

These loose and inappropriate notions of "natural" and "unnatural"
motions, were unfit to lead to any scientific truths; and, with the
habits of thought which dictated these speculations a perception of
the true grounds of mechanical properties was impossible.

7. Thus, in this instance, the error of Aristotle was the neglect of
the Idea _appropriate_ to the facts, namely, the Idea of Mechanical
Cause, which is Force; and the substitution of vague or inapplicable
notions involving only relations of space or emotions of wonder. The
errors of those who failed similarly in other instances, were of the
same kind. To detail or classify these would lead us too far into
the philosophy of science; since we should have to enumerate the
Ideas which are appropriate, and the various classes of Facts on
which the different sciences are founded,--a task not to be now
lightly undertaken. But it will be perceived, without further
explanation, that it is necessary, in order to obtain from facts any
general truth, that we should apply to them that appropriate Idea,
by which permanent and definite relations are established among them.

In such Ideas the ancients were very poor, and the stunted and
deformed growth of their physical science was the result of this
penury. The Ideas of Space and Time, Number and Motion, they did
indeed possess distinctly; and so far as these went, their science
was tolerably healthy. They also caught a glimpse of the Idea of a
Medium by which the qualities of bodies, as colors and sounds, are
perceived. But the idea of Substance remained barren in their hands;
{90} in speculating about elements and qualities, they went the
wrong way, assuming that the properties of Compounds must _resemble_
those of the Elements which determine them; and their loose notions
of Contrariety never approached the form of those ideas of Polarity,
which, in modern times, regulate many parts of physics and
chemistry.

If this statement should seem to any one to be technical or
arbitrary, we must refer, for the justification of it, to the
Philosophy of Science, of which we hope hereafter to treat. But it
will appear, even from what has been here said, that there are
certain Ideas or Forms of mental apprehension, which may be applied
to Facts in such a manner as to bring into view fundamental
principles of science; while the same Facts, however arrayed or
reasoned about, so long as these appropriate ideas are not employed,
cannot give rise to any exact or substantial knowledge.

[2d Ed.] This account of the cause of failure in the physical
speculations of the ancient Greek philosophers has been objected to
as unsatisfactory. I will offer a few words in explanation of it.

The mode of accounting for the failure of the Greeks in physics is,
in substance;--that the Greeks in their physical speculations fixed
their attention upon the wrong aspects and relations of the
phenomena; and that the aspects and relations in which phenomena are
to be viewed in order to arrive at scientific truths may be arranged
under certain heads, which I have termed _Ideas_; such as Space,
Time, Number, Cause, Likeness. In every case, there is an Idea to
which the phenomena may be referred, so as to bring into view the
Laws by which they are governed; this Idea I term the _appropriate_
Idea in such case; and in order that the reference of the phenomena
to the Law may be clearly seen, the Idea must be _distinctly_
possessed.

Thus the reason of Aristotle's failure in his attempts at Mechanical
Science is, that he did not refer the facts to the appropriate Idea,
namely Force, the Cause of Motion, but to relations of Space and the
like; that is, he introduces _Geometrical_ instead of _Mechanical_
Ideas. It may be said that we learn little by being told that
Aristotle's failure in this and the like cases arose from his
referring to the wrong class of Ideas; or, as I have otherwise
expressed it, fixing his attention upon the wrong aspects and
relations of the facts; since, it may be said, this is only to state
in other words that he _did_ fail. But this criticism is, I think,
ill-founded. The account which I have given is not only a statement
that Aristotle, and others who took a like course, did fail; but
also, that they failed in one certain point out of several {91}
which are enumerated. They did not fail because they neglected to
observe facts; they did not fail because they omitted to class
facts; they did not fail because they had not ideas to reason from;
but they failed because they did not take the right ideas in each
case. And so long as they were in the wrong in this point, no
industry in collecting facts, or ingenuity in classing them and
reasoning about them, could lead them to solid truth.

Nor is this account of the nature of their mistake without its
instruction for us; although we are not to expect to derive from the
study of their failure any technical rule which shall necessarily
guide us to scientific discovery. For their failure teaches us that,
in the formation of science, an Error in the Ideas is as fatal to
the discovery of Truth as an Error in the Facts; and may as
completely impede the progress of knowledge. I have in Books II. to
X. of the _Philosophy_, shown historically how large a portion of
the progress of Science consists in the establishment of Appropriate
Ideas as the basis of each science. Of the two main processes by
which science is constructed, as stated in Book XI. of that work,
namely the _Explication of Conceptions_ and the _Colligation of
Facts_, the former must precede the latter. In Book XII. chap. 5, of
the _Philosophy_, I have stated the maxim concerning appropriate
Ideas in this form, that _the Idea and the Facts must be
homogeneous_.

When I say that the failure of the Greeks in physical science arose
from their not employing _appropriate_ Ideas to connect the facts, I
do not use the term "appropriate" in a loose popular sense; but I
employ it as a somewhat technical term, to denote _the_ appropriate
Idea, out of that series of Ideas which have been made (as I have
shown in the _Philosophy_) the foundation of sciences; namely,
Space, Time, Number, Cause, Likeness, Substance, and the rest. It
appears to me just to say that Aristotle's failure in his attempts
to deal with problems of equilibrium, arose from his referring to
circles, velocities, notions of natural and unnatural, and the
like,--conceptions depending upon Ideas of Space, of Nature,
&c.--which are not appropriate to these problems, and from his
missing the Idea of Mechanical Force or Pressure, which is the
appropriate Idea.

I give this, not as an account of _all_ failures in attempts at
science, but only as the account of such radical and fundamental
failures as this of Aristotle; who, with a knowledge of the facts,
failed to connect them into a really scientific view. If I had to
compare rival theories of a more complex kind, I should not
necessarily say that one involved {92} an appropriate Idea and the
other did not, though I might judge one to be true and the other to
be false. For instance, in comparing the emissive and the undulatory
theory of light, we see that both involve the same Idea;--the Idea
of a Medium acting by certain mechanical properties. The question
there is, What is the true view of the mechanism of the Medium?

It may be remarked, however, that the example of Aristotle's failure
in physics, given in p. 87, namely, his attempted explanation of the
round image of a square hole, is a specimen rather of _indistinct_
than of inappropriate ideas.

The geometrical explanation of this phenomenon, which I have there
inserted, was given by Maurolycus, and before him, by Leonardo da
Vinci.

We shall, in the next Book, see the influence of the appropriate
general Ideas, in the formation of various sciences. It need only be
observed, before we proceed, that, in order to do full justice to
the physical knowledge of the Greek Schools of philosophy, it is not
necessary to study their course after the time of their founders.
Their fortunes, in respect of such acquisitions as we are now
considering, were not progressive. The later chiefs of the Schools
followed the earlier masters; and though they varied much, they
added little. The Romans adopted the philosophy of their Greek
subjects; but they were always, and, indeed, acknowledged themselves
to be, inferior to their teachers. They were as arbitrary and loose
in their ideas as the Greeks, without possessing their invention,
acuteness, and spirit of system.

In addition to the vagueness which was combined with the more
elevated trains of philosophical speculation among the Greeks, the
Romans introduced into their treatises a kind of declamatory
rhetoric, which arose probably from their forensic and political
habits, and which still further obscured the waning gleams of truth.
Yet we may also trace in the Roman philosophers to whom this charge
mostly applies (Lucretius, Pliny, Seneca), the national vigor and
ambition. There is something Roman in the public spirit and
anticipation of universal empire which they display, as citizens of
the intellectual republic. Though they speak sadly or slightingly of
the achievements of their own generation, they betray a more abiding
and vivid belief in the dignity and destined advance of human
knowledge as a whole, than is obvious among the Greeks.

We must, however, turn back, in order to describe steps of more
definite value to the progress of science than those which we have
hitherto noticed.



{{93}}
BOOK II.

HISTORY
OF THE
PHYSICAL SCIENCES
IN
ANCIENT GREECE.




  Ναρθηκοπλήρωτον δὲ θηρῶμαι πυρὸς
  Πηγὴν κλοπαίαν, ἣ διδάσκαλος τέχνης
  Πάσης βροτοῖς πεφῆνε καὶ μέγας πόρος.
          Prom. Vinct. 109.

  I brought to earth the spark of heavenly fire,
  Concealed at first, and small, but spreading soon
  Among the sons of men, and burning on,
  Teacher of art and use, and fount of power.



{{95}}
INTRODUCTION.


IN order to the acquisition of any such exact and real knowledge of
nature as that which we properly call Physical Science, it is
requisite, as has already been said, that men should possess Ideas
both distinct and appropriate, and should apply them to ascertained
Facts. They are thus led to propositions of a general character,
which are obtained by Induction, as will elsewhere be more fully
explained. We proceed now to trace the formation of Sciences among
the Greeks by such processes. The provinces of knowledge which thus
demand our attention are, Astronomy, Mechanics and Hydrostatics,
Optics and Harmonics; of which I must relate, first, the earliest
stages, and next, the subsequent progress.

Of these portions of human knowledge, Astronomy is, beyond doubt or
comparison, much the most ancient and the most remarkable; and
probably existed, in somewhat of a scientific form, in Chaldea and
Egypt, and other countries, before the period of the intellectual
activity of the Greeks. But I will give a brief account of some of
the other Sciences before I proceed to Astronomy, for two reasons;
first, because the origin of Astronomy is lost in the obscurity of a
remote antiquity; and therefore we cannot exemplify the conditions
of the first rise of science so well in that subject as we can in
others which assumed their scientific form at known periods; and
next, in order that I may not have to interrupt, after I have once
begun it, the history of the only progressive Science which the
ancient world produced.

It has been objected to the arrangement here employed that it is not
symmetrical; and that Astronomy, as being one of the Physical
Sciences, ought to have occupied a chapter in this Second Book,
instead of having a whole Book to itself (Book III). I do not pretend
that the arrangement is symmetrical, and have employed it only on the
ground of convenience. The importance and extent of the history of
Astronomy are such that this science could not, with a view to our
purposes, be made co-ordinate with Mechanics or Optics. {96}




CHAPTER I.

EARLIEST STAGES OF MECHANICS AND HYDROSTATICS.


_Sect._ 1.--_Mechanics._

ASTRONOMY is a science so ancient that we can hardly ascend to a
period when it did not exist; Mechanics, on the other hand, is a
science which did not begin to be till after the time of Aristotle;
for Archimedes must be looked upon as the author of the first sound
knowledge on this subject. What is still more curious, and shows
remarkably how little the continued progress of science follows
inevitably from the nature of man, this department of knowledge,
after the right road had been fairly entered upon, remained
absolutely stationary for nearly two thousand years; no single step
was made, in addition to the propositions established by Archimedes,
till the time of Galileo and Stevinus. This extraordinary halt will
be a subject of attention hereafter; at present we must consider the
original advance.

The great step made by Archimedes in Mechanics was the establishing,
upon true grounds, the general proposition concerning a straight
lever, loaded with two heavy bodies, and resting upon a fulcrum. The
proposition is, that two bodies so circumstanced will balance each
other, when the distance of the smaller body from the fulcrum is
greater than the distance of the other, in exactly the same
proportion in which the weight of the body is less.

This proposition is proved by Archimedes in a work which is still
extant, and the proof holds its place in our treatises to this day,
as the simplest which can be given. The demonstration is made to
rest on assumptions which amount in effect to such Definitions and
Axioms as these: That those bodies are of equal weight which balance
each other at equal arms of a straight lever; and that in every
heavy body there is a definite point called a _Centre of Gravity_,
in which point we may suppose the weight of the body collected.

The principle, which is really the foundation of the validity of the
demonstration thus given, and which is the condition of all
experimental knowledge on the subject, is this: that when two equal
weights are supported on a lever, they act on the fulcrum of the lever
with the {97} same effect as if they were both together supported
immediately at that point. Or more generally, we may state the
principle to be this: that the pressure by which a heavy body is
supported continues the same, however we alter the form or position of
the body, so long as the magnitude and material continue the same.

The experimental truth of this principle is a matter of obvious and
universal experience. The weight of a basket of stones is not
altered by shaking the stones into new positions. We cannot make the
direct burden of a stone less by altering its position in our hands;
and if we try the effect on a balance or a machine of any kind, we
shall see still more clearly and exactly that the altered position
of one weight, or the altered arrangement of several, produces no
change in their effect, so long as their point of support remains
unchanged.

This general fact is obvious, when we possess in our minds the ideas
which are requisite to apprehend it clearly. But when we are so
prepared, the truth appears to be manifest, even independent of
experience, and is seen to be a rule to which experience must
conform. What, then, is the leading idea which thus enables us to
reason effectively upon mechanical subjects? By attention to the
course of such reasonings, we perceive that it is the idea of
_Pressure_; Pressure being conceived as a measurable effect of heavy
bodies at rest, distinguishable from all other effects, such as
motion, change of figure, and the like. It is not here necessary to
attempt to trace the history of this idea in our minds; but it is
certain that such an idea may be distinctly formed, and that upon it
the whole science of statics may be built. _Pressure_, _load_,
_weight_, are names by which this idea is denoted when the effect
tends directly downwards; but we may have pressure without motion,
or _dead pull_, in other cases, as at the critical instant when two
nicely-matched wrestlers are balanced by the exertion of the utmost
strength of each.

Pressure in any direction may thus exist without any motion
whatever. But the causes which produce such pressure are capable of
producing motion, and are generally seen producing motion, as in the
above instance of the wrestlers, or in a pair of scales employed in
weighing; and thus men come to consider pressure as the exception,
and motion as the rule: or perhaps they image to themselves the
motion which _might_ or _would_ take place; for instance, the motion
which the arms of a lever _would_ have if they _did_ move. They turn
away from the case really before them, which is that of bodies at
rest, and balancing each other, and pass to another case, which is
arbitrarily {98} assumed to represent the first. Now this arbitrary
and capricious evasion of the question we consider as opposed to the
introduction of the distinct and proper idea of Pressure, by means
of which the true principles of this subject can be apprehended.

We have already seen that Aristotle was in the number of those who
thus evaded the difficulties of the problem of the lever, and
consequently lost the reward of success. He failed, as has before
been stated, in consequence of his seeking his principles in
notions, either vague and loose, as the distinction of natural and
unnatural motions, or else inappropriate, as the circle which the
weight _would_ describe, the velocity which it _would_ have if it
moved; circumstances which are not part of the fact under
consideration. The influence of such modes of speculation was the
main hindrance to the prosecution of the true Archimedean form of
the science of Mechanics.

The mechanical doctrine of Equilibrium, is _Statics_. It is to be
distinguished from the mechanical doctrine of Motion, which is
termed _Dynamics_, and which was not successfully treated till the
time of Galileo.


_Sect._ 2.--_Hydrostatics._

ARCHIMEDES not only laid the foundations of the Statics of solid
bodies, but also solved the principal problem of _Hydrostatics_, or
the Statics of Fluids; namely, the conditions of the floating of
bodies. This is the more remarkable, since not only did the
principles which Archimedes established on this subject remain
unpursued till the revival of science in modern times, but, when
they were again put forward, the main proposition was so far from
obvious that it was termed, and is to this day called, the
_hydrostatic paradox_. The true doctrine of Hydrostatics, however,
assuming the Idea of Pressure, which it involves, in common with the
Mechanics of solid bodies, requires also a distinct Idea of a Fluid,
as a body of which the parts are perfectly movable among each other
by the slightest partial pressure, and in which all pressure exerted
on one part is transferred to all other parts. From this idea of
Fluidity, necessarily follows that multiplication of pressure which
constitutes the hydrostatic paradox; and the notion being seen to be
verified in nature, the consequences were also realized as facts.
This notion of Fluidity is expressed in the postulate which stands
at the head of Archimedes' "Treatise on Floating Bodies." And from
this principle are deduced the solutions, not only of the simple
problems of the science, but of some problems of considerable
complexity. {99}

The difficulty of holding fast this Idea of Fluidity so as to trace
its consequences with infallible strictness of demonstration, may be
judged of from the circumstance that, even at the present day, men
of great talents, not unfamiliar with the subject, sometimes admit
into their reasonings an oversight or fallacy with regard to this
very point. The importance of the Idea when clearly apprehended and
securely held, may be judged of from this, that the whole science of
Hydrostatics in its most modern form is only the development of the
Idea. And what kind of attempts at science would be made by persons
destitute of this Idea, we may see in the speculations of Aristotle
concerning light and heavy bodies, which we have already quoted;
where, by considering light and heavy as opposite qualities,
residing in things themselves, and by an inability to apprehend the
effect of surrounding fluids in supporting bodies, the subject was
made a mass of false or frivolous assertions, which the utmost
ingenuity could not reconcile with facts, and could still less
deduce from the asserted doctrines any new practical truths.

In the case of Statics and Hydrostatics, the most important
condition of their advance was undoubtedly the distinct apprehension
of these two _appropriate Ideas_--_Statical Pressure_, and
_Hydrostatical Pressure_ as included in the idea of Fluidity. For
the Ideas being once clearly possessed, the experimental laws which
they served to express (that the whole pressure of a body downwards
was always the same; and that water, and the like, were fluids
according to the above idea of fluidity), were so obvious, that
there was no doubt nor difficulty about them. These two ideas lie at
the root of all mechanical science; and the firm possession of them
is, to this day, the first requisite for a student of the subject.
After being clearly awakened in the mind of Archimedes, these ideas
slept for many centuries, till they were again called up in Galileo,
and more remarkably in Stevinus. This time, they were not destined
again to slumber; and the results of their activity have been the
formation of two Sciences, which are as certain and severe in their
demonstrations as geometry itself and as copious and interesting in
their conclusions; but which, besides this recommendation, possess
one of a different order,--that they exhibit the exact impress of
the laws of the physical world, and unfold a portion of the rules
according to which the phenomena of nature take place, and must take
place, till nature herself shall alter. {100}




CHAPTER II.

EARLIEST STAGES OF OPTICS.


THE progress made by the ancients in Optics was nearly proportional
to that which they made in Statics. As they discovered the true
grounds of the doctrine of Equilibrium, without obtaining any sound
principles concerning Motion, so they discovered the law of the
Reflection of light, but had none but the most indistinct notions
concerning Refraction.

The extent of the principles which they really possessed is easily
stated. They knew that vision is performed by _rays_ which proceed
in straight lines, and that these rays are _reflected_ by certain
surfaces (mirrors) in such manner that the angles which they make
with the surface on each side are equal. They drew various
conclusions from these premises by the aid of geometry; as, for
instance, the convergence of rays which fall on a concave speculum.

It may be observed that the _Idea_ which is here introduced, is that
of visual _rays_, or lines along which vision is produced and light
carried. This idea once clearly apprehended, it was not difficult to
show that these lines are straight lines, both in the case of light
and of sight. In the beginning of Euclid's "Treatise on Optics," some
of the arguments are mentioned by which this was established. We are
told in the Proem, "In explaining what concerns the sight, he adduced
certain arguments from which he inferred that all light is carried in
straight lines. The greatest proof of this is shadows, and the bright
spots which are produced by light coming through windows and cracks,
and which could not be, except the rays of the sun were carried in
straight lines. So in fires, the shadows are greater than the bodies
if the fire be small, but less than the bodies if the fire be
greater." A clear comprehension of the principle would lead to the
perception of innumerable proofs of its truth on every side.

The Law of Equality of Angles of Incidence and Reflection was not
quite so easy to verify; but the exact resemblance of the object and
its image in a plane mirror, (as the surface of still water, for
instance), which is a consequence of this law, would afford
convincing evidence of its truth in that case, and would be
confirmed by the examination of other cases. {101}

With these true principles was mixed much error and indistinctness,
even in the best writers. Euclid, and the Platonists, maintained
that vision is exercised by rays proceeding _from_ the eye, not _to_
it; so that when we see objects, we learn their form as a blind man
would do, by feeling it out with his staff. This mistake, however,
though Montucla speaks severely of it, was neither very
discreditable nor very injurious; for the mathematical conclusions
on each supposition are necessarily the same. Another curious and
false assumption is, that those visual rays are not close together,
but separated by intervals, like the fingers when the hand is
spread. The motive for this invention was the wish to account for
the fact, that in looking for a small object, as a needle, we often
cannot see it when it is under our nose; which it was conceived
would be impossible if the visual rays reached to all points of the
surface before us.

These errors would not have prevented the progress of the science.
But the Aristotelian physics, as usual, contained speculations more
essentially faulty. Aristotle's views led him to try to describe the
kind of causation by which vision is produced, instead of the laws
by which it is exercised; and the attempt consisted, as in other
subjects, of indistinct principles, and ill-combined facts.
According to him, vision must be produced by a Medium,--by something
_between_ the object and the eye,--for if we press the object on the
eye, we do not see it; this Medium is Light, or "the transparent in
action;" darkness occurs when the transparency is potential, not
actual; color is not the "absolute visible," but something which is
_on_ the absolute visible; color has the power of setting the
transparent in action; it is not, however, all colors that are seen
by means of light, but only the proper color of each object; for
some things, as the heads, and scales, and eyes of fish, are seen in
the dark; but they are not seen with their proper color.**[1\2]

[Note 1\2: De Anim. ii. **7.]

In all this there is no steady adherence either to one notion, or to
one class of facts. The distinction of Power and Act is introduced
to modify the Idea of Transparency, according to the formula of the
school; then Color is made to be something unknown in addition to
Visibility; and the distinction of "proper" and "improper" colors is
assumed, as sufficient to account for a phenomenon. Such
classifications have in them nothing of which the mind can take
steady hold; nor is it difficult to see that they do not come under
those {102} conditions of successful physical speculation, which we
have laid down.

It is proper to notice more distinctly the nature of the Geometrical
Propositions contained in Euclid's work. The _Optica_ contains
Propositions concerning Vision and Shadows, derived from the
principle that the rays of light are rectilinear: for instance, the
Proposition that the shadow is greater than the object, if the
illuminating body be less and _vice versa_. The _Catoptrica_
contains Propositions concerning the effects of Reflection, derived
from the principle that the Angles of Incidence and Reflection are
equal: as, that in a convex mirror the object appears convex, and
smaller than the object. We see here an example of the promptitude
of the Greeks in deduction. When they had once obtained a knowledge
of a principle, they followed it to its mathematical consequences
with great acuteness. The subject of concave mirrors is pursued
further in Ptolemy's _Optics_.

The Greek writers also cultivated the subject of _Perspective_
speculatively, in mathematical treatises, as well as practically, in
pictures. The whole of this theory is a consequence of the principle
that vision takes place in straight lines drawn from the object to
the eye.

"The ancients were in some measure acquainted with the Refraction as
well as the Reflection of Light," as I have shown in Book IX. Chap.
2 [2d Ed.] of the _Philosophy_. The current knowledge on this
subject must have been very slight and confused; for it does not
appear to have enabled them to account for one of the simplest
results of Refraction, the magnifying effect of convex transparent
bodies. I have noticed in the passage just referred to, Seneca's
crude notions on this subject; and in like manner Ptolemy in his
_Optics_ asserts that an object placed in water must always appear
larger then when taken out. Aristotle uses the term ἀνακλάσις
(_Meteorol_. iii. 2), but apparently in a very vague manner. It is
not evident that he distinguished Refraction from Reflection. His
Commentators however do distinguish these as διακλάσις and
ἀνακλάσις. See Olympiodorus in Schneider's _Eclogæ Physicæ_, vol. i.
p. 397. And Refraction had been the subject of special attention
among the Greek Mathematicians. Archimedes had noticed (as we learn
from the same writer) that in certain cases, a ring which cannot be
seen over the edge of the empty vessel in which it is placed,
becomes visible when the vessel is filled with water. The same fact
is stated in the _Optics_ of Euclid. We do not find this fact
explained in that work as we now have it; but in Ptolemy's _Optics_
the fact is explained by a flexure of the visual ray: it is {103}
noticed that this flexure is different at different angles from the
perpendicular, and there is an elaborate collection of measures of
the flexure at different angles, made by means of an instrument
devised for the purpose. There is also a collection of similar
measures of the refraction when the ray passes from air to glass,
and when it passes from glass to water. This part of Ptolemy's work
is, I think, the oldest extant example of a collection of
experimental measures in any other subject than astronomy; and in
astronomy our measures are the result of _observation_ rather than
of _experiment_. As Delambre says (_Astron. Anc._ vol. ii. p. 427),
"On y voit des expériences de physique bien faites, ce qui est sans
exemple chez les anciens."

Ptolemy's Optical work was known only by Roger Bacon's references to
it (_Opus Majus_, p. 286, &c.) till 1816; but copies of Latin
translations of it were known to exist in the Royal Library at Paris,
and in the Bodleian at Oxford. Delambre has given an account of the
contents of the Paris copy in his _Astron. Anc._ ii. 414, and in the
_Connoissance des Temps_ for 1816; and Prof. Rigaud's account of the
Oxford copy is given in the article _Optics_, in the _Encyclopædia
Britannica_. Ptolemy shows great sagacity in applying the notion of
Refraction to the explanation of the displacement of astronomical
objects which is produced by the atmosphere,--_Astronomical
Refraction_, as it is commonly called. He represents the visual ray as
refracted in passing from the _ether_, which is above the air, into
the air; the air being bounded by a spherical surface which has for
its centre "the centre of all the elements, the centre of the earth;"
and the refraction being a flexure towards the line drawn
perpendicular to this surface. He thus constructs, says Delambre, the
same figure on which Cassini afterwards founded the whole of his
theory; and gives a theory more complete than that of any astronomer
previous to him. Tycho, for instance, believed that astronomical
refraction was caused only by the _vapors_ of the atmosphere, and did
not exist above the altitude of 45°.

Cleomedes, about the time of Augustus, had guessed at Refraction, as
an explanation of an eclipse in which the sun and moon are both seen
at the same time. "Is it not possible," he says, "that the ray which
proceeds from the eye and traverses moist and cloudy air may bend
downwards to the sun, even when he is below the horizon?" And Sextus
Empiricus, a century later, says, "The air being dense, by the
refraction of the visual ray, a constellation may be seen above the
horizon when it is yet below the horizon." But from what follows, it
{104} appears doubtful whether he clearly distinguished Refraction
and Reflection.

In order that we may not attach too much value to the vague
expressions of Cleomedes and Sextus Empiricus, we may remark that
Cleomedes conceives such an eclipse as he describes not to be
possible, though he offers an explanation of it if it be: (the fact
must really occur whenever the moon is seen in the horizon in the
middle of an eclipse:) and that Sextus Empiricus gives his
suggestion of the effect of refraction as an argument why the
Chaldean astrology cannot be true, since the constellation which
appears to be rising at the moment of a birth is not the one which
is truly rising. The Chaldeans might have answered, says Delambre,
that the star begins to shed its influence, not when it is really in
the horizon, but when its light is seen. (_Ast. Anc._ vol. i. p.
231, and vol. ii. p. 548.)

It has been said that Vitellio, or Vitello, whom we shall hereafter
have to speak of in the history of Optics, took his Tables of
Refractions from Ptolemy. This is contrary to what Delambre states.
He says that Vitello may be accused of plagiarism from Alhazen, and
that Alhazen did not borrow his Tables from Ptolemy. Roger Bacon had
said (_Opus Majus_, p. 288), "Ptolemæus in libro de Opticis, id est,
de Aspectibus, seu in Perspectivâ suâ, qui prius quam Alhazen dedit
hanc sententiam, quam a Ptolemæo acceptam Alhazen exposuit." This
refers only to the opinion that visual rays proceed from the eye.
But this also is erroneous; for Alhazen maintains the contrary:
"Visio fit radiis a visibili extrinsecus ad visum manantibus."
(_Opt._ Lib. i. cap. 5.) Vitello says of his Table of Refractions,
"Acceptis instrumentaliter, prout potuimus propinquius, angulis
omnium refractionum . . . invenimus quod semper iidem sunt anguli
refractionum: . . . secundum hoc fecimus has tabulas." "Having
measured, by means of instruments, as exactly as we could, the whole
range of the angles of refraction, we found that the refraction is
always the same for the same angle; and hence we have constructed
these Tables." {105}




CHAPTER III.

EARLIEST STAGES OF HARMONICS.


AMONG the ancients, the science of Music was an application of
Arithmetic, as Optics and Mechanics were of Geometry. The story
which is told concerning the origin of their arithmetical music, is
the following, as it stands in the Arithmetical Treatise of
Nicomachus.

Pythagoras, walking one day, meditating on the means of measuring
musical notes, happened to pass near a blacksmith's shop, and had
his attention arrested by hearing the hammers, as they struck the
anvil, produce the sounds which had a musical relation to each
other. On listening further, he found that the intervals were a
Fourth, a Fifth, and an Octave; and on weighing the hammers, it
appeared that the one which gave the Octave was _one-half_ the
heaviest, the one which gave the Fifth was _two-thirds_, and the one
which gave the Fourth was _three-quarters_. He returned home,
reflected upon this phenomenon, made trials, and finally discovered,
that if he stretched musical strings of equal lengths, by weights
which have the proportion of one-half, two-thirds, and
three-fourths, they produced intervals which were an Octave, a
Fifth, and a Fourth. This observation gave an arithmetical measure
of the principal Musical Intervals, and made Music an arithmetical
subject of speculation.

This story, if not entirely a philosophical fable, is undoubtedly
inaccurate; for the musical intervals thus spoken of would not be
produced by striking with hammers of the weights there stated. But
it is true that the notes of strings have a definite relation to the
forces which stretch them; and this truth is still the groundwork of
the theory of musical concords and discords.

Nicomachus says that Pythagoras found the weights to be, as I have
mentioned, in the proportion of 12, 6, 8, 9; and the intervals, an
Octave, corresponding to the proportion 12 to 6, or 2 to 1; a Fifth,
corresponding to the proportion 12 to 8, or 3 to 2; and a Fourth,
corresponding to the proportion 12 to 9, or 4 to 3. There is no
doubt that this statement of the ancient writer is inexact as to the
physical fact, for the rate of vibration of a string, on which its
note depends, is, {106} other things being equal, not as the weight,
but as the square root of the weight. But he is right as to the
essential point, that those ratios of 2 to 1, 3 to 2, and 4 to 3,
are the characteristic ratios of the Octave, Fifth, and Fourth. In
order to produce these intervals, the appended weights must be, not
as 12, 9, 8, and 6, but as 12, 6¾, 5⅓, and 3.

The numerical relations of the other intervals of the musical scale,
as well as of the Octave, Fifth, and Fourth, were discovered by the
Greeks. Thus they found that the proportion in a Major Third was 5
to 4; in a Minor Third, 6 to 5; in a Major Tone, 9 to 8; in a
Semitone or _Diesis_, 16 to 15. They even went so far as to
determine the _Comma_, in which the interval of two notes is so
small that they are in the proportion of 81 to 80. This is the
interval between two notes, each of which may be called the
Seventeenth above the key-note;--the one note being obtained by
ascending a Fifth four times over; the other being obtained by
ascending through two Octaves and a Major Third. The want of exact
coincidence between these two notes is an inherent arithmetical
imperfection in the musical scale, of which the consequences are
very extensive.

The numerical properties of the musical scale were worked out to a
very great extent by the Greeks, and many of their Treatises on this
subject remain to us. The principal ones are the seven authors
published by Meibomius.[2\2] These arithmetical elements of Music
are to the present day important and fundamental portions of the
Science of Harmonics.

[Note 2\2: _Antiquæ Musicæ Scriptores septem_, 1652.]

It may at first appear that the truth, or even the possibility of
this history, by referring the discovery to accident, disproves our
doctrine, that this, like all other fundamental discoveries,
required a distinct and well-pondered Idea as its condition. In
this, however, as in all cases of supposed accidental discoveries in
science, it will be found, that it was exactly the possession of
such an Idea which made the accident possible.

Pythagoras, assuming the truth of the tradition, must have had an
exact and ready apprehension of those relations of musical sounds,
which are called respectively an Octave, a Fifth, and a Fourth. If
he had not been able to conceive distinctly this relation, and to
apprehend it when heard, the sounds of the anvil would have struck
his ears to no more purpose than they did those of the smiths
themselves. He {107} must have had, too, a ready familiarity with
numerical ratios; and, moreover (that in which, probably, his
superiority most consisted), a disposition to connect one notion
with the other--the musical relation with the arithmetical, if it
were found possible. When the connection was once suggested, it was
easy to devise experiments by which it might be confirmed.

"The philosophers of the Pythagorean School,[3\2] and in particular,
Lasus of Hermione, and Hippasus of Metapontum, made many such
experiments upon strings; varying both their lengths and the weights
which stretched them; and also upon vessels filled with water, in a
greater or less degree." And thus was established that connection of
the Idea with the Fact, which this Science, like all others,
requires.

[Note 3\2: Montucla, iii. 10.]


I shall quit the Physical Sciences of Ancient Greece, with the above
brief statement of the discovery of the fundamental principles which
they involved; not only because such initial steps must always be
the most important in the progress of science, but because, in
reality, the Greeks made no advances beyond these. There took place
among them no additional inductive processes, by which new facts
were brought under the dominion of principles, or by which
principles were presented in a more comprehensive shape than before.
Their advance terminated in a single stride. Archimedes had stirred
the intellectual world, but had not put it in progressive motion:
the science of Mechanics stopped where he left it. And though, in
some objects, as in Harmonics, much was written, the works thus
produced consisted of deductions from the fundamental principles, by
means of arithmetical calculations; occasionally modified, indeed,
by reference to the pleasures which music, as an art, affords, but
not enriched by any new scientific truths.

[3d Ed.] We should, however, quit the philosophy of the ancient
Greeks without a due sense of the obligations which Physical Science
in all succeeding ages owes to the acute and penetrating spirit in
which their inquiries in that region of human knowledge were
conducted, and to the large and lofty aspirations which were
displayed, even in their failure, if we did not bear in mind both
the multifarious and comprehensive character of their attempts, and
some of the causes which limited their progress in positive science.
They speculated and {108} theorized under a lively persuasion that a
Science of every part of nature was possible, and was a fit object
for the exercise of man's best faculties; and they were speedily led
to the conviction that such a science must clothe its conclusions in
the language of mathematics. This conviction is eminently
conspicuous in the writings of Plato. In the _Republic_, in the
_Epinomis_, and above all in the _Timæus_, this conviction makes him
return, again and again, to a discussion of the laws which had been
established or conjectured in his time, respecting Harmonics and
Optics, such as we have seen, and still more, respecting Astronomy,
such as we shall see in the next Book. Probably no succeeding step
in the discovery of the Laws of Nature was of so much importance as
the full adoption of this pervading conviction, that there must be
Mathematical Laws of Nature, and that it is the business of
Philosophy to discover these Laws. This conviction continues,
through all the succeeding ages of the history of science, to be the
animating and supporting principle of scientific investigation and
discovery. And, especially in Astronomy, many of the erroneous
guesses which the Greeks made, contain, if not the germ, at least
the vivifying life-blood, of great truths, reserved for future ages.

Moreover, the Greeks not only sought such theories of special parts
of nature, but a general Theory of the Universe. An essay at such a
theory is the _Timæus_ of Plato; too wide and too ambitious an
attempt to succeed at that time; or, indeed, on the scale on which
he unfolds it, even in our time; but a vigorous and instructive
example of the claim which man's Intellect feels that it may make to
understand the universal frame of things, and to render a reason for
all that is presented to it by the outward senses.

Further; we see in Plato, that one of the grounds of the failure in
this attempt, was the assumption that the _reason why_ every thing is
what it is and as it is, must be that so it is _best_, according to
some view of better or worse attainable by man. Socrates, in his
dying conversation, as given in the _Phædo_, declares this to have
been what he sought in the philosophy of his time; and tells his
friends that he turned away from the speculations of Anaxagoras
because they did not give him such reasons for the constitution of
the world; and Plato's _Timæus_ is, in reality, an attempt to supply
this deficiency, and to present a Theory of the Universe, in which
every thing is accounted for by such reasons. Though this is a
failure, it is a noble as well as an instructive failure.



{{109}}
BOOK III.

HISTORY
OF
GREEK ASTRONOMY.


Τόδε δὲ μηδείς ποτε φοβηθῇ τῶν Ἑλλήνων, ὡς οὐ χρὴ περὶ τὰ θεῖα ποτὲ
πραγματεύεσθαι θνητοὺς ὄντας· πᾶν δε τούτου διανοηθῆναι τοὐναντίον,
ὡς οὔτε ἄφρον ἔστι ποτὲ τὸ θεῖον, οὔτε ἀγνοεῖ που τὴν ἀνθρωπίνην
φυσιν· ἀλλ' οἶδεν ὅτι, διδάσκοντος αὐτοῦ, ξυνακολουθήσει καὶ
μαθήσεται τὰ διδάσκομενα.--PLATO, _Epinomis_, p. 988.

Nor should any Greek have any misgiving of this kind; that it is not
fitting for us to inquire narrowly into the operations of Superior
Powers, such as those by which the motions of the heavenly bodies
are produced: but, on the contrary, men should consider that the
Divine Powers never act without purpose, and that they know the
nature of man: they know that by their guidance and aid, man may
follow and comprehend the lessons which are vouchsafed him on such
subjects.



{{111}}
INTRODUCTION.


THE earliest and fundamental conceptions of men respecting the
objects with which Astronomy is concerned, are formed by familiar
processes of thought, without appearing to have in them any thing
technical or scientific. Days, Years, Months, the Sky, the
Constellations, are notions which the most uncultured and incurious
minds possess. Yet these are elements of the Science of Astronomy.
The reasons why, in this case alone, of all the provinces of human
knowledge, men were able, at an early and unenlightened period, to
construct a science out of the obvious facts of observation, with
the help of the common furniture of their minds, will be more
apparent in the course of the philosophy of science: but I may here
barely mention two of these reasons. They are, first, that the
familiar act of thought, exercised for the common purposes of life,
by which we give to an assemblage of our impressions such a unity as
is implied in the above notions and terms, a Month, a Year, the Sky,
and the like, is, in reality, an _inductive act_, and shares the
nature of the processes by which all sciences are formed; and, in
the next place, that the ideas appropriate to the induction in this
case, are those which, even in the least cultivated minds, are very
clear and definite; namely, the ideas of Space and Figure, Time and
Number, Motion and Recurrence. Hence, from their first origin, the
modifications of those ideas assume a scientific form.

We must now trace in detail the peculiar course which, in
consequence of these causes, the knowledge of man respecting the
heavenly bodies took, from the earliest period of his history. {112}




CHAPTER I.

EARLIEST STAGES OF ASTRONOMY.


_Sect._ 1.--_Formation of the Notion of a Year._

THE notion of a _Day_ is early and obviously impressed upon man in
almost any condition in which we can imagine him. The recurrence of
light and darkness, of comparative warmth and cold, of noise and
silence, of the activity and repose of animals;--the rising,
mounting, descending, and setting of the sun;--the varying colors of
the clouds, generally, notwithstanding their variety, marked by a
daily progression of appearances;--the calls of the desire of food
and of sleep in man himself, either exactly adjusted to the period
of this change, or at least readily capable of being accommodated to
it;--the recurrence of these circumstances at intervals, equal, so
far as our obvious judgment of the passage of time can decide; and
these intervals so short that the repetition is noticed with no
effort of attention or memory;--this assemblage of suggestions makes
the notion of a Day necessarily occur to man, if we suppose him to
have the conception of Time, and of Recurrence. He naturally marks
by a term such a portion of time, and such a cycle of recurrence; he
calls each portion of time, in which this series of appearances and
occurrences come round, a _Day_; and such a group of particulars are
considered as appearing or happening _in_ the same day.

_A Year_ is a notion formed in the same manner; implying in the same
way the notion of recurring facts; and also the faculty of arranging
facts in time, and of appreciating their recurrence. But the notion
of a Year, though undoubtedly very obvious, is, on many accounts,
less so than that of a Day. The repetition of similar circumstances,
at equal intervals, is less manifest in this case, and the intervals
being much longer, some exertion of memory becomes requisite in
order that the recurrence may be perceived. A child might easily be
persuaded that successive years were of unequal length; or, if the
summer were cold, and the spring and autumn warm, might be made to
believe, if all who spoke in its hearing agreed to support the
delusion, that one year was two. It would be impossible to practise
such a deception with regard to the day, without the use of some
artifice beyond mere words. {113}

Still, the recurrence of the appearances which suggest the notion of
a Year is so obvious, that we can hardly conceive man without it.
But though, in all climes and times, there would be a recurrence,
and at the same interval in all, the recurring appearances would be
extremely different in different countries; and the contrasts and
resemblances of the seasons would be widely varied. In some places
the winter utterly alters the face of the country, converting grassy
hills, deep leafy woods of various hues of green, and running
waters, into snowy and icy wastes, and bare snow-laden branches;
while in others, the field retains its herbage, and the tree its
leaves, all the year; and the rains and the sunshine alone, or
various agricultural employments quite different from ours, mark the
passing seasons. Yet in all parts of the world the yearly cycle of
changes has been singled out from all others, and designated by a
peculiar name. The inhabitant of the equatorial regions has the sun
vertically over him at the end of every period of six months, and
similar trains of celestial phenomena fill up each of these
intervals, yet we do not find years of six months among such
nations. The Arabs alone,[1\3] who practise neither agriculture nor
navigation, have a year depending upon the moon only; and borrow the
word from other languages, when they speak of the solar year.

[Note 1\3: Ideler, _Berl. Trans._ 1813, p. 51.]

In general, nations have marked this portion of time by some word
which has a reference to the returning circle of seasons and
employments. Thus the Latin _annus_ signified a ring, as we see in
the derivative _annulus_: the Greek term ἐνιαυτὸς implies something
which _returns into itself_: and the word as it exists in Teutonic
languages, of which our word _year_ is an example, is said to have
its origin in the word _yra_ which means a ring in Swedish, and is
perhaps connected with the Latin _gyrus_.


_Sect._ 2.--_Fixation of the Civil Year._

THE year, considered as a recurring cycle of seasons and of general
appearances, must attract the notice of man as soon as his attention
and memory suffice to bind together the parts of a succession of the
length of several years. But to make the same term imply a certain
fixed number of days, we must know how many days the cycle of the
seasons occupies; a knowledge which requires faculties and artifices
beyond what we have already mentioned. For instance, men cannot
reckon as far as any number at all approaching the number of days in
the year, without possessing a system of numeral terms, and methods
{114} of practical numeration on which such a system of terms is
always founded.[2\3] The South American Indians, the Koussa Caffres
and Hottentots, and the natives of New Holland, all of whom are said
to be unable to reckon further than the fingers of their hands and
feet,[3\3] cannot, as we do, include in their notion of a year the
fact of its consisting of 365 days. This fact is not likely to be
known to any nation except those which have advanced far beyond that
which may be considered as the earliest scientific process which we
can trace in the history of the human race, the formation of a
method of designating the successive numbers to an indefinite
extent, by means of names, framed according to the decimal, quinary,
or vigenary scale.

[Note 2\3: _Arithmetic_ in _Encyc. Metrop._ (by Dr. Peacock), Art. 8.]

[Note 3\3: Ibid. Art. 32.]

But even if we suppose men to have the habit of recording the
passage of each day, and of counting the score thus recorded, it
would be by no means easy for them to determine the exact number of
days in which the cycle of the seasons recurs; for the
indefiniteness of the appearances which mark the same season of the
year, and the changes to which they are subject as the seasons are
early or late, would leave much uncertainty respecting the duration
of the year. They would not obtain any accuracy on this head, till
they had attended for a considerable time to the motions and places
of the sun; circumstances which require more precision of notice
than the general facts of the degrees of heat and light. The motions
of the sun, the succession of the places of his rising and setting
at different times of the year, the greatest heights which he
reaches, the proportion of the length of day and night, would all
exhibit several cycles. The turning back of the sun, when he had
reached the greatest distance to the south or to the north, as shown
either by his rising or by his height at noon, would perhaps be the
most observable of such circumstances. Accordingly the τροπαὶ
ἠελίοιο, the turnings of the sun, are used repeatedly by Hesiod as a
mark from which he reckons the seasons of various employments.
"Fifty days," he says, "after the turning of the sun, is a
seasonable time for beginning a voyage."[4\3]

[Note 4\3:  Ἤματα πεντήκοντα μετὰ τροπὰς ἠελίοιο
            Ἐς τέλος ἐλθόντος θέρεος.--_Op. et Dies_, 661.]

The phenomena would be different in different climates, but the
recurrence would be common to all. Any one of these kinds of
phenomena, noted with moderate care for a year, would show what was
the number of days of which a year consisted; and if several years
{115} were included in the interval through which the scrutiny
extended, the knowledge of the length of the year so acquired would
be proportionally more exact.

Besides those notices of the sun which offered exact indications of
the seasons, other more indefinite natural occurrences were used; as
the arrival of the swallow (χελιδών) and the kite (ἰκτίν), The
birds, in Aristophanes' play of that name, mention it as one of
their offices to mark the seasons; Hesiod similarly notices the cry
of the crane as an indication of the departure of winter.[5\3]

[Note 5\3: Ideler, i. 240.]

Among the Greeks the seasons were at first only summer and winter
(θέρος and χειμών), the latter including all the rainy and cold
portion of the year. The winter was then subdivided into the χειμών
and ἔαρ (winter proper and spring), and the summer, less definitely,
into θέρος and ὀπώρα (summer and autumn). Tacitus says that the
Germans knew neither the blessings nor the name of autumn, "Autumni
perinde nomen ac bona ignorantur." Yet _harvest_, _herbst_, is
certainly an old German word.[6\3]

[Note 6\3: Ib. i. 243.]

In the same period in which the sun goes through his cycle of
positions, the stars also go through a cycle of appearances
belonging to them; and these appearances were perhaps employed at as
early a period as those of the sun, in determining the exact length
of the year. Many of the groups of fixed stars are readily
recognized, as exhibiting always the same configuration; and
particular bright stars are singled out as objects of attention.
These are observed, at particular seasons, to appear in the west
after sunset; but it is noted that when they do this, they are found
nearer and nearer to the sun every successive evening, and at last
disappear in his light. It is observed also, that at a certain
interval after this, they rise visibly before the dawn of day
renders the stars invisible; and after they are seen to do this,
they rise every day at a longer interval before the sun. The risings
and settings of the stars under these circumstances, or under others
which are easily recognized, were, in countries where the sky is
usually clear, employed at an early period to mark the seasons of
the year. Eschylus[7\3] makes Prometheus mention this among the
benefits of which {116} he, the teacher of arts to the earliest race
of men, was the communicator.

[Note 7\3: Οὔκ ἤν γαρ αὐτοῖς οὔτε χείματος τέκμαρ,
           Οὔτ' ἀνθεμώδους ἦρος, οὔδε καρπίμου
           Θέρους βέβαιον· ἀλλ' ἄτερ γνώμης τὸ πᾶν
           Ἔπρασσον, ἔστε δή σφιν ἀνατολὰς ἐγὼ
           Ἄστρων ἔδειξα, τάς τε δυσκρίτους δύσεις.--_Prom. V._ 454.]

Thus, for instance, the rising[8\3] of the Pleiades in the evening
was a mark of the approach of winter. The rising of the waters of
the Nile in Egypt coincided with the heliacal rising of Sirius,
which star the Egyptians called Sothis. Even without any artificial
measure of time or position, it was not difficult to carry
observations of this kind to such a degree of accuracy as to learn
from them the number of days which compose the year; and to fix the
precise season from the appearance of the stars.

[Note 8\3: Ideler (Chronol. i. 242) says that _this_ rising of the
Pleiades took place at a time of the year which corresponds to our
11th May, and the setting to the 20th October; but this does not
agree with the forty days of their being "concealed," which, from
the context, must mean, I conceive, the interval between their
setting and rising. Pliny, however, says, "Vergiliarum exortu æstas
incipit, occasu hiems; _semestri_ spatio intra se messes
vindemiasque et omnium maturitatem complexæ." (H. N. xviii. 69.)

The autumn of the Greeks, ὀπώρα, was earlier than our autumn, for
Homer calls Sirius ἀστὴρ ὀπωρινός, which rose at the end of July.]

A knowledge concerning the stars appears to have been first
cultivated with the last-mentioned view, and makes its first
appearance in literature with this for its object. Thus Hesiod
directs the husbandman when to reap by the rising, and when to
plough by the setting of the Pleiades.[9\3] In like manner
Sirius,[10\3] Arcturus,[11\3] the Hyades and Orion,[12\3] are
noticed. {117}

[Note 9\3: Πληίαδων Ἀτλαγενέων ἐπιτελλομενάων.
           Ἄρχεσθ' ἀμητοῦ· ἀρότοιο δὲ, δυσομενάων.
           Αἵ δή τοι νύκτας τε καὶ ἤματα τεσσεράκοντα
           Κεκρύφαται, αὔτις δὲ περιπλομένου ἐνιαυτοῦ
           Φαίνονται.               _Op. et Dies_, l. 381.]

[Note 10\3: Ib. l. 413.]

[Note 11\3: Εὖτ' ἂν δ' ἑξήκοντα μετὰ τροπὰς ἠελίοιο
            Χειμέρι', ἐκτελέσῃ Ζεὺς ἤματα, δή ῥα τότ' ἀστὴρ
            Ἀρκτοῦρος, προλιπὼν ἱερὸν ῥόον Ὠκεανοῖο
            Πρῶτον παμφαίνων ἐπιτέλλεται ἀκροκνέφαιος.
                                    _Op. et Dies_, l. 562.

            Εὖτ' ἂν δ' Ὠρίων καὶ Σείριος ἐς μέσον ἔλθῃ
            Οὐρανὸν, Ἀρκτοῦρον δ' ἐσὶδῃ ῥοδοδάκτυλος ἠὼς.
                                          Ib. 607.]

[Note 12\3: . . . . . . . αὐτὰρ ἐπὴν δὴ
            Πληϊάδες Ὑάδες τε τὸ τε σθένος Ὠρίωνος
            Δύνωσιν.                      Ib. 612.

These methods were employed to a late period, because the Greek
months, being lunar, did not correspond to the seasons. Tables of
such motions were called παραπήγματα.--Ideler, _Hist.
Untersuchungen_, p. 209.]

By such means it was determined that the year consisted, at least,
nearly, of 365 days. The Egyptians, as we learn from
Herodotus,[13\3] claimed the honor of this discovery. The priests
informed him, he says, "that the Egyptians were the first men who
discovered the year, dividing it into twelve equal parts; and this
they asserted that they discovered from the stars." Each of these
parts or months consisted of 30 days, and they added 5 days more at
the end of the year, "and thus the circle of the seasons come
round." It seems, also, that the Jews, at an early period, had a
similar reckoning of time, for the Deluge which continued 150 days
(Gen. vii. 24), is stated to have lasted from the 17th day of the
second month (Gen. vii. 11) to the 17th day of the seventh month
(Gen. viii. 4), that is, 5 months of 30 days.

[Note 13\3: Ib. ii. 4.]

A year thus settled as a period of a certain number of days is
called a _Civil Year_. It is one of the earliest discoverable
institutions of States possessing any germ of civilization; and one
of the earliest portions of human systematic knowledge is the
discovery of the length of the civil year, so that it should agree
with the natural year, or year of the seasons.


_Sect._ 3.--_Correction of the Civil Year._ (_Julian Calendar._)

IN reality, by such a mode of reckoning as we have described, the
circle of the seasons would not come round exactly. The real length of
the year is very nearly 365 days and a quarter. If a year of 365 days
were used, in four years the year would begin a day too soon, when
considered with reference to the sun and stars; and in 60 years it
would begin 15 days too soon: a quantity perceptible to the loosest
degree of attention. The civil year would be found not to coincide
with the year of the seasons; the beginning of the former would take
place at different periods of the latter; it would _wander_ into
various seasons, instead of remaining fixed to the same season; the
term _year_, and any number of years, would become ambiguous: some
correction, at least some comparison, would be requisite.

We do not know by whom the insufficiency of the year of 365 days was
first discovered;[14\3] we find this knowledge diffused among all
civilized nations, and various artifices used in making the
correction. The method which we employ, and which consists in
reckoning an {118} additional day at the end of February every fourth
or _leap_ year, is an example of the principle of _intercalation_, by
which the correction was most commonly made. Methods of intercalation
for the same purpose were found to exist in the new world. The
Mexicans added 13 days at the end of every 52 years. The method of the
Greeks was more complex (by means of the _octaëteris_ or cycle of 8
years); but it had the additional object of accommodating itself to
the motions of the moon, and therefore must be treated of hereafter.
The Egyptians, on the other hand, knowingly permitted their civil year
to _wander_, at least so far as their religious observances were
concerned. "They do not wish," says Geminus,[15\3] "the same
sacrifices of the gods to be made perpetually at the same time of the
year, but that they should go through all the seasons, so that the
same feast may happen in summer and winter, in spring and autumn." The
period in which any festival would thus pass through all the seasons
of the year is 1461 years; for 1460 years of 365¼ days are equal to
1461 years of 365 days. This period of 1461 years is called the
_Sothic_ Period, from Sothis, the name of the Dog-star, by which their
_fixed_ year was determined; and for the same reason it is called the
_Canicular_ Period.[16\3]

[Note 14\3: Syncellus (_Chronographia_, p. 123) says that according
to the legend, it was King Aseth who first added the 5 additional
days to 360, for the year, in the eighteenth century, B. C.]

[Note 15\3: _Uranol._ p. 33.]

[Note 16\3: Censorinus _de Die Natali_, c. 18.]

Other nations did not regulate their civil year by intercalation at
short intervals, but rectified it by a _reform_ when this became
necessary. The Persians are said to have added a month of 30 days
every 120 years. The Roman calendar, at first very rude in its
structure, was reformed by Numa, and was directed to be kept in
order by the perpetual interposition of the augurs. This, however,
was, from various causes, not properly done; and the consequence
was, that the reckoning fell into utter disorder, in which state it
was found by Julius Cæsar, when he became dictator. By the advice of
Sosigenes, he adopted the mode of intercalation of one day in 4
years, which we still retain; and in order to correct the
derangement which had already been produced, he added 90 days to a
year of the usual length, which thus became what was called _the
year of confusion_. The _Julian Calendar_, thus reformed, came into
use, January 1, B. C. 45.


_Sect._ 4.--_Attempts at the Fixation of the Month._

THE circle of changes through which the moon passes in about thirty
days, is marked, in the earliest stages of language, by a word which
implies the space of time which one such circle occupies; just {119}
as the circle of changes of the seasons is designated by the word
_year_. The lunar changes are, indeed, more obvious to the sense,
and strike a more careless person, than the annual; the moon, when
the sun is absent, is almost the sole natural object which attracts
our notice; and we look at her with a far more tranquil and
agreeable attention than we bestow on any other celestial object.
Her changes of form and place are definite and striking to all eyes;
they are uninterrupted, and the duration of their cycle is so short
as to require no effort of memory to embrace it. Hence it appears to
be more easy, and in earlier stages of civilization more common, to
count time by _moons_ than by years.

The words by which this period of time is designated in various
languages, seem to refer us to the early history of language. Our
word _month_ is connected with the word _moon_, and a similar
connection is noticeable in the other branches of the Teutonic. The
Greek word μὴν in like manner is related to μήνη, which though not
the common word for the moon, is found in Homer with that
signification. The Latin word _mensis_ is probably connected with
the same group.[17\3]

[Note 17\3: Cicero derives this word from the verb _to measure_:
"quia _mensa_ spatia conficiunt, _menses_ nominantur;" and other
etymologists, with similar views, connect the above-mentioned words
with the Hebrew _manah_, to measure (with which the Arabic word
_almanach_ is connected). Such a derivation would have some analogy
with that of _annus_, &c., noticed above: but if we are to attempt
to ascend to the earliest condition of language, we must conceive it
probable that men would have a name for a most conspicuous visible
object, _the moon_, before they would have a verb denoting the very
abstract and general notion, _to measure_.]

The month is not any exact number of days, being more than 29, and
less than 30. The latter number was first tried, for men more
readily select numbers possessing some distinction of regularity. It
existed for a long period in many countries. A very few months of 30
days, however, would suffice to derange the agreement between the
days of the months and the moon's appearance. A little further trial
would show that months of 29 and 30 days alternately, would
preserve, for a considerable period, this agreement.

The Greeks adopted this calendar, and, in consequence, considered
the days of their month as representing the changes of the moon: the
last day of the month was called ἔνη καὶ νέα, "the old and new" as
belonging to both the waning and the reappearing moon:[18\3] and
their {120} festivals and sacrifices, as determined by the calendar,
were conceived to be necessarily connected with the same periods of
the cycles of the sun and moon. "The laws and the oracles," says
Geminus, "which directed that they should in sacrifices observe
three things, months, days, years, were so understood." With this
persuasion, a correct system of intercalation became a religious
duty.

[Note 18\3: Aratus says of the moon, in a passage quoted by Geminus,
p. 33:
  Αἴει δ' ἄλλοθεν ἄλλα παρακλίνουσα μετωπὰ
  Εἴρῃ, ὁποσταίη μήνος περιτέλλεται ἡὼς
  As still her shifting visage changing turns,
  By her we count the monthly round of morns.]

The above rule of alternate months of 29 and 30 days, supposes the
length of the months 29 days and a half, which is not exactly the
length of a lunar month. Accordingly the Months and the Moon were
soon at variance. Aristophanes, in "The Clouds," makes the Moon
complain of the disorder when the calendar was deranged.

                        Οὐκ ἄγειν τὰς ἡμέρας
  Οὐδὲν ὀρθῶς, ἀλλ' ἀνω τε καὶ κάτω κυδοιδοπᾶν
  Ὥστ' ἀπειλεῖν φησὶν αὐτῇ τοὐς θεοὺς ἑκάστοτε
  Ἡνίκ' ἂν ψευσθῶσι δείπνου κἀπίωσιν οἴκαδε
  Τῆς ἑορτῆς μὴ τυχόντες κατὰ λόγον τῶν ἡμερῶν.
          _Nubes_, 615-19.

     CHORUS OF CLOUDS.

  The Moon by us to you her greeting sends,
  But bids us say that she's an ill-used moon,
  And takes it much amiss that you should still
  Shuffle her days, and turn them topsy-turvy:
  And that the gods (who know their feast-days well)
  By your false count are sent home supperless,
  And scold and storm at her for your neglect.[19\3]

[Note 19\3: This passage is supposed by the commentators to be
intended as a satire upon those who had introduced the cycle of
Meton (spoken of in Sect. 5), which had been done at Athens a few
years before "The Clouds" was acted.]

The correction of this inaccuracy, however, was not pursued
separately, but was combined with another object, the securing a
correspondence between the lunar and solar years, the main purpose
of all early cycles.


_Sect._ 5.--_Invention of Lunisolar Years._

THERE are 12 complete lunations in a year; which according to the
above rule (of 29½ days to a lunation) would make 354 days, leaving
12¼ days of difference between such a lunar year and a solar year.
It is said that, at an early period, this was attempted to be
corrected by interpolating a month of 30 days every alternate year;
and Herodotus[20\3] relates a conversation of Solon, implying a
still ruder mode of {121} intercalation. This can hardly be
considered as an improvement in the Greek calendar already
described.

[Note 20\3: B. i. c. 15.]

The first cycle which produced any near correspondence of the
reckoning of the moon and the sun, was the _Octaëteris_, or period
of 8 years: 8 years of 354 days, together with 3 months of 30 days
each, making up (in 99 lunations) 2922 days; which is exactly the
amount of 8 years of 365¼ days each. Hence this period would answer
its purpose, so far as the above lengths of the lunar and solar
cycles are exact; and it might assume various forms, according to
the manner in which the three intercalary months were distributed.
The customary method was to add a thirteenth month at the end of the
third, fifth, and eighth year of the cycle. This period is ascribed
to various persons and times; probably different persons proposed
different forms of it. Dodwell places its introduction in the 59th
Olympiad, or in the 6th century, B. C.: but Ideler thinks the
astronomical knowledge of the Greeks of that age was too limited to
allow of such a discovery.

This cycle, however, was imperfect. The duration of 99 lunations is
something more than 2922 days; it is more nearly 2923½; hence in 16
years there was a deficiency of 3 days, with regard to the motions
of the moon. This cycle of 16 years (_Heccædecaëteris_), with 3
interpolated days at the end, was used, it is said, to bring the
calculation right with regard to the moon; but in this way the
origin of the year was displaced with regard to the sun. After 10
revolutions of this cycle, or 160 years, the interpolated days would
amount to 30, and hence the end of the lunar year would be a month
in advance of the end of the solar. By terminating the lunar year at
the end of the preceding month, the two years would again be brought
into agreement: and we have thus a cycle of 160 years.[21\3]

[Note 21\3: Geminus. Ideler.]

This cycle of 160 years, however, was calculated from the cycle of
16 years; and it was probably never used in civil reckoning; which
the others, or at least that of 8 years, appear to have been.

The cycles of 16 and 160 years were corrections of the cycle of 8
years; and were readily suggested, when the length of the solar and
lunar periods became known with accuracy. But a much more exact
cycle, independent of these, was discovered and introduced by
Meton,[22\3] 432 years B. C. This cycle consisted of 19 years, and
is so correct and convenient, that it is in use among ourselves to
this day. The time occupied by 19 years, and by 235 lunations, is
very nearly the same; {122} (the former time is less than 6940 days
by 9½ hours, the latter, by 7½ hours). Hence, if the 19 years be
divided into 235 months, so as to agree with the changes of the
moon, at the end of that period the same succession may begin again
with great exactness.

[Note 22\3: Ideler, _Hist. Unters._ p. 208.]

In order that 235 months, of 30 and 29 days, may make up 6940 days,
we must have 125 of the former, which were called _full_ months, and
110 of the latter, which were termed _hollow_. An artifice was used
in order to distribute 110 hollow months among 6940 days. It will be
found that there is a hollow month for each 63 days nearly. Hence if
we reckon 30 days to every month, but at every 63d day leap over a
day in the reckoning, we shall, in the 19 years, omit 110 days; and
this accordingly was done. Thus the 3d day of the 3d month, the 6th
day of the 5th month, the 9th day of the 7th, must be omitted, so as
to make these months "hollow." Of the 19 years, seven must consist
of 13 months; and it does not appear to be known according to what
order these seven years were selected. Some say they were the 3d,
6th, 8th, 11th, 14th, 17th, and 19th; others, the 3d, 5th, 8th,
11th, 13th, 16th, and 19th.

The near coincidence of the solar and lunar periods in this cycle of
19 years, was undoubtedly a considerable discovery at the time when
it was first accomplished. It is not easy to trace the way in which
such a discovery was made at that time; for we do not even know the
manner in which men then recorded the agreement or difference
between the calendar day and the celestial phenomenon which ought to
correspond to it. It is most probable that the length of the month
was obtained with some exactness by the observation of eclipses, at
considerable intervals of time from each other; for eclipses are
very noticeable phenomena, and must have been very soon observed to
occur only at new and full moon.[23\3]

[Note 23\3: Thucyd. vii. 50. Ἡ σελήνη ἐκλείπει· ἐτύγχανε γὰρ
_πανσέληνος_ οὖσα. iv. 52, Τοῦ ἡλίου ἐκλιπές τι ἐγένετο _περὶ
νουμηνίαν_. ii. 28. Νουμηνίᾳ κατὰ _σελήνην_ (ὥσπερ καὶ μόνον δοκεῖ
εἶναι γίγνεσθαι δυνατὸν) ὁ ἡλίος ἐξέλιπε μετὰ μεσημβρίαν καὶ πάλιν
ἀν ἐπληρώθη, γενόμενος μηνοειδὴς καὶ ἀστέρων τινῶν ἐκφανέντων.]

The exact length of a certain number of months being thus known, the
discovery of a cycle which should regulate the calendar with
sufficient accuracy would be a business of arithmetical skill, and
would depend, in part, on the existing knowledge of arithmetical
methods; but in making the discovery, a natural arithmetical
sagacity was probably more efficacious than method. It is very
possible that the _Cycle of Meton_ is correct more nearly than its
author was aware, and {123} nearly than he could ascertain from any
evidence and calculation known to him. It is so exact that it is
still used in calculating the new moon for the time of Easter; and
the _Golden Number_, which is spoken of in stating such rules, is
the number of this Cycle corresponding to the current year.[24\3]

[Note 24\3: The same cycle of 19 years has been used by the Chinese
for a very great length of time; their civil year consisting, like
that of the Greeks, of months of 29 and 30 days. The Siamese also
have this period. (_Astron._ Lib. U. K.)]

Meton's Cycle was corrected a hundred years later (330 B. C.), by
Calippus, who discovered the error of it by observing an eclipse of
the moon six years before the death of Alexander.[25\3] In this
corrected period, four cycles of 19 years were taken, and a day left
out at the end of the 76 years, in order to make allowance for the
hours by which, as already observed, 6940 days are greater than 19
years, and than 235 lunations: and this _Calippic period_ is used in
Ptolemy's Almagest, in stating observations of eclipses.

[Note 25\3: Delamb. _A. A._ p. 17.]

The Metonic and Calippic periods undoubtedly imply a very
considerable degree of accuracy in the knowledge which the
astronomers, to whom they are due, had of the length of the month;
and the first is a very happy invention for bringing the solar and
lunar calendars into agreement.

The Roman Calendar, from which our own is derived, appears to have
been a much less skilful contrivance than the Greek; though scholars
are not agreed on the subject of its construction, we can hardly
doubt that months, in this as in other cases, were intended
originally to have a reference to the moon. In whatever manner the
solar and lunar motions were intended to be reconciled, the attempt
seems altogether to have failed, and to have been soon abandoned.
The Roman months, both before and after the Julian correction, were
portions of the year, having no reference to full and new moons; and
we, having adopted this division of the year, have thus, in our
common calendar, the traces of one of the early attempts of mankind
to seize the law of the succession of celestial phenomena, in a case
where the attempt was a complete failure.

Considered as a part of the progress of our astronomical knowledge,
improvements in the calendar do not offer many points to our
observation, but they exhibit a few very important steps. Calendars
which, belonging apparently to unscientific ages and nations,
possess a great degree of accordance with the true motions of the
sun and moon (like {124} the solar calendar of the Mexicans, and the
lunar calendar of the Greeks), contain the only record now extant of
discoveries which must have required a great deal of observation, of
thought, and probably of time. The later improvements in calendars,
which take place when astronomical observation has been attentively
pursued, are of little consequence to the history of science; for
they are generally founded on astronomical determinations, and are
posterior in time, and inferior in accuracy, to the knowledge on
which they depend. But cycles of correction, which are both short
and close to exactness, like that of Meton, may perhaps be the
original form of the knowledge which they imply; and certainly
require both accurate facts and sagacious arithmetical reasonings.
The discovery of such a cycle must always have the appearance of a
happy guess, like other discoveries of laws of nature. Beyond this
point, the interest of the study of calendars, as bearing on our
subject, ceases: they may be considered as belonging rather to Art
than to Science; rather as an application of a part of our knowledge
to the uses of life, than a means or an evidence of its extension.


_Sect._ 6.--_The Constellations._

SOME tendency to consider the stars as formed into groups, is
inevitable when men begin to attend to them; but how men were led to
the fanciful system of names of Stars and of Constellations, which
we find to have prevailed in early times, it is very difficult to
determine. Single stars, and very close groups, as the Pleiades,
were named in the time of Homer and Hesiod, and at a still earlier
period, as we find in the book of Job.[26\3]

[Note 26\3: Job xxxviii. 31. "Canst thou bind the sweet influences
of Chima (the Pleiades), or loose the bands of Kesil (Orion)? Canst
thou bring forth Mazzaroth (Sirius) in his season? or canst thou
guide Ash (or Aisch) (Arcturus) with his sons?"

And ix. 9. "Which maketh Arcturus, Orion, and Pleiades, and the
chambers of the south."

Dupuis, vi. 545, thinks that Aisch was αἴξ, the goat and kids. See
Hyde, _Ulughbeigh_.]

Two remarkable circumstances with respect to the Constellations are,
first, that they appear in most cases to be arbitrary combinations;
the artificial figures which are made to include the stars, not
having any resemblance to their obvious configurations; and second,
that these figures, in different countries, are so far similar, as
to imply some communication. The arbitrary nature of these figures
shows that they {125} were rather the work of the imaginative and
mythological tendencies of man, than of mere convenience and love of
arrangement. "The constellations," says an astronomer of our own
time,[27\3] "seem to have been almost purposely named and delineated
to cause as much confusion and inconvenience as possible.
Innumerable snakes twine through long and contorted areas of the
heavens, where no memory can follow them: bears, lions, and fishes,
large and small, northern and southern, confuse all nomenclature. A
better system of constellations might have been a material help as
an artificial memory." When men indicate the stars by figures,
borrowed from obvious resemblances, they are led to combinations
quite different from the received constellations. Thus the common
people in our own country find a wain or wagon, or a plough, in a
portion of the great bear.[28\3]

[Note 27\3: Sir J. Herschel.]

[Note 28\3: So also the Greeks, Homer, _Il._ XVIII. 487.
  Ἄρκτον ἢν καὶ ἄμαξαν ἐπίκλησιν καλέουσιν.
  The Northern Bear which oft the Wain they call.
Ἄρκτος was the traditional name; ἄμαξα, that suggested by the
form.]

The similarity of the constellations recognized in different
countries is very remarkable. The Chaldean, the Egyptian, and the
Grecian skies have a resemblance which cannot be overlooked. Some
have conceived that this resemblance may be traced also in the
Indian and Arabic constellations, at least in those of the
zodiac.[29\3] But while the figures are the same, the names and
traditions connected with them are different, according to the
histories and localities of each country;[30\3] the river among the
stars which the Greeks called the Eridanus, the Egyptians asserted
to be the Nile. Some conceive that the Signs of the _Zodiac_, or
path along which the sun and moon pass, had its divisions marked by
signs which had a reference to the course of the seasons, to the
motion of the sun, or the employments of the husbandman. If we take
the position of the heavens, which, from the knowledge we now
possess, we are sure they must have had 15,000 years ago, the
significance of the signs of the zodiac, in which the sun was, as
referred to the Egyptian year, becomes very marked,[31\3] and has
led some to suppose that the zodiac was invented at such a period.
Others have rejected this as an improbably great antiquity, and have
thought it more likely that the constellation assigned to each
season was that which, at that season, rose at the beginning of the
night: {126} thus the balance (which is conceived to designate the
equality of days and nights) was placed among the stars which rose
in the evening when the spring began: this would fix the origin of
these signs 2500 years before our era.

[Note 29\3: Dupuis, vi. 548. The Indian zodiac contains, in the
place of our Capricorn, a ram _and_ a fish, which proves the
resemblance without chance of mistake. Bailly, i. p. 157.]

[Note 30\3: Dupuis, vi. 549.]

[Note 31\3: Laplace, _Hist. Astron._ p. 8.]

It is clear, as has already been said, that Fancy, and probably
Superstition, had a share in forming the collection of
constellations. It is certain that, at an early period,
superstitious notions were associated with the stars.[32\3]
Astrology is of very high antiquity in the East. The stars were
supposed to influence the character and destiny of man, and to be in
some way connected with superior natures and powers.

[Note 32\3: Dupuis, vi. 546.]

We may, I conceive, look upon the formation of the constellations,
and the notions thus connected with them, as a very early attempt to
find a meaning in the relations of the stars; and as an utter
failure. The first effort to associate the appearances and motions
of the skies by conceptions implying unity and connection, was made
in a wrong direction, as may very easily be supposed. Instead of
considering the appearances only with reference to space, time,
number, in a manner purely rational, a number of other elements,
imagination, tradition, hope, fear, awe of the supernatural, belief
in destiny, were called into action. Man, still young, as a
philosopher at least, had yet to learn what notions his successful
guesses on these subjects must involve, and what they must exclude.
At that period, nothing could be more natural or excusable than this
ignorance; but it is curious to see how long and how obstinately the
belief lingered (if indeed it be yet extinct) that the motions of
the stars, and the dispositions and fortunes of men, may come under
some common conceptions and laws, by which a connection between the
one and the other may be established.

We cannot, therefore, agree with those who consider Astrology in the
early ages as "only a degraded Astronomy, the abuse of a more
ancient science."[33\3] It was the first step to astronomy by
leading to habits and means of grouping phenomena; and, after a
while, by showing that pictorial and mythological relations among
the stars had no very obvious value. From that time, the inductive
process went on steadily in the true road, under the guidance of
ideas of space, time, and number.

[Note 33\3: Ib. vi. 546.]


_Sect._ 7.--_The Planets._

WHILE men were becoming familiar with the fixed stars, the planets
must have attracted their notice. Venus, from her brightness, and
{127} from her accompanying the sun at no great distance, and thus
appearing as the morning and evening star, was very conspicuous.
Pythagoras is said to have maintained that the evening and morning
star are the same body, which certainly must have been one of the
earliest discoveries on this subject; and indeed we can hardly
conceive men noticing the stars for a year or two without coming to
this conclusion.

Jupiter and Mars, sometimes still brighter than Venus, were also
very noticeable. Saturn and Mercury were less so, but in fine
climates they and their motion would soon be detected by persons
observant of the heavens. To reduce to any rule the movements of
these luminaries must have taken time and thought; probably before
this was done, certainly very early, these heavenly bodies were
brought more peculiarly under those views which we have noticed as
leading to astrology.

At a time beyond the reach of certain history, the planets, along
with the sun and moon, had been arranged in a certain recognized
order by the Egyptians or some other ancient nation. Probably this
arrangement had been made according to the slowness of their motions
among the stars; for though the motion of each is very variable, the
gradation of their velocities is, on the whole, very manifest; and
the different rate of travelling of the different planets, and
probably other circumstances of difference, led, in the ready fancy
of early times, to the attribution of a peculiar character to each
luminary. Thus Saturn was held to be of a cold and gelid nature;
Jupiter, who, from his more rapid motion, was supposed to be lower
in place, was temperate; Mars, fiery, and the like.[34\3]

[Note 34\3: Achilles Tatius (_Uranol._ pp. 135, 136), gives the
Grecian and Egyptian names of the planets.
                Egyptian.                Greek.
Saturn          Νεμεσέως           Κρόνου     ἀστὴρ φαίνων
Jupiter         Ὀσίριδος           Δῖος       φαέθων
Mars            Ἡρακλεοῦς          Ἀρέος      πυρόεις
Venus                              Ἀφροδίτης  ἑώσφορος
Mercury         Ἀπόλλωνος          Ἑρμοῦ      στίλβων]

It is not necessary to dwell on the details of these speculations,
but we may notice a very remarkable evidence of their antiquity and
generality in the structure of one of the most familiar of our
measures of time, the _Week_. This distribution of time according to
periods of seven days, comes down to us, as we learn from the Jewish
scriptures, from the beginning of man's existence on the earth. The
same usage is found over all the East; it existed among the
Arabians, Assyrians, {128} Egyptians.[35\3] The same week is found
in India among the Bramins; it has there, also, its days marked by
those of the heavenly bodies; and it has been ascertained that the
same day has, in that country, the name corresponding with its
designation in other nations.

[Note 35\3: Laplace, _Hist. Astron._ p. 16.]

The notion which led to the usual designations of the days of the
week is not easily unravelled. The days each correspond to one of
the heavenly bodies, which were, in the earliest systems of the
world, conceived to be the following, enumerating them in the order
of their remoteness from the earth:[36\3] Saturn, Jupiter, Mars, the
Sun, Venus, Mercury, the Moon. At a later period, the received
systems placed the seven luminaries in _the seven spheres_. The
knowledge which was implied in this view, and the time when it was
obtained, we must consider hereafter. The order in which the names
are assigned to the days of the week (beginning with Saturday) is,
Saturn, the Sun, the Moon, Mars, Mercury, Jupiter, Venus; and
various accounts are given of the manner in which one of these
orders is obtained from the other; all the methods proceeding upon
certain arbitrary arithmetical processes, connected in some way with
astrological views. It is perhaps not worth our while here to
examine further the steps of this process; it would be difficult to
determine with certainty why the former order of the planets was
adopted, and how and why the latter was deduced from it. But there
is something very remarkable in the universality of the notions,
apparently so fantastic, which have produced this result; and we may
probably consider the Week, with Laplace,[37\3] as "the most ancient
monument of astronomical knowledge." This period has gone on without
interruption or irregularity from the earliest recorded times to our
own days, traversing the extent of ages and the revolutions of
empires; the names of the ancient deities which were associated with
the stars have been replaced by those of the objects of the worship
of our Teutonic ancestors, according to their views of the
correspondence of the two mythologies; and the Quakers, in rejecting
these names of days, have cast aside the most ancient existing relic
of astrological as well as idolatrous superstition.

[Note 36\3: _Philol. Mus._ No. 1.]

[Note 37\3: _Hist. Ast._ p. 17.]


_Sect._ 8.--_The Circles of the Sphere._

THE inventions hitherto noticed, though undoubtedly they were steps
in astronomical knowledge, can hardly be considered as purely
abstract and scientific speculations; for the exact reckoning of
time is one of {129} the wants, even of the least civilized nations.
But the distribution of the places and motions of the heavenly
bodies by means of a celestial sphere with imaginary lines drawn
upon it, is a step in _speculative_ astronomy, and was occasioned
and rendered important by the scientific propensities of man.

It is not easy to say with whom this notion originated. Some parts
of it are obvious. The appearance of the sky naturally suggests the
idea of a concave Sphere, with the stars fixed on its surface. Their
motions during any one night, it would be readily seen, might be
represented by supposing this Sphere to turn round a Pole or Axis;
for there is a conspicuous star in the heavens which apparently
stands still (the Pole-star); all the others travel round this in
circles, and keep the same positions with respect to each other.
This stationary star is every night the same, and in the same place;
the other stars also have the same relative position; but their
general position at the same time of night varies gradually from
night to night, so as to go through its cycle of appearances once a
year. All this would obviously agree with the supposition that the
sky is a concave sphere or dome, that the stars have fixed places on
this sphere, and that it revolves perpetually and uniformly about
the Pole or fixed point.

But this supposition does not at all explain the way in which the
appearances of different nights succeed each other. This, however,
may be explained, it appears, by supposing the _sun_ also _to move
among the stars_ on the surface of the concave sphere. The sun by
his brightness makes the stars invisible which are on his side of
the heavens: this we can easily believe; for the moon, when bright,
also puts out all but the largest stars; and we see the stars
appearing in the evening, each in its place, according to their
degree of splendor, as fast as the declining light of day allows
them to become visible. And as the sun brings day, and his absence
night, if he move through the circuit of the stars in a year, we
shall have, in the course of that time, every part of the starry
sphere in succession presented to us as our nocturnal sky.

This notion, _that the sun moves round among the stars in a year_,
is the basis of astronomy, and a considerable part of the science is
only the development and particularization of this general
conception. It is not easy to ascertain either the exact method by
which the path of the sun among the stars was determined, or the
author and date of the discovery. That there is some difficulty in
tracing the course of the sun among the stars will be clearly seen,
when it is considered that no {130} star can ever be seen at the
same time with the sun. If the whole circuit of the sky be divided
into twelve parts or _signs_, it is estimated by Autolycus, the
oldest writer on these subjects whose works remain to us,[38\3] that
the stars which occupy one of these parts are absorbed by the solar
rays, so that they cannot be seen. Hence the stars which are seen
nearest to the place of the setting and the rising sun in the
evening and in the morning, are distant from him by the half of a
sign: the evening stars being to the west, and the morning stars to
the east of him. If the observer had previously obtained a knowledge
of the places of all the principal stars, he might in this way
determine the position of the sun each night, and thus trace his
path in a year.

[Note 38\3: Delamb. _A. A._ p. xiii.]

In this, or some such way, the sun's path was determined by the
early astronomers of Egypt. Thales, who is mentioned as the father
of Greek astronomy, probably learnt among the Egyptians the results
of such speculations, and introduced them into his own country. His
knowledge, indeed, must have been a great deal more advanced than
that which we are now describing, if it be true, as is asserted,
that he predicted an eclipse. But his having done so is not very
consistent with what we are told of the steps which his successors
had still to make.

The Circle of the Signs, in which the sun moves among the stars, is
obliquely situated with regard to the circles in which the stars
move about the poles. Pliny[39\3] states that Anaximander,[40\3] a
scholar of Thales, was the first person who pointed out this
obliquity, and thus, as he says, "opened the gate of nature."
Certainly, the person who first had a clear view of the nature of
the sun's path in the celestial sphere, made that step which led to
all the rest; but it is difficult to conceive that the Egyptians and
Chaldeans had not already advanced so far.

[Note 39\3: Lib. ii. c. (viii.)]

[Note 40\3: Plutarch, _De Plac. Phil._ lib. ii. cap. xii. says
Pythagoras was the author of this discovery.]

The diurnal motion of the celestial sphere, and the motion of the
moon in the circle of the signs, gave rise to a mathematical
science, _the Doctrine of the Sphere_, which was one of the earliest
branches of applied mathematics. A number of technical conceptions
and terms were soon introduced. The _Sphere_ of the heavens was
conceived to be complete, though we see but a part of it; it was
supposed to turn about the visible _pole_ and another pole opposite
to this, and these poles were connected by an imaginary _Axis_. The
circle which divided the sphere exactly midway between these poles
was called the _Equator_ (ἰσημέρινος). {131} The two circles
parallel to this which bounded the sun's path among the stars were
called _Tropics_ (τροπικαί), because the sun _turns_ back again
towards the equator when he reaches them. The stars which never set
are bounded by a circle called the _Arctic Circle_ (ἄρκτικος, from
ἄρκτος, the Bear, the constellation to which some of the principal
stars within that circle belong.) A circle about the opposite pole
is called _Antarctic_, and the stars which are within it can never
rise to us.[41\3] The sun's path or circle of the signs is called
the _Zodiac_, or circle of animals; the points where this circle
meets the equator are the _Equinoctial Points_, the days and nights
being equal when the sun is in them; the _Solstitial Points_ are
those where the sun's path touches the tropics; his motion to the
south or to the north ceases when he is there, and he appears in
that respect to stand still. The _Colures_ (κόλουροι, mutilated) are
circles which pass through the poles and through the equinoctial and
solstitial points; they have their name because they are only
visible in part, a portion of them being below the horizon.

[Note 41\3: The Arctic and Antarctic Circles of modern astronomers
are different from these.]

The _Horizon_ (ὁρίζων) is commonly understood as the boundary of the
visible earth and heaven. In the doctrine of the sphere, this
boundary is _a great circle_, that is, a circle of which the plane
passes through the centre of the sphere; and, therefore, an entire
hemisphere is always above the horizon. The term occurs for the
first time in the work of Euclid, called _Phænomena_ (Φαινόμενα). We
possess two treatises written by Autolycus[42\3] (who lived about
300 B. C.) which trace _deductively_ the results of the doctrine of
the sphere. Supposing its diurnal motion to be uniform, in a work
entitled Περὶ Κινουμένης Σφαῖρας, "On the Moving Sphere," he
demonstrates various properties of the diurnal risings, settings,
and motions of the stars. In another work, Περὶ Ἐπιτολῶν καὶ Δύσεων,
"On Risings and Settings,"[43\3] _tacitly_ assuming the sun's motion
in his circle to be uniform, he proves certain propositions, with
regard to those risings and settings of the stars, which take place
at the same time when the sun rises and sets,[44\3] or _vice
versâ_;[45\3] and also their _apparent_ risings and settings when
they cease to be visible after sunset, or begin to be visible after
sunrise.[46\3] {132} Several of the propositions contained in the
former of these treatises are still necessary to be understood, as
fundamental parts of astronomy.

[Note 42\3: Delambre, _Astron. Ancienne_, p. 19.]

[Note 43\3: Delambre, _Astron. Anc._ p. 25.]

[Note 44\3: _Cosmical_ rising and setting.]

[Note 45\3: _Acronycal_ rising and setting; (ἀκρονυκίος, happening
at the extremity of the night.)]

[Note 46\3: _Heliacal_ rising and setting.]

The work of Euclid, just mentioned, is of the same kind.
Delambre[47\3] finds in it evidence that Euclid was merely a
book-astronomer, who had never observed the heavens.

[Note 47\3: _Ast. Anc._ p. 53.]

We may here remark the first instance of that which we shall find
abundantly illustrated in every part of the history of science; that
man is _prone_ to become a deductive reasoner;--that as soon as he
obtains principles which can be traced to details by logical
consequence, he sets about forming a body of science, by making a
system of such reasonings. Geometry has always been a favorite mode
of exercising this propensity: and that science, along with
Trigonometry, Plane and Spherical, to which the early problems of
astronomy gave rise, have, up to the present day, been a constant
field for the exercise of mathematical ingenuity; a few simple
astronomical truths being assumed as the basis of the reasoning.


_Sect._ 9.--_The Globular Form of the Earth._

THE establishment of the globular form of the earth is an important
step in astronomy, for it is the first of those convictions,
directly opposed to the apparent evidence of the senses, which
astronomy irresistibly proves. To make men believe that _up_ and
_down_ are different directions in different places; that the sea,
which seems so level, is, in fact, convex; that the earth, which
appears to rest on a solid foundation, is, in fact, not supported at
all; are great triumphs both of the power of discovering and the
power of convincing. We may readily allow this, when we recollect
how recently the doctrine of the _antipodes_, or the existence of
inhabitants of the earth, who stand on the opposite side of it, with
their feet turned towards ours, was considered both monstrous and
heretical.

Yet the different positions of the horizon at different places,
necessarily led the student of spherical astronomy towards this
notion of the earth as a round body. Anaximander[48\3] is said by
some to have held the earth to be globular, and to be detached or
suspended; he is also stated to have constructed a sphere, on which
were shown the extent of land and water. As, however, we do not know
the arguments upon which he maintained the earth's globular form, we
cannot judge of the {133} value of his opinion; it may have been no
better founded than a different opinion ascribed to him by Laertius,
that the earth had the shape of a pillar. Probably, the authors of
the doctrine of the globular form of the earth were led to it, as we
have said, by observing the different height of the pole at
different places. They would find that the space which they passed
over from north to south on the earth, was proportional to the
change of place of the horizon in the celestial sphere; and as the
horizon is, at every place, in the direction of the earth's
apparently level surface, this observation would naturally suggest
to them the opinion that the earth is placed within the celestial
sphere, as a small globe in the middle of a much larger one.

[Note 48\3: See Brucker, _Hist. Phil._ vol. i. p. 486.]

We find this doctrine so distinctly insisted on by Aristotle, that we
may almost look on him as the establisher of it.[49\3] "As to the
figure of the earth, it must necessarily be spherical." This he
proves, first by the tendency of things, in all places, downwards. He
then adds,[50\3] "And, moreover, from the phenomena according to the
sense: for if it were not so, the eclipses of the moon would not have
such sections as they have. For in the configurations in the course of
a month, the deficient part takes all different shapes; it is
straight, and concave, and convex; but in eclipses it always has the
line of division convex; wherefore, since the moon is eclipsed in
consequence of the interposition of the earth, the periphery of the
earth must be the cause of this by having a spherical form. And again,
from the appearances of the stars, it is clear, not only that the
earth is round, but that its size is not very large: for when we make
a small removal to the south or the north, the circle of the horizon
becomes palpably different, so that the stars overhead undergo a great
change, and are not the same to those that travel to the north and to
the south. For some stars are seen in Egypt or at Cyprus, but are not
seen in the countries to the north of these; and the stars that in the
north are visible while they make a complete circuit, there undergo a
setting. So that from this it is manifest, not only that the form of
the earth is round, but also that it is a part of not a very large
sphere: for otherwise the difference would not be so obvious to
persons making so small a change of place. Wherefore we may judge that
those persons _who connect the region in the neighborhood of the
pillars of Hercules with that towards India, and who assert that in
this way the sea is_ ONE, do not assert things very improbable. They
confirm this conjecture moreover by the {134} elephants, which are
said to be of the same species (γένος) towards each extreme; as if
this circumstance was a consequence of the conjunction of the
extremes. The mathematicians, who try to calculate the measure of the
circumference, make it amount to 400,000 stadia; whence we collect
that the earth is not only spherical, but is not large compared with
the magnitude of the other stars."

[Note 49\3: Arist. _de Cœlo_, lib. ii. cap. xiv. ed. Casaub. p.
290.]

[Note 50\3: p. 291 C.]

When this notion was once suggested, it was defended and confirmed
by such arguments as we find in later writers: for instance,[51\3]
that the tendency of all things was to fall to the place of heavy
bodies, and that this place being the centre of the earth, the whole
earth had no such tendency; that the inequalities on the surface
were so small as not materially to affect the shape of so vast a
mass; that drops of water naturally form themselves into figures
with a convex surface; that the end of the ocean would fall if it
were not rounded off; that we see ships, when they go out to sea,
disappearing downwards, which shows the surface to be convex. These
are the arguments still employed in impressing the doctrines of
astronomy upon the student of our own days; and thus we find that,
even at the early period of which we are now speaking, truths had
begun to accumulate which form a part of our present treasures.

[Note 51\3: Pliny, _Nat. Hist._ ii. LXV.]


_Sect._ 10.--_The Phases of the Moon._

WHEN men had formed a steady notion of the Moon as a solid body,
revolving about the earth, they had only further to conceive it
spherical, and to suppose the sun to be beyond the region of the
moon, and they would find that they had obtained an explanation of
the varying forms which the bright part of the moon assumes in the
course of a month. For the convex side of the crescent-moon, and her
full edge when she is gibbous, are always turned towards the sun.
And this explanation, once suggested, would be confirmed, the more
it was examined. For instance, if there be near us a spherical
stone, on which the sun is shining, and if we place ourselves so
that this stone and the moon are seen in the same direction (the
moon appearing just over the top of the stone), we shall find that
the visible part of the stone, which is then illuminated by the sun,
is exactly similar in form to the moon, at whatever period of her
changes she may be. The stone and the moon being in the same
position with respect to us, and both being enlightened by the sun,
the bright parts are the same in figure; {135} the only difference
is, that the dark part of the moon is usually not visible at all.

This doctrine is ascribed to Anaximander. Aristotle was fully aware
of it.[52\3] It could not well escape the Chaldeans and Egyptians,
if they speculated at all about the causes of the appearances in the
heavens.

[Note 52\3: Probl. Cap. XV. Art. 7.]


_Sect._ 11.--_Eclipses._

ECLIPSES of the sun and moon were from the earliest tunes regarded
with a peculiar interest. The notions of superhuman influences and
relations, which, as we have seen, were associated with the
luminaries of the sky, made men look with alarm at any sudden and
striking change in those objects; and as the constant and steady
course of the celestial revolutions was contemplated with a feeling
of admiration and awe, any marked interruption and deviation in this
course, was regarded with surprise and terror. This appears to be
the case with all nations at an early stage of their civilization.

This impression would cause Eclipses to be noted and remembered; and
accordingly we find that the records of Eclipses are the earliest
astronomical information which we possess. When men had discovered
some of the laws of succession of other astronomical phenomena, for
instance, of the usual appearances of the moon and sun, it might
then occur to them that these unusual appearances also might
probably be governed by some rule.

The search after this rule was successful at an early period. The
Chaldeans were able to predict Eclipses of the Moon. This they did,
probably, by means of their Cycle of 223 months, or about 18 years;
for at the end of this time, the eclipses of the moon begin to return,
at the same intervals and in the same order as at the beginning.[53\3]
Probably this was the first instance of the prediction of peculiar
astronomical phenomena. The Chinese have, indeed, a legend, in which
it is related that a solar eclipse happened in the reign of
Tchongkang, above 2000 years before Christ, and that the emperor was
so much irritated against two great officers of state, who had
neglected to predict this eclipse, that he put them to death. But this
cannot be accepted as a real event: for, during the next ten
centuries, we find no single observation or fact connected with
astronomy in the Chinese {136} histories; and their astronomy has
never advanced beyond a very rude and imperfect condition.

[Note 53\3: The eclipses of the sun are more difficult to calculate;
since they depend upon the place of the spectator on the earth.]

We can only conjecture the mode in which the Chaldeans discovered
their Period of 18 years; and we may make very different
suppositions with regard to the degree of science by which they were
led to it. We may suppose, with Delambre,[54\3] that they carefully
recorded the eclipses which happened, and then, by the inspection of
their registers, discovered that those of the moon recurred after a
certain period. Or we may suppose, with other authors, that they
sedulously determined the motions of the moon, and having obtained
these with considerable accuracy, sought and found a period which
should include cycles of these motions. This latter mode of
proceeding would imply a considerable degree of knowledge.

[Note 54\3: _A. A._ p. 212.]

It appears probable rather that such a period was discovered by
noticing the _recurrence_ of eclipses, than by studying the moon's
_motions_. After 6585⅓ days, or 223 lunations, the same eclipses
nearly will recur. It is not contested that the Chaldeans were
acquainted with this period, which they called _Saros_; or that they
calculated eclipses by means of it.


_Sect._ 12.--_Sequel to the Early Stages of Astronomy._

EVERY stage of science has its train of practical applications and
systematic inferences, arising both from the demands of convenience
and curiosity, and from the pleasure which, as we have already said,
ingenuous and active-minded men feel in exercising the process of
deduction. The earliest condition of astronomy, in which it can be
looked upon as a science, exhibits several examples of such
applications and inferences, of which we may mention a few.

_Prediction of Eclipses._--The Cycles which served to keep in order
the Calendar of the early nations of antiquity, in some instances
enabled them also, as has just been stated, to predict Eclipses; and
this application of knowledge necessarily excited great notice.
Cleomedes, in the time of Augustus, says, "We never see an eclipse
happen which has not been predicted by those who made use of the
Tables." (ὑπὸ τῶν κανονικῶν.)

_Terrestrial Zones._--The globular form of the earth being assented
to, the doctrine of the sphere was applied to the earth as well as
the heavens; and the earth's surface was divided by various
imaginary {137} circles; among the rest, the equator, the tropics,
and circles, at the same distance from the poles as the tropics are
from the equator. One of the curious consequences of this division
was the _assumption_ that there must be some marked difference in
the stripes or _zones_ into which the earth's surface was thus
divided. In going to the south, Europeans found countries hotter and
hotter, in going to the north, colder and colder; and it was
supposed that the space between the tropical circles must be
uninhabitable from heat, and that within the polar circles, again,
uninhabitable from cold. This fancy was, as we now know, entirely
unfounded. But the principle of the globular form of the earth, when
dealt with by means of spherical geometry, led to many true and
important propositions concerning the lengths of days and nights at
different places. These propositions still form a part of our
Elementary Astronomy.

_Gnomonic._--Another important result of the doctrine of the sphere
was _Gnomonic_ or _Dialling_. Anaximenes is said by Pliny to have
first taught this art in Greece; and both he and Anaximander are
reported to have erected the first dial at Lacedemon. Many of the
ancient dials remain to us; some of these are of complex forms, and
must have required great ingenuity and considerable geometrical
knowledge in their construction.

_Measure of the Sun's Distance._--The explanation of the phases of the
moon led to no result so remarkable as the attempt of Aristarchus of
Samos to obtain from this doctrine a measure of the Distance of the
Sun as compared with that of the Moon. If the moon was a perfectly
smooth sphere, when she was exactly midway between the new and full in
position (that is, a quadrant from the sun), she would be somewhat
more than a half moon; and the place when she was _dichotomized_, that
is, was an exact semicircle, the bright part being bounded by a
straight line, would depend upon the sun's distance from the earth.
Aristarchus endeavored to fix the exact place of this Dichotomy; but
the irregularity of the edge which bounds the bright part of the moon,
and the difficulty of measuring with accuracy, by means then in use,
either the precise time when the boundary was most nearly a straight
line, or the exact distance of the moon from the sun at that time,
rendered his conclusion false and valueless. He collected that the sun
is at 18 times the distance of the moon from us; we now know that he
is at 400 times the moon's distance.

It would be easy to dwell longer on subjects of this kind; but we
have already perhaps entered too much in detail. We have been {138}
tempted to do this by the interest which the mathematical spirit of
the Greeks gave to the earliest astronomical discoveries, when these
were the subjects of their reasonings; but we must now proceed to
contemplate them engaged in a worthier employment, namely, in adding
to these discoveries.




CHAPTER II.

PRELUDE TO THE INDUCTIVE EPOCH OF HIPPARCHUS.


WITHOUT pretending that we have exhausted the consequences of the
elementary discoveries which we have enumerated, we now proceed to
consider the nature and circumstances of the next great discovery
which makes an Epoch in the history of Astronomy; and this we shall
find to be the Theory of Epicycles and Eccentrics. Before, however,
we relate the establishment of this theory, we must, according to
the general plan we have marked out, notice some of the conjectures
and attempts by which it was preceded, and the growing acquaintance
with facts, which made the want of such an explanation felt.

In the steps previously made in astronomical knowledge, no ingenuity
had been required to devise the view which was adopted. The motions of
the stars and sun were most naturally and almost irresistibly
conceived as the results of motion in a revolving sphere; the
indications of position which we obtain from different places on the
earth's surface, when clearly combined, obviously imply a globular
shape. In these cases, the first conjectures, the supposition of the
simplest form, of the most uniform motion, required no
after-correction. But this manifest simplicity, this easy and obvious
explanation, did not apply to the movement of all the heavenly bodies.
The Planets, the "wandering stars," could not be so easily understood;
the motion of each, as Cicero says, "undergoing very remarkable
changes in its course, going before and behind, quicker and slower,
appearing in the evening, but gradually lost there, and emerging again
in the morning."[55\3] A continued attention to these stars would,
however, {139} detect a kind of intricate regularity in their motions,
which might naturally be described as "a dance." The Chaldeans are
stated by Diodorus[56\3] to have observed assiduously the risings and
settings of the planets, from the top of the temple of Belus. By doing
this, they would find the times in which the forward and backward
movements of Saturn, Jupiter, and Mars recur; and also the time in
which they come round to the same part of the heavens.[57\3] Venus and
Mercury never recede far from the sun, and the intervals which elapse
while either of them leaves its greatest distance from the sun and
returns again to the greatest distance on the same side, would easily
be observed.

[Note 55\3: Cic. _de Nat. D._ lib. ii. p. 450. "Ea quæ Saturni
stella dicitur, φαίνωνque a Græcis nominatur, quæ a terra abest
plurimum, xxx fere annis cursum suum conficit; in quo cursu multa
mirabiliter efficiens, tum antecedendo, tum retardando, tum
vespertinis temporibus delitescendo, tum matutinis se rursum
aperiendo, nihil immutat sempiternis sæculorum ætatibus, quin eadem
iisdem temporibus efficiat." And so of the other planets.]

[Note 56\3: _A. A._ i. p. 4.]

[Note 57\3: Plin. _H. N._ ii. p. 204.]

Probably the manner in which the motions of the planets were
originally reduced to rule was something like the following:--In
about 30 of our years, Saturn goes 29 times through his _Anomaly_,
that is, the succession of varied motions by which he sometimes goes
forwards and sometimes backwards among the stars. During this time,
he goes once round the heavens, and returns nearly to the same
place. This is the cycle of his apparent motions.

Perhaps the eastern nations contented themselves with thus referring
these motions to cycles of time, so as to determine their recurrence.
Something of this kind was done at an early period, as we have seen.

But the Greeks soon attempted to frame to themselves a sensible image
of the mechanism by which these complex motions were produced; nor did
they find this difficult. Venus, for instance, who, upon the whole,
moves from west to east among the stars, is seen, at certain
intervals, to return or move _retrograde_ a short way back from east
to west, then to become for a short time _stationary_, then to turn
again and resume her _direct_ motion westward, and so on. Now this can
be explained by supposing that she is placed in the rim of a wheel,
which is turned edgeways to us, and of which the centre turns round in
the heavens from west to east, while the wheel, carrying the planet in
its motion, moves round its own centre. In this way the motion of the
wheel about its centre, would, in some situations, counterbalance the
general motion of the centre, and make the planet retrograde, while,
on the whole, the westerly motion would prevail. Just as if we suppose
that a person, holding a lamp in his hand in the dark, and at a {140}
distance, so that the lamp alone is visible, should run on turning
himself round; we should see the light sometimes stationary, sometimes
retrograde, but on the whole progressive.

A mechanism of this kind was imagined for each of the planets, and the
wheels of which we have spoken were in the end called _Epicycles_.

The application of such mechanism to the planets appears to have
arisen in Greece about the time of Aristotle. In the works of Plato we
find a strong taste for this kind of mechanical speculation. In the
tenth book of the "Polity," we have the apologue of Alcinus the
Pamphylian, who, being supposed to be killed in battle, revived when
he was placed on the funeral pyre, and related what he had seen during
his trance. Among other revelations, he beheld the machinery by which
all the celestial bodies revolve. The axis of these revolutions is the
adamantine distaff which Destiny holds between her knees; on this are
fixed, by means of different sockets, flat rings, by which the planets
are carried. The order and magnitude of these spindles are minutely
detailed. Also, in the "Epilogue to the Laws" (_Epinomis_), he again
describes the various movements of the sky, so as to show a distinct
acquaintance with the general character of the planetary motions; and,
after speaking of the Egyptians and Syrians as the original
cultivators of such knowledge, he adds some very remarkable
exhortations to his countrymen to prosecute the subject. "Whatever we
Greeks," he says, "receive from the barbarians, we improve and
perfect; there is good hope and promise, therefore, that Greeks will
carry this knowledge far beyond that which was introduced from
abroad." To this task, however, he looks with a due appreciation of
the qualities and preparation which it requires. "An astronomer must
be," he says, "the wisest of men; his mind must be duly disciplined in
youth; especially is mathematical study necessary; both an
acquaintance with the doctrine of number, and also with that other
branch of mathematics, which, closely connected as it is with the
science of the _heavens_, we very absurdly call _geometry_, the
measurement of the _earth_."[58\3]

[Note 58\3: _Epinomis_, pp. 988, 990.]

Those anticipations were very remarkably verified in the subsequent
career of the Greek Astronomy.

The theory, once suggested, probably made rapid progress.
Simplicius[59\3] relates, that Eudoxus of Cnidus introduced the
hypothesis of revolving circles or spheres. Calippus of Cyzicus,
having visited {141} Polemarchus, an intimate friend of Eudoxus,
they went together to Athens, and communicated to Aristotle the
invention of Eudoxus, and with his help improved and corrected it.

[Note 59\3: Lib. ii. _de Cœlo_. Bullialdus, p. 18.]

Probably at first this hypothesis was applied only to account for
the general phenomena of the progressions, retrogradations, and
stations of the planet; but it was soon found that the motions of
the sun and moon, and the circular motions of the planets, which the
hypothesis supposed, had other _anomalies_ or irregularities, which
made a further extension of the hypothesis necessary.

The defect of uniformity in these motions of the sun and moon,
though less apparent than in the planets, is easily detected, as
soon as men endeavor to obtain any accuracy in their observations.
We have already stated (Chap. I.) that the Chaldeans were in
possession of a period of about eighteen years, which they used in
the calculation of eclipses, and which might have been discovered by
close observation of the moon's motions; although it was probably
rather hit upon by noting the recurrence of eclipses. The moon moves
in a manner which is not reducible to regularity without
considerable care and time. If we trace her path among the stars, we
find that, like the path of the sun, it is oblique to the equator,
but it does not, like that of the sun, pass over the same stars in
successive revolutions. Thus its _latitude_, or distance from the
equator, has a cycle different from its revolution among the stars;
and its _Nodes_, or the points where it cuts the equator, are
perpetually changing their position. In addition to this, the moon's
motion in her own path is not uniform; in the course of each
lunation, she moves alternately slower and quicker, passing
gradually through the intermediate degrees of velocity; and goes
through the cycle of these changes in something less than a month;
this is called a revolution of _Anomaly_. When the moon has gone
through a complete number of revolutions of Anomaly, and has, in the
same time, returned to the same position with regard to the sun, and
also with regard to her Nodes, her motions with respect to the sun
will thenceforth be the same as at the first, and all the
circumstances on which lunar eclipses depend being the same, the
eclipses will occur in the same order. In 6585⅓ days there are 239
revolutions of anomaly, 241 revolutions with regard to one of the
Nodes, and, as we have said, 223 lunations or revolutions with
regard to the sun. Hence this Period will bring about a succession
of the same lunar eclipses.

If the Chaldeans observed the moon's motion among the stars with any
considerable accuracy, so as to detect this period by that means,
{142} they could hardly avoid discovering the anomaly or unequal
motion of the moon; for in every revolution, her daily progression
in the heavens varies from about twenty-two to twenty-six times her
own diameter. But there is not, in their knowledge of this Period,
any evidence that they had measured the amount of this variation;
and Delambre[60\3] is probably right in attributing all such
observations to the Greeks.

[Note 60\3: _Astronomie Ancienne_, i. 212.]

The sun's motion would also be seen to be irregular as soon as men
had any exact mode of determining the lengths of the four seasons,
by means of the passage of the sun through the equinoctial and
solstitial points. For spring, summer, autumn, and winter, which
would each consist of an equal number of days if the motions were
uniform, are, in fact, found to be unequal in length.

It was not very difficult to see that the mechanism of epicycles
might be applied so as to explain irregularities of this kind. A
wheel travelling round the earth, while it revolved upon its centre,
might produce the effect of making the sun or moon fixed in its rim
go sometimes faster and sometimes slower in appearance, just in the
same way as the same suppositions would account for a planet going
sometimes forwards and sometimes backwards: the epicycles of the sun
and moon would, for this purpose, be less than those of the planets.
Accordingly, it is probable that, at the time of Plato and
Aristotle, philosophers were already endeavoring to apply the
hypothesis to these cases, though it does not appear that any one
fully succeeded before Hipparchus.

The problem which was thus present to the minds of astronomers, and
which Plato is said to have proposed to them in a distinct form,
was, "To reconcile the celestial phenomena by the combination of
equable circular motions." That the circular motions should be
equable as well as circular, was a condition, which, if it had been
merely tried at first, as the most simple and definite conjecture,
would have deserved praise. But this condition, which is, in
reality, inconsistent with nature, was, in the sequel, adhered to
with a pertinacity which introduced endless complexity into the
system. The history of this assumption is one of the most marked
instances of that love of simplicity and symmetry which is the
source of all general truths, though it so often produces and
perpetuates error. At present we can easily see how fancifully the
notion of simplicity and perfection was interpreted, in the
arguments by which the opinion was defended, that the {143} real
motions of the heavenly bodies must be circular and uniform. The
Pythagoreans, as well as the Platonists, maintained this dogma.
According to Geminus, "They supposed the motions of the sun, and the
moon, and the five planets, to be circular and equable: for they
would not allow of such disorder among divine and eternal things, as
that they should sometimes move quicker, and sometimes slower, and
sometimes stand still; for no one would tolerate such anomaly in the
movements, even of a man, who was decent and orderly. The occasions
of life, however, are often reasons for men going quicker or slower,
but in the incorruptible nature of the stars, it is not possible
that any cause can be alleged of quickness and slowness. Whereupon
they propounded this question, how the phenomena might be
represented by equable and circular motions."

These conjectures and assumptions led naturally to the establishment
of the various parts of the Theory of Epicycles. It is probable that
this theory was adopted with respect to the Planets at or before the
time of Plato. And Aristotle gives us an account of the system thus
devised.[61\3] "Eudoxus," he says, "attributed four spheres to each
Planet: the first revolved with the fixed stars (and this produced
the diurnal motion); the second gave the planet a motion along the
ecliptic (the mean motion in longitude); the third had its axis
perpendicular[62\3] to the ecliptic (and this gave the inequality of
each planetary motion, really arising from its special motion about
the sun); the fourth produced the oblique motion transverse to this
(the motion in latitude)." He is also said to have attributed a
motion in latitude and a corresponding sphere to the Sun as well as
to the Moon, of which it is difficult to understand the meaning, if
Aristotle has reported rightly of the theory; for it would be absurd
to ascribe to Eudoxus a knowledge of the motions by which the sun
deviates from the ecliptic. Calippus conceived that two additional
spheres must be given to the sun and to the moon, in order to
explain the phenomena: probably he was aware of the inequalities of
the motions of these luminaries. He also proposed an additional
sphere for each planet, to account, we may suppose, for the results
of the eccentricity of the orbits.

[Note 61\3: Metaph. xi. 8.]

[Note 62\3: Aristotle says "has its poles in the ecliptic," but this
must be a mistake of his. He professes merely to receive these
opinions from the mathematical astronomers, "ἐκ τῆς οἰκειοτάτης
φιλοσοφίας τῶν μαθηματικῶν."]

The hypothesis, in this form, does not appear to have been reduced
to measure, and was, moreover, unnecessarily complex. The resolution
{144} of the oblique motion of the moon into two separate motions,
by Eudoxus, was not the simplest way of conceiving it; and Calippus
imagined the connection of these spheres in some way which made it
necessary nearly to double their number; in this manner his system
had no less than 55 spheres.

Such was the progress which the _Idea_ of the hypothesis of
epicycles had made in men's minds, previously to the establishment
of the theory by Hipparchus. There had also been a preparation for
this step, on the other side, by the collection of _Facts_. We know
that observations of the Eclipses of the Moon were made by the
Chaldeans 367 B. C. at Babylon, and were known to the Greeks; for
Hipparchus and Ptolemy founded their Theory of the Moon on these
observations. Perhaps we cannot consider, as equally certain, the
story that, at the time of Alexander's conquest, the Chaldeans
possessed a series of observations, which went back 1903 years, and
which Aristotle caused Callisthenes to bring to him in Greece. All
the Greek observations which are of any value, begin with the school
of Alexandria. Aristyllus and Timocharis appear, by the citations of
Hipparchus, to have observed the Places of Stars and Planets, and
the Times of the Solstices, at various periods from B. C. 295 to B.
C. 269. Without their observations, indeed, it would not have been
easy for Hipparchus to establish either the Theory of the Sun or the
Precession of the Equinoxes.

In order that observations at distant intervals may be compared with
each other, they must be referred to some common era. The Chaldeans
dated by the era of Nabonassar, which commenced 749 B. C. The Greek
observations were referred to the Calippic periods of 76 years, of
which the first began 331 B. C. These are the dates used by
Hipparchus and Ptolemy. {145}




CHAPTER III.

INDUCTIVE EPOCH OF HIPPARCHUS.


_Sect._ 1.--_Establishment of the Theory of Epicycles and
Eccentrics._

ALTHOUGH, as we have already seen, at the time of Plato, the Idea of
Epicycles had been suggested, and the problem of its general
application proposed, and solutions of this problem offered by his
followers; we still consider Hipparchus as the real discoverer and
founder of that theory; inasmuch as he not only guessed that it
_might_, but showed that it _must_, account for the phenomena, both
as to their nature and as to their quantity. The assertion that "he
only discovers who proves," is just; not only because, until a
theory is proved to be the true one, it has no pre-eminence over the
numerous other guesses among which it circulates, and above which
the proof alone elevates it; but also because he who takes hold of
the theory so as to apply calculation to it, possesses it with a
distinctness of conception which makes it peculiarly his.

In order to establish the Theory of Epicycles, it was necessary to
assign the magnitudes, distances, and positions of the circles or
spheres in which the heavenly bodies were moved, in such a manner as
to account for their apparently irregular motions. We may best
understand what was the problem to be solved, by calling to mind
what we now know to be the real motions of the heavens. The true
motion of the earth round the sun, and therefore the apparent annual
motion of the sun, is performed, not in a circle of which the earth
is the centre, but in an ellipse or oval, the earth being nearer to
one end than to the other; and the motion is most rapid when the sun
is at the nearer end of this oval. But instead of an oval, we may
suppose the sun to move uniformly in a circle, the earth being now,
not in the centre, but nearer to one side; for on this supposition,
the sun will appear to move most quickly when he is nearest to the
earth, or in his _Perigee_, as that point is called. Such an orbit
is called an _Eccentric_, and the distance of the earth from the
centre of the circle is called the _Eccentricity_. It may easily be
shown by geometrical reasoning, that the inequality of apparent
motion so produced, is exactly the same in {146} detail, as the
inequality which follows from the hypothesis of a small _Epicycle_,
turning uniformly on its axis, and carrying the sun in its
circumference, while the centre of this epicycle moves uniformly in
a circle of which the earth is the centre. This identity of the
results of the hypothesis of the Eccentric and the Epicycle is
proved by Ptolemy in the third book of the "Almagest."

_The Sun's Eccentric._--When Hipparchus had clearly conceived these
hypotheses, as _possible_ ways of accounting for the sun's motion,
the task which he had to perform, in order to show that they
deserved to be adopted, was to assign a place to the _Perigee_, a
magnitude to the _Eccentricity_, and an _Epoch_ at which the sun was
at the perigee; and to show that, in this way, he had produced a
true representation of the motions of the sun. This, accordingly, he
did; and having thus determined, with considerable exactness, both
the law of the solar irregularities, and the numbers on which their
amount depends, he was able to assign the motions and places of the
sun for any moment of future time with corresponding exactness; he
was able, in short, to construct _Solar Tables_, by means of which
the sun's place with respect to the stars could be correctly found
at any time. These tables (as they are given by Ptolemy)[63\3] give
the _Anomaly_, or inequality of the sun's motion; and this they
exhibit by means of the _Prosthapheresis_, the quantity of which, at
any distance of the sun from the _Apogee_, it is requisite to add to
or subtract from the arc, which he would have described if his
motion had been equable.

[Note 63\3: Syntax. 1. iii.]

The reader might perhaps expect that the calculations which thus
exhibited the motions of the sun for an indefinite future period
must depend upon a considerable number of observations made at all
seasons of the year. That, however, was not the case; and the genius
of the discoverer appeared, as such genius usually does appear, in
his perceiving how small a number of facts, rightly considered, were
sufficient to form a foundation for the theory. The number of days
contained in two seasons of the year sufficed for this purpose to
Hipparchus. "Having ascertained," says Ptolemy, "that the time from
the vernal equinox to the summer tropic is 94½ days, and the time
from the summer tropic to the autumnal equinox 92½ days, from these
phenomena alone he demonstrates that the straight line joining the
centre of the sun's eccentric path with the centre of the zodiac
(the spectator's eye) is nearly the 24th part of the radius of the
eccentric path; and that {147} its _apogee_ precedes the summer
solstice by 24½ degrees nearly, the zodiac containing 360."

The exactness of the Solar Tables, or _Canon_, which was founded on
these data, was manifested, not only by the coincidence of the sun's
calculated place with such observations as the Greek astronomers of
this period were able to make (which were indeed very rude), but by
its enabling them to calculate solar and lunar eclipses; phenomena
which are a very precise and severe trial of the accuracy of such
tables, inasmuch as a very minute change in the apparent place of
the sun or moon would completely alter the obvious features of the
eclipse. Though the tables of this period were by no means perfect,
they bore with tolerable credit this trying and perpetually
recurring test; and thus proved the soundness of the theory on which
the tables were calculated.

_The Moon's Eccentric._--The moon's motions have many
irregularities; but when the hypothesis of an Eccentric or an
Epicycle had sufficed in the case of the sun, it was natural to try
to explain, in the same way, the motions of the moon; and it was
shown by Hipparchus that such hypotheses would account for the more
obvious anomalies. It is not very easy to describe the several ways
in which these hypotheses were applied, for it is, in truth, very
difficult to explain in words even the mere facts of the moon's
motion. If she were to leave a visible bright line behind her in the
heavens wherever she moved, the path thus exhibited would be of an
extremely complex nature; the circle of each revolution slipping
away from the preceding, and the traces of successive revolutions
forming a sort of band of net-work running round the middle of the
sky.[64\3] In each revolution, the motion in longitude is affected
by an anomaly of the same nature as the sun's anomaly already spoken
of; but besides this, the path of the moon deviates from the
ecliptic to the north and to the south of the ecliptic, and thus she
has a motion in latitude. This motion in latitude would be
sufficiently known if we knew the period of its _restoration_, that
is, the time which the moon occupies in moving from any latitude
till she is restored to the same latitude; as, for instance, from
the ecliptic on one side of the heavens to the ecliptic on the same
side of the heavens again. But it is found that the period of the
restoration of the latitude is not the same as the period of the
restoration of the longitude, that is, as the period of the moon's
revolution among the {148} stars; and thus the moon describes a
different path among the stars in every successive revolution, and
her path, as well as her velocity, is constantly variable.

[Note 64\3: The reader will find an attempt to make the nature of
this path generally intelligible in the _Companion to the British
Almanac_ for 1814.]

Hipparchus, however, reduced the motions of the moon to rule and to
Tables, as he did those of the sun, and in the same manner. He
determined, with much greater accuracy than any preceding
astronomer, the mean or average equable motions of the moon in
longitude and in latitude; and he then represented the anomaly of
the motion in longitude by means of an eccentric, in the same manner
as he had done for the sun.

But here there occurred still an additional change, besides those of
which we have spoken. The Apogee of the Sun was always in the same
place in the heavens; or at least so nearly so, that Ptolemy could
detect no error in the place assigned to it by Hipparchus 250 years
before. But the Apogee of the Moon was found to have a motion among
the stars. It had been observed before the time of Hipparchus, that
in 6585⅓ days, there are 241 revolutions of the moon with regard to
the stars, but only 239 revolutions with regard to the anomaly. This
difference could be suitably represented by supposing the eccentric,
in which the moon moves, to have itself an angular motion,
perpetually carrying its apogee in the same direction in which the
moon travels; but this supposition being made, it was necessary to
determine, not only the eccentricity of the orbit, and place of the
apogee at a certain time, but also the rate of motion of the apogee
itself, in order to form tables of the moon.

This task, as we have said, Hipparchus executed; and in this instance,
as in the problem of the reduction of the sun's motion to tables, the
data which he found it necessary to employ were very few. He deduced
all his conclusions from six eclipses of the moon.[65\3] Three of
these, the records of which were brought from Babylon, where a
register of such occurrences was kept, happened in the 366th and 367th
years from the era of Nabonassar, and enabled Hipparchus to determine
the eccentricity and apogee of the moon's orbit at that time. The
three others were observed at Alexandria, in the 547th year of
Nabonassar, which gave him another position of the orbit at an
interval of 180 years; and he thus became acquainted with the motion
of the orbit itself, as well as its form.[66\3] {149}

[Note 65\3: Ptol. _Syn._ iv. 10.]

[Note 66\3: Ptolemy uses the hypothesis of an epicycle for the
moon's first inequality; but Hipparchus employs an eccentric.]

The moon's motions are really affected by several other
inequalities, of very considerable amount, besides those which were
thus considered by Hipparchus; but the lunar paths, constructed on
the above data, possessed a considerable degree of correctness, and
especially when applied, as they were principally, to the
calculation of eclipses; for the greatest of the additional
irregularities which we have mentioned disappear at new and full
moon, which are the only times when eclipses take place.

The numerical explanation of the motions of the sun and moon, by
means of the Hypothesis of Eccentrics, and the consequent
construction of tables, was one of the great achievements of
Hipparchus. The general explanation of the motions of the planets,
by means of the hypothesis of epicycles, was in circulation
previously, as we have seen. But the special motions of the planets,
in their epicycles, are, in reality, affected by anomalies of the
same kind as those which render it necessary to introduce eccentrics
in the cases of the sun and moon.

Hipparchus determined, with great exactness, the _Mean Motions_ of
the Planets; but he was not able, from want of data, to explain the
planetary _Irregularities_ by means of Eccentrics. The whole mass of
good observations of the planets which he received from preceding
ages, did not contain so many, says Ptolemy, as those which he has
transmitted to us of his own. "Hence[67\3] it was," he adds, "that
while he labored, in the most assiduous manner to represent the
motions of the sun and moon by means of equable circular motions;
with respect to the planets, so far as his works show, he did not
even make the attempt, but merely put the extant observations in
order, added to them himself more than the whole of what he received
from preceding ages, and showed the insufficiency of the hypothesis
current among astronomers to explain the phenomena." It appears that
preceding mathematicians had already pretended to construct "a
Perpetual Canon," that is, Tables which should give the places of
the planets at any future time; but these being constructed without
regard to the eccentricity of the orbits, must have been very
erroneous.

[Note 67\3: _Synt._ ix. 2.]

Ptolemy declares, with great reason, that Hipparchus showed his
usual love of truth, and his right sense of the responsibility of
his task, in leaving this part of it to future ages. The Theories of
the Sun and Moon, which we have already described, constitute him a
great astronomical discoverer, and justify the reputation he has
always {150} possessed. There is, indeed, no philosopher who is so
uniformly spoken of in terms of admiration. Ptolemy, to whom we owe
our principal knowledge of him, perpetually couples with his name
epithets of praise: he is not only an excellent and careful
observer, but "a[68\3] most truth-loving and labor-loving person,"
one who had shown extraordinary sagacity and remarkable desire of
truth in every part of science. Pliny, after mentioning him and
Thales, breaks out into one of his passages of declamatory
vehemence: "Great men! elevated above the common standard of human
nature, by discovering the laws which celestial occurrences obey,
and by freeing the wretched mind of man from the fears which
eclipses inspired--Hail to you and to your genius, interpreters of
heaven, worthy recipients of the laws of the universe, authors of
principles which connect gods and men!" Modern writers have spoken
of Hipparchus with the same admiration; and even the exact but
severe historian of astronomy, Delambre, who bestows his praise so
sparingly, and his sarcasm so generally;--who says[69\3] that it is
unfortunate for the memory of Aristarchus that his work has come to
us entire, and who cannot refer[70\3] to the statement of an eclipse
rightly predicted by Halicon of Cyzicus without adding, that if the
story be true, Halicon was more lucky than prudent;--loses all his
bitterness when he comes to Hipparchus.[71\3] "In Hipparchus," says
he, "we find one of the most extraordinary men of antiquity; the
_very greatest_, in the sciences which require a combination of
observation with geometry." Delambre adds, apparently in the wish to
reconcile this eulogium with the depreciating manner in which he
habitually speaks of all astronomers whose observations are inexact,
"a long period and the continued efforts of many industrious men are
requisite to produce good instruments, but energy and assiduity
depend on the man himself."

[Note 68\3: _Synt._ ix. 2.]

[Note 69\3: _Astronomie Ancienne_, i. 75.]

[Note 70\3: Ib. i. 17.]

[Note 71\3: Ib. i. 186.]

Hipparchus was the author of other great discoveries and
improvements in astronomy, besides the establishment of the Doctrine
of Eccentrics and Epicycles; but this, being the greatest advance in
the _theory_ of the celestial motions which was made by the
ancients, must be the leading subject of our attention in the
present work; our object being to discover in what the progress of
real theoretical knowledge consists, and under what circumstances it
has gone on. {151}


_Sect._ 2.--_Estimate of the Value of the Theory of Eccentrics and
Epicycles._

IT may be useful here to explain the value of the theoretical step
which Hipparchus thus made; and the more so, as there are, perhaps,
opinions in popular circulation, which might lead men to think
lightly of the merit of introducing or establishing the Doctrine of
Epicycles. For, in the first place, this doctrine is now
acknowledged to be false; and some of the greatest men in the more
modern history of astronomy owe the brightest part of their fame to
their having been instrumental in overturning this hypothesis. And,
moreover, in the next place, the theory is not only false, but
extremely perplexed and entangled, so that it is usually looked upon
as a mass of arbitrary and absurd complication. Most persons are
familiar with passages in which it is thus spoken of.[72\3]

  . . . . .  He his fabric of the heavens
  Hath left to their disputes, perhaps to move
  His laughter at their quaint opinions wide;
  Hereafter, when they come to model heaven
  And calculate the stars, how will they wield
  The mighty frame! how build, unbuild, contrive,
  To save appearances! how gird the sphere
  With centric and eccentric scribbled o'er,
  Cycle in epicycle, orb in orb!

And every one will recollect the celebrated saying of Alphonso X.,
king of Castile,[73\3] when this complex system was explained to
him; that "if God had consulted him at the creation, the universe
should have been on a better and simpler plan." In addition to this,
the system is represented as involving an extravagant conception of
the nature of the orbs which it introduces; that they are
crystalline spheres, and that the vast spaces which intervene
between the celestial luminaries are a solid mass, formed by the
fitting together of many masses perpetually in motion; an
imagination which is presumed to be incredible and monstrous.

[Note 72\3: _Paradise Lost_, viii.]

[Note 73\3: A. D. 1252.]

We must endeavor to correct or remove these prejudices, not only in
order that we may do justice to the Hipparchian, or, as it is
usually called, Ptolemaic system of astronomy, and to its founder;
but for another reason, much more important to the purpose of this
work; {152} namely, that we may see how theories may be highly
estimable, though they contain false representations of the real
state of things, and may be extremely useful, though they involve
unnecessary complexity. In the advance of knowledge, the value of
the true part of a theory may much outweigh the accompanying error,
and the use of a rule may be little impaired by its want of
simplicity. The first steps of our progress do not lose their
importance because they are not the last; and the outset of the
journey may require no less vigor and activity than its close.

That which is true in the Hipparchian theory, and which no
succeeding discoveries have deprived of its value, is the
_Resolution_ of the apparent motions of the heavenly bodies into an
assemblage of circular motions. The test of the truth and reality of
this Resolution is, that it leads to the construction of theoretical
Tables of the motions of the luminaries, by which their places are
given at any time, agreeing nearly with their places as actually
observed. The assumption that these circular motions, thus
introduced, are all exactly uniform, is the fundamental principle of
the whole process. This assumption is, it may be said, false; and we
have seen how fantastic some of the arguments were, which were
originally urged in its favor. But _some_ assumption is necessary,
in order that the motions, at different points of a revolution, may
be somehow connected, that is, in order that we may have any theory
of the motions; and no assumption more simple than the one now
mentioned can be selected. The merit of the theory is this;--that
obtaining the amount of the eccentricity, the place of the apogee,
and, it may be, other elements, from _few_ observations, it deduces
from these, results agreeing with _all_ observations, however
numerous and distant. To express an inequality by means of an
epicycle, implies, not only that there is an inequality, but
further,--that the inequality is at its greatest value at a certain
known place,--diminishes in proceeding from that place by a known
law,--continues its diminution for a known portion of the revolution
of the luminary,--then increases again; and so on: that is, the
introduction of the epicycle represents the inequality of motion, as
completely as it can be represented with respect to its _quantity_.

We may further illustrate this, by remarking that such a Resolution
of the unequal motions of the heavenly bodies into equable circular
motions, is, in fact, equivalent to the most recent and improved
processes by which modern astronomers deal with such motions. Their
universal method is to resolve all unequal motions into a series of
{153} _terms_, or expressions of partial motions; and these terms
involve _sines_ and _cosines_, that is, certain technical modes of
measuring circular motion, the circular motion having some constant
relation to the time. And thus the problem of the resolution of the
celestial motions into equable circular ones, which was propounded
above two thousand years ago in the school of Plato, is still the
great object of the study of modern astronomers, whether observers
or calculators.

That Hipparchus should have succeeded in the first great steps of
this resolution for the sun and moon, and should have seen its
applicability in other cases, is a circumstance which gives him one
of the most distinguished places in the roll of great astronomers.
As to the charges or the sneers against the complexity of his
system, to which we have referred, it is easy to see that they are
of no force. As a system of _calculation_, his is not only good,
but, as we have just said, in many cases no better has yet been
discovered. If, when the actual motions of the heavens are
calculated in the best possible way, the process is complex and
difficult, and if we are discontented at this, nature, and not the
astronomer, must be the object of our displeasure. This plea of the
astronomers must be allowed to be reasonable. "We must not be
repelled," says Ptolemy,[74\3] "by the complexity of the hypotheses,
but explain the phenomena as well as we can. If the hypotheses
satisfy each apparent inequality separately, the combination of them
will represent the truth; and why should it appear wonderful to any
that such a complexity should exist in the heavens, when we know
nothing of their nature which entitles us to suppose that any
inconsistency will result?"

[Note 74\3: _Synt._ xiii. 2.]

But it may be said, we now know that the motions are more simple
than they were thus represented, and that the Theory of Epicycles
was false, as a conception of the real construction of the heavens.
And to this we may reply, that it does not appear that the best
astronomers of antiquity conceived the cycles and epicycles to have
a material existence. Though the dogmatic philosophers, as the
Aristotelians, appear to have taught that the celestial spheres were
real solid bodies, they are spoken of by Ptolemy as imaginary;[75\3]
and it is clear, from his proof of the identity of the results of
the hypothesis of an eccentric and an epicycle, that they are
intended to pass for no more than geometrical conceptions, in which
view they are true representations of the apparent motions. {154}

[Note 75\3: Ibid. iii. 3.]

It is true, that the real motions of the heavenly bodies are simpler
than the apparent motions; and that we, who are in the habit of
representing to our minds their real arrangement, become impatient
of the seeming confusion and disorder of the ancient hypotheses. But
this real arrangement never could have been detected by
philosophers, if the apparent motions had not been strictly examined
and successfully analyzed. How far the connection between the facts
and the true theory is from being obvious or easily traced, any one
may satisfy himself by endeavoring, from a general conception of the
moon's real motions, to discover the rules which regulate the
occurrences of eclipses; or even to explain to a learner, of what
nature the apparent motions of the moon among the stars will be.

The unquestionable evidence of the merit and value of the Theory of
Epicycles is to be found in this circumstance;--that it served to
embody all the most exact knowledge then extant, to direct
astronomers to the proper methods of making it more exact and
complete, to point out new objects of attention and research; and
that, after doing this at first, it was also able to take in, and
preserve, all the new results of the active and persevering labors
of a long series of Greek, Latin, Arabian, and modern European
astronomers, till a new theory arose which could discharge this
office. It may, perhaps, surprise some readers to be told, that the
author of this next _great_ step in astronomical theory, Copernicus,
adopted the theory of epicycles; that is, he employed that which we
have spoken of as its really valuable characteristic. "We[76\3] must
confess," he says, "that the celestial motions are circular, or
compounded of several circles, since their inequalities observe a
fixed law and recur in value at certain intervals, which could not
be, except that they were circular; for a circle alone can make that
which has been, recur again."

[Note 76\3: Copernicus. _De Rev._ 1. i. c. 4.]

In this sense, therefore, the Hipparchian theory was a real and
indestructible truth, which was not rejected, and replaced by
different truths, but was adopted and incorporated into every
succeeding astronomical theory; and which can never cease to be one
of the most important and fundamental parts of our astronomical
knowledge.

A moment's reflection will show that, in the events just spoken of,
the introduction and establishment of the Theory of Epicycles, those
characteristics were strictly exemplified, which we have asserted to
be the conditions of every real advance in progressive science;
namely, {155} the application of distinct and appropriate Ideas to a
real series of Facts. The distinctness of the geometrical
conceptions which enabled Hipparchus to assign the Orbits of the Sun
and Moon, requires no illustration; and we have just explained how
these ideas combined into a connected whole the various motions and
places of those luminaries. To make this step in astronomy, required
diligence and care, exerted in collecting observations, and
mathematical clearness and steadiness of view, exercised in seeing
and showing that the theory was a successful analysis of them.


_Sect._ 3.--_Discovery of the Precession of the Equinoxes._

THE same qualities which we trace in the researches of Hipparchus
already examined,--diligence in collecting observations, and
clearness of idea in representing them,--appear also in other
discoveries of his, which we must not pass unnoticed. The Precession
of the Equinoxes, in particular, is one of the most important of
these discoveries.

The circumstance here brought into notice was a Change of Longitude
of the Fixed Stars. The longitudes of the heavenly bodies, being
measured from the point where the sun's annual path cuts the
equator, will change if that path changes. Whether this happens,
however, is not very easy to decide; for the sun's path among the
stars is made out, not by merely looking at the heavens, but by a
series of inferences from other observable facts. Hipparchus used
for this purpose eclipses of the moon; for these, being exactly
opposite to the sun, afford data in marking out his path. By
comparing the eclipses of his own time with those observed at an
earlier period by Timocharis, he found that the bright star, Spica
Virginis, was six degrees behind the equinoctial point in his own
time, and had been eight degrees behind the same point at an earlier
epoch. The suspicion was thus suggested, that the longitudes of all
the stars increase perpetually; but Hipparchus had too truly
philosophical a spirit to take this for granted. He examined the
places of Regulus, and those of other stars, as he had done those of
Spica; and he found, in all these instances, a change of place which
could be explained by a certain alteration of position in the
circles to which the stars are referred, which alteration is
described as the Precession of the Equinoxes.

The distinctness with which Hipparchus conceived this change of
relation of the heavens, is manifested by the question which, as we
are told by Ptolemy, he examined and decided;--that this motion of
the {156} heavens takes place about the poles of the ecliptic, and
not about those of the equator. The care with which he collected
this motion from the stars themselves, may be judged of from this,
that having made his first observations for this purpose on Spica
and Regulus, zodiacal stars, his first suspicion was that the stars
of the zodiac alone changed their longitude, which suspicion he
disproved by the examination of other stars. By his processes, the
idea of the nature of the motion, and the evidence of its existence,
the two conditions of a discovery, were fully brought into view. The
scale of the facts which Hipparchus was thus able to reduce to law,
may be in some measure judged of by recollecting that the
precession, from his time to ours, has only carried the stars
through one sign of the zodiac; and that, to complete one revolution
of the sky by the motion thus discovered, would require a period of
25,000 years. Thus this discovery connected the various aspects of
the heavens at the most remote periods of human history; and,
accordingly, the novel and ingenious views which Newton published in
his chronology, are founded on this single astronomical fact, the
Precession of the Equinoxes.

The two discoveries which have been described, the mode of
constructing Solar and Lunar Tables, and the Precession, were
advances of the greatest importance in astronomy, not only in
themselves, but in the new objects and undertakings which they
suggested to astronomers. The one discovery detected a constant law
and order in the midst of perpetual change and apparent disorder;
the other disclosed mutation and movement perpetually operating
where every thing had been supposed fixed and stationary. Such
discoveries were well adapted to call up many questionings in the
minds of speculative men; for, after this, nothing could be supposed
constant till it had been ascertained to be so by close examination;
and no apparent complexity or confusion could justify the
philosopher in turning away in despair from the task of
simplification. To answer the inquiries thus suggested, new methods
of observing the facts were requisite, more exact and uniform than
those hitherto employed. Moreover, the discoveries which were made,
and others which could not fail to follow in their train, led to
many consequences, required to be reasoned upon, systematized,
completed, enlarged. In short, the _Epoch of Induction_ led, as we
have stated that such epochs must always lead, to a _Period of
Development_, _of Verification_, _Application_, _and Extension_.
{157}



CHAPTER IV.

SEQUEL TO THE INDUCTIVE EPOCH OF HIPPARCHUS.


_Sect._ 1.--_Researches which verified the Theory._

THE discovery of the leading Laws of the Solar and Lunar Motions,
and the detection of the Precession, may be considered as the great
positive steps in the Hipparchian astronomy;--the parent
discoveries, from which many minor improvements proceeded. The task
of pursuing the collateral and consequent researches which now
offered themselves,--of bringing the other parts of astronomy up to
the level of its most improved portions,--was prosecuted by a
succession of zealous observers and calculators, first, in the
school of Alexandria, and afterwards in other parts of the world. We
must notice the various labors of this series of astronomers; but we
shall do so very briefly; for the ulterior development of doctrines
once established is not so important an object of contemplation for
our present purpose, as the first conception and proof of those
fundamental truths on which systematic doctrines are founded. Yet
Periods of Verification, as well as Epochs of Induction, deserve to
be attended to; and they can nowhere be studied with so much
advantage as in the history of astronomy.

In truth, however, Hipparchus did not leave to his successors the
task of pursuing into detail those views of the heavens to which his
discoveries led him. He examined with scrupulous care almost every
part of the subject. We must briefly mention some of the principal
points which were thus settled by him.

The verification of the laws of the changes which he assigned to the
skies, implied that the condition of the heavens was constant,
except so far as it was affected by those changes. Thus, the
doctrine that the changes of position of the stars were rightly
represented by the precession of the equinoxes, supposed that the
stars were fixed with regard to each other; and the doctrine that
the unequal number of days, in certain subdivisions of months and
years, was adequately explained by the theory of epicycles, assumed
that years and days were always of constant lengths. But Hipparchus
was not content with assuming these bases of his theory, he
endeavored to prove them. {158}

1. _Fixity of the Stars._--The question necessarily arose after the
discovery of the precession, even if such a question had never
suggested itself before, whether the stars which were called
_fixed_, and to which the motions of the other luminaries are
referred, do really retain constantly the same relative position. In
order to determine this fundamental question, Hipparchus undertook
to construct a _Map_ of the heavens; for though the result of his
survey was expressed in words, we may give this name to his
Catalogue of the positions of the most conspicuous stars. These
positions are described by means of _alineations_; that is, three or
more such stars are selected as can be touched by an apparent
straight line drawn in the heavens. Thus Hipparchus observed that
the southern claw of Cancer, the bright star in the same
constellation which precedes the head of the Hydra, and the bright
star Procyon, were nearly in the same line. Ptolemy quotes this and
many other of the configurations which Hipparchus had noted, in
order to show that the positions of the stars had not changed in the
intermediate time; a truth which the catalogue of Hipparchus thus
gave astronomers the means of ascertaining. It contained 1080 stars.

The construction of this catalogue of the stars by Hipparchus is an
event of great celebrity in the history of astronomy. Pliny,[77\3]
who speaks of it with admiration as a wonderful and superhuman task
("ausus rem etiam Deo improbam, annumerare posteris stellas"),
asserts the undertaking to have been suggested by a remarkable
astronomical event, the appearance of a new star; "novam stellam et
alium in ævo suo genitam deprehendit; ejusque motu, qua die fulsit,
ad dubitationem est adductus anne hoc sæpius fieret, moverenturque
et eæ quas putamus affixas." There is nothing inherently improbable
in this tradition, but we may observe, with Delambre,[78\3] that we
are not informed whether this new star remained in the sky, or soon
disappeared again. Ptolemy makes no mention of the star or the
story; and his catalogue contains no _bright_ star which is not
found in the "Catasterisms" of Eratosthenes. These Catasterisms were
an enumeration of 475 of the principal stars, according to the
constellations in which they are, and were published about sixty
years before Hipparchus.

[Note 77\3: _Nat. Hist._ lib. ii. (xxvi.)]

[Note 78\3: _A. A._ i. 290.]

2. _Constant Length of Years._--Hipparchus also attempted to
ascertain whether successive years are all of the same length; and
though, with his scrupulous love of accuracy,[79\3] he does not
appear to have {159} thought himself justified in asserting that the
years were always exactly equal, he showed, both by observations of
the time when the sun passed the equinoxes, and by eclipses, that
the difference of successive years, if there were any difference,
must be extremely slight. The observations of succeeding
astronomers, and especially of Ptolemy, confirmed this opinion, and
proved, with certainty, that there is no progressive increase or
diminution in the duration of the year.

[Note 79\3: Ptolem. _Synt._ iii. 2.]

3. _Constant Length of Days. Equation of Time._--The equality of
days was more difficult to ascertain than that of years; for the
year is measured, as on a natural scale, by the number of days which
it contains; but the day can be subdivided into hours only by
artificial means; and the mechanical skill of the ancients did not
enable them to attain any considerable accuracy in the measure of
such portions of time; though clepsydras and similar instruments
were used by astronomers. The equality of days could only be proved,
therefore, by the consequences of such a supposition; and in this
manner it appears to have been assumed, as the fact really is, that
the apparent revolution of the stars is accurately uniform, never
becoming either quicker or slower. It followed, as a consequence of
this, that the solar days (or rather the _nycthemers_, compounded of
a night and a day) would be unequal, in consequence of the sun's
unequal motion, thus giving rise to what we now call the _Equation
of Time_,--the interval by which the time, as marked on a dial, is
before or after the time, as indicated by the accurate timepieces
which modern skill can produce. This inequality was fully taken
account of by the ancient astronomers; and they thus in fact assumed
the equality of the sidereal days.


_Sect._ 2.--_Researches which did not verify the Theory._

SOME of the researches of Hipparchus and his followers fell upon the
weak parts of his theory; and if the observations had been
sufficiently exact, must have led to its being corrected or rejected.

Among these we may notice the researches which were made concerning
the _Parallax_ of the heavenly bodies, that is, their apparent
displacement by the alteration of position of the observer from one
part of the earth's surface to the other. This subject is treated of
at length by Ptolemy; and there can be no doubt that it was well
examined by Hipparchus, who invented a _parallactic instrument_ for
that purpose. The idea of parallax, as a geometrical possibility,
was indeed too obvious to be overlooked by geometers at any time;
and when the doctrine of the sphere was established, it must have
appeared strange {160} to the student, that every place on the
earth's surface might alike be considered as the centre of the
celestial motions. But if this was true with respect to the motions
of the fixed stars, was it also true with regard to those of the sun
and moon? The displacement of the sun by parallax is so small, that
the best observers among the ancients could never be sure of its
existence; but with respect to the moon, the case is different. She
may be displaced by this cause to the amount of twice her own
breadth, a quantity easily noticed by the rudest process of
instrumental observation. The law of the displacement thus produced
is easily obtained by theory, the globular form of the earth being
supposed known; but the amount of the displacement depends upon the
distance of the moon from the earth, and requires at least one good
observation to determine it. Ptolemy has given a table of the
effects of parallax, calculated according to the apparent altitude
of the moon, assuming certain supposed distances; these distances,
however, do not follow the real law of the moon's distances, in
consequence of their being founded upon the Hypothesis of the
Eccentric and Epicycle.

In fact this Hypothesis, though a very close representation of the
truth, so far as the _positions_ of the luminaries are concerned,
fails altogether when we apply it to their _distances_. The radius
of the epicycle, or the eccentricity of the eccentric, are
determined so as to satisfy the observations of the apparent
_motions_ of the bodies; but, inasmuch as the hypothetical motions
are different altogether from the real motions, the Hypothesis does
not, at the same time, satisfy the observations of the _distances_
of the bodies, if we are able to make any such observations.

Parallax is one method by which the distances of the moon, at
different times, may be compared; her Apparent Diameters afford
another method. Neither of these modes, however, is easily capable
of such accuracy as to overturn at once the Hypothesis of epicycles;
and, accordingly, the Hypothesis continued to be entertained in
spite of such measures; the measures being, indeed, in some degree
falsified in consequence of the reigning opinion. In fact, however,
the imperfection of the methods of measuring parallax and magnitude,
which were in use at this period, was such, their results could not
lead to any degree of conviction deserving to be set in opposition
to a theory which was so satisfactory with regard to the more
certain observations, namely, those of the motions.

The Eccentricity, or the Radius of the Epicycle, which would satisfy
{161} the inequality of the _motions_ of the moon, would, in fact,
double the inequality of the _distances_. The Eccentricity of the
moon's orbit is determined by Ptolemy as 1/12 of the radius of the
orbit; but its real amount is only half as great; this difference is
a necessary consequence of the supposition of uniform circular
motions, on which the Epicyclic Hypothesis proceeds.

We see, therefore, that this part of the Hipparchian theory carries
in itself the germ of its own destruction. As soon as the art of
celestial measurement was so far perfected, that astronomers could
be sure of the apparent diameter of the moon within 1/30 or 1/40 of
the whole, the inconsistency of the theory with itself would become
manifest. We shall see, hereafter, the way in which this
inconsistency operated; in reality a very long period elapsed before
the methods of observing were sufficiently good to bring it clearly
into view.


_Sect._ 3._--Methods of Observation of the Greek Astronomers._

WE must now say a word concerning the Methods above spoken of. Since
one of the most important tasks of verification is to ascertain with
accuracy the magnitude of the quantities which enter, as elements,
into the theory which occupies men during the period; the
improvement of instruments, and the methods of observing and
experimenting, are principal features in such periods. We shall,
therefore, mention some of the facts which bear upon this point.

The estimation of distances among the stars by the eye, is an
extremely inexact process. In some of the ancient observations,
however, this appears to have been the method employed; and stars
are described as being _a cubit_ or _two cubits_ from other stars.
We may form some notion of the scale of this kind of measurement,
from what Cleomedes remarks,[80\3] that the sun appears to be about
a foot broad; an opinion which he confutes at length.

[Note 80\3: Del. _A. A._ i. 222.]

A method of determining the positions of the stars, susceptible of a
little more exactness than the former, is the use of _alineations_,
already noticed in speaking of Hipparchus's catalogue. Thus, a
straight line passing through two stars of the Great Bear passes
also through the pole-star; this is, indeed, even now a method
usually employed to enable us readily to fix on the pole-star; and
the two stars β and α of Ursa Major, are hence often called "the
pointers." {162}

But nothing like accurate measurements of any portions of the sky
were obtained, till astronomers adopted the method of making visual
coincidences of the objects with the instruments, either by means of
_shadows_ or of _sights_.

Probably the oldest and most obvious measurements of the positions
of the heavenly bodies were those in which the elevation of the sun
was determined by comparing the length of the shadow of an upright
staff or _gnomon_, with the length of the staff itself. It
appears,[81\3] from a memoir of Gautil, first printed in the
_Connaissance des Temps_ for 1809, that, at the lower town of
Loyang, now called Hon-anfou, Tchon-kong found the length of the
shadow of the gnomon, at the summer solstice, equal to one foot and
a half, the gnomon itself being eight feet in length. This was about
1100 B. C. The Greeks, at an early period, used the same method.
Strabo says[82\3] that "Byzantium and Marseilles are on the same
parallel of latitude, because the shadows at those places have the
same proportion to the gnomon, according to the statement of
Hipparchus, who follows Pytheas."

[Note 81\3: Lib. U. K. _Hist. Ast._ p. 5.]

[Note 82\3: Del. _A. A._ i. 257.]

But the relations of position which astronomy considers, are, for
the most part, angular distances; and these are most simply
expressed by the intercepted portion of a circumference described
about the angular point. The use of the gnomon might lead to the
determination of the angle by the graphical methods of geometry; but
the numerical expression of the circumference required some progress
in trigonometry; for instance, a table of the tangents of angles.

Instruments were soon invented for measuring angles, by means of
circles, which had a border or _limb_, divided into equal parts. The
whole circumference was divided into 360 _degrees_: perhaps because
the circles, first so divided, were those which represented the
sun's annual path; one such degree would be the sun's daily advance,
more nearly than any other convenient aliquot part which could be
taken. The position of the sun was determined by means of the shadow
of one part of the instrument upon the other. The most ancient
instrument of this kind appears to be the _Hemisphere of Berosus_. A
hollow hemisphere was placed with its rim horizontal, and a style
was erected in such a manner that the extremity of the style was
exactly at the centre of the sphere. The shadow of this extremity,
on the concave surface, had the same position with regard to the
lowest point of the sphere which the sun had with regard to the
highest point of the heavens. {163} But this instrument was in fact
used rather for dividing the day into portions of time than for
determining position.

Eratosthenes[83\3] observed the amount of the obliquity of the sun's
path to the equator: we are not informed what instruments he used
for this purpose; but he is said to have obtained, from the
munificence of Ptolemy Euergetes, two _Armils_, or instruments
composed of circles, which were placed in the portico at Alexandria,
and long used for observations. If a circular rim or hoop were
placed so as to coincide with the plane of the equator, the inner
concave edge would be enlightened by the sun's rays which came under
the front edge, when the sun was south of the equator, and by the
rays which came over the front edge, when the sun was north of the
equator: the moment of the transition would be the time of the
equinox. Such an instrument appears to be referred to by Hipparchus,
as quoted by Ptolemy.[84\3] "The circle of copper, which stands at
Alexandria in what is called the Square Porch, appears to mark, as
the day of the equinox, that on which the concave surface begins to
be enlightened from the other side." Such an instrument was called
an _equinoctial armil_.

[Note 83\3: Delambre, _A. A._ i. 86.]

[Note 84\3: Ptol. _Synt._ iii. 2.]

A _solstitial armil_ is described by Ptolemy, consisting of two
circular rims, one sliding round within the other, and the inner one
furnished with two pegs standing out from its surface at right
angles, and diametrically opposite to each other. These circles
being fixed in the plane of the meridian, and the inner one turned,
till, at noon, the shadow of the peg in front falls upon the peg
behind, the position of the sun at noon would be determined by the
degrees on the outer circle.

In calculation, the degree was conceived to be divided into 60
_minutes_, the minute into 60 _seconds_, and so on. But in practice
it was impossible to divide the limb of the instrument into parts so
small. The armils of Alexandria were divided into no parts smaller
than sixths of degrees, or divisions of 10 minutes.

The angles, observed by means of these divisions, were expressed as
a fraction of the circumference. Thus Eratosthenes stated the
interval between the tropics to be 11/83 of the circumference.[85\3]

[Note 85\3: Delambre, _A. A._ i. 87. It is probable that his
observation gave him 47⅔ degrees. The fraction 47⅔/360 = 143/1080 =
11 ∙ 13/1080  = 11/(83+1/13), which is very nearly 11/83.]

It was soon remarked that the whole circumference of the circle
{164} was not wanted for such observations. Ptolemy[86\3] says that
he found it more convenient to observe altitudes by means of a
square flat piece of stone or wood, with a _quadrant_ of a circle
described on one of its flat faces, about a centre near one of the
angles. A peg was placed at the centre, and one of the extreme radii
of the quadrant being perpendicular to the horizon, the elevation of
the sun above the horizon was determined by observing the point of
the arc of the quadrant on which the shadow of the peg fell.

[Note 86\3: _Synt._ i. 1.]

As the necessity of accuracy in the observations was more and more
felt, various adjustments of such instruments were practised. The
instruments were placed in the meridian by means of a _meridian
line_ drawn by astronomical methods on the floor on which they
stood. The plane of the instrument was made vertical by means of a
plumb-line: the bounding radius, from which angles were measured,
was also adjusted by the _plumb-line_.[87\3]

[Note 87\3: The curvature of the plane of the circle, by warping,
was noticed. Ptol. iii. 2. p. 155, observes that his equatorial
circle was illuminated on the hollow side twice in the same day. (He
did not know that this might arise from refraction.)]

In this manner, the places of the sun and of the moon could be
observed by means of the shadows which they cast. In order to
observe the stars,[88\3] the observer looked along the face of the
circle of the armil, so as to see its two edges apparently brought
together, and the star apparently touching them.[89\3]

[Note 88\3: Delamb. _A. A._ i. 185.]

[Note 89\3: Ptol. _Synt._ i. 1. Ὥσπερ κεκολλήμενος ἀμφοτέραις αὐτῶν
ταῖς ἐπιφανείαις ὁ ἀστὴρ ἐν τῷ δι' αὐτῶν ἐπιπέδῳ διοπτεύηται.]

It was afterwards found important to ascertain the position of the
sun with regard to the ecliptic: and, for this purpose, an
instrument, called an _astrolabe_, was invented, of which we have a
description in Ptolemy.[90\3] This also consisted of circular rims,
movable within one another, or about poles; and contained circles
which were to be brought into the position of the ecliptic, and of a
plane passing through the sun and the poles of the ecliptic. The
position of the moon with regard to the ecliptic, and its position
in longitude with regard to the sun or a star, were thus determined.

[Note 90\3: _Synt._ v. 1.]

The astrolabe continued long in use, but not so long as the quadrant
described by Ptolemy; this, in a larger form, is the _mural
quadrant_, which has been used up to the most recent times.

It may be considered surprising,[91\3] that Hipparchus, after having
{165} observed, for some time, right ascensions and declinations,
quitted equatorial armils for the astrolabe, which immediately
refers the stars to the ecliptic. He probably did this because,
after the discovery of precession, he found the latitudes of the
stars constant, and wanted to ascertain their motion in longitude.

[Note 91\3: Del. _A. A._ 181.]

To the above instruments, may be added the _dioptra_, and the
_parallactic instrument_ of Hipparchus and Ptolemy. In the latter,
the distance of a star from the zenith was observed by looking
through two sights fixed in a rule, this being annexed to another
rule, which was kept in a vertical position by a plumb-line; and the
angle between the two rules was measured.

The following example of an observation, taken from Ptolemy, may
serve to show the form in which the results of the instruments, just
described, were usually stated.[92\3]

[Note 92\3: Del. _A. A._ ii. 248.]

"In the 2d year of Antoninus, the 9th day of Pharmouthi, the sun
being near setting, the last division of Taurus being on the
meridian (that is, 5½ equinoctial hours after noon), the moon was in
3 degrees of Pisces, by her distance from the sun (which was 92
degrees, 8 minutes); and half an hour after, the sun being set, and
the quarter of Gemini on the meridian, Regulus appeared, by the
other circle of the astrolabe, 57½ degrees more forwards than the
moon in longitude." From these data the longitude of Regulus is
calculated.

From what has been said respecting the observations of the
Alexandrian astronomers, it will have been seen that their
instrumental observations could not be depended on for any close
accuracy. This defect, after the general reception of the
Hipparchian theory, operated very unfavorably on the progress of the
science. If they could have traced the moon's place distinctly from
day to day, they must soon have discovered all the inequalities
which were known to Tycho Brahe; and if they could have measured her
parallax or her diameter with any considerable accuracy, they must
have obtained a confutation of the epicycloidal form of her orbit.
By the badness of their observations, and the imperfect agreement of
these with calculation, they not only were prevented making such
steps, but were led to receive the theory with a servile assent and
an indistinct apprehension, instead of that rational conviction and
intuitive clearness which would have given a progressive impulse to
their knowledge. {166}


_Sect._ 4.--_Period from Hipparchus to Ptolemy._

WE have now to speak of the cultivators of astronomy from the time
of Hipparchus to that of Ptolemy, the next great name which occurs
in the history of this science; though even he holds place only
among those who verified, developed, and extended the theory of
Hipparchus. The astronomers who lived in the intermediate time,
indeed, did little, even in this way; though it might have been
supposed that their studies were carried on under considerable
advantages, inasmuch as they all enjoyed the liberal patronage of
the kings of Egypt.[93\3] The "divine school of Alexandria," as it
is called by Synesius, in the fourth century, appears to have
produced few persons capable of carrying forwards, or even of
verifying, the labors of its great astronomical teacher. The
mathematicians of the school wrote much, and apparently they
observed sometimes; but their observations are of little value; and
their books are expositions of the theory and its geometrical
consequences, without any attempt to compare it with observation.
For instance, it does not appear that any one verified the
remarkable discovery of the precession, till the time of Ptolemy,
250 years after; nor does the statement of this motion of the
heavens appear in the treatises of the intermediate writers; nor
does Ptolemy quote a single observation of any person made in this
long interval of time; while his references to those of Hipparchus
are perpetual; and to those of Aristyllus and Timocharis, and of
others, as Conon, who preceded Hipparchus, are not unfrequent.

[Note 93\3: Delamb. _A. A._ ii. 240.]

This Alexandrian period, so inactive and barren in the history of
science, was prosperous, civilized, and literary; and many of the
works which belong to it are come down to us, though those of
Hipparchus are lost. We have the "Uranologion" of Geminus,[94\3] a
systematic treatise on Astronomy, expounding correctly the
Hipparchian Theories and their consequences, and containing a good
account of the use of the various Cycles, which ended in the
adoption of the Calippic Period. We have likewise "The Circular
Theory of the Celestial Bodies" of Cleomedes,[95\3] of which the
principal part is a development of the doctrine of the sphere,
including the consequences of the globular form of the earth. We
have also another work on "Spherics" by Theodosius of
Bithynia,[96\3] which contains some of the most important
propositions of the subject, and has been used as a book of {167}
instruction even in modern times. Another writer on the same subject
is Menelaus, who lived somewhat later, and whose Three Books on
Spherics still remain.

[Note 94\3: B. C. 70.]

[Note 95\3: B. C. 60.]

[Note 96\3: B. C. 50.]

One of the most important kinds of deduction from a geometrical
theory, such as that of the doctrine of the sphere, or that of
epicycles, is the calculation of its numerical results in particular
cases. With regard to the latter theory, this was done in the
construction of Solar and Lunar Tables, as we have already seen; and
this process required the formation of a _Trigonometry_, or system
of rules for calculating the relations between the sides and angles
of triangles. Such a science had been formed by Hipparchus, who
appears to be the author of every great step in ancient
astronomy.[97\3] He wrote a work in twelve books, "On the
Construction of the Tables of Chords of Arcs;" such a table being
the means by which the Greeks solved their triangles. The Doctrine
of the Sphere required, in like manner, a _Spherical Trigonometry_,
in order to enable mathematicians to calculate its results; and this
branch of science also appears to have been formed by
Hipparchus,[98\3] who gives results that imply the possession of
such a method. Hypsicles, who was a contemporary of Ptolemy, also
made some attempts at the solution of such problems: but it is
extraordinary that the writers whom we have mentioned as coming
after Hipparchus, namely, Theodosius, Cleomedes, and Menelaus, do
not even mention the calculation of triangles,[99\3] either plain or
spherical; though the latter writer[100\3] is said to have written
on "the Table of Chords," a work which is now lost.

[Note 97\3: Delamb. _A. A._ ii. 37.]

[Note 98\3: _A. A._ i. 117.]

[Note 99\3: _A. A._ i. 249.]

[Note 100\3: _A. A._ ii. 37.]

We shall see, hereafter, how prevalent a disposition in literary
ages is that which induces authors to become commentators. This
tendency showed itself at an early period in the school of
Alexandria. Aratus,[101\3] who lived 270 B. C. at the court of
Antigonus, king of Macedonia, described the celestial constellations
in two poems, entitled "Phænomena," and "Prognostics." These poems
were little more than a versification of the treatise of Eudoxus on
the acronycal and heliacal risings and settings of the stars. The
work was the subject of a comment by Hipparchus, who perhaps found
this the easiest way of giving connection and circulation to his
knowledge. Three Latin translations of this poem gave the Romans the
means of becoming acquainted with it: the first is by Cicero, of
which we have numerous fragments {168} extant;[102\3] Germanicus
Cæsar, one of the sons-in-law of Augustus, also translated the poem,
and this translation remains almost entire. Finally, we have a
complete translation by Avienus.[103\3] The "Astronomica" of
Manilius, the "Poeticon Astronomicon" of Hyginus, both belonging to
the time of Augustus, are, like the work of Aratus, poems which
combine mythological ornament with elementary astronomical
exposition; but have no value in the history of science. We may pass
nearly the same judgment upon the explanations and declamations of
Cicero, Seneca, and Pliny, for they do not apprise us of any
additions to astronomical knowledge; and they do not always indicate
a very clear apprehension of the doctrines which the writers adopt.

[Note 101\3:  _A. A._ i. 74.]

[Note 102\3: Two copies of this translation, illustrated by drawings
of different ages, one set Roman, and the other Saxon, according to
Mr. Ottley, are described in the _Archæologia_, vol. xviii.]

[Note 103\3: Montucla, i. 221.]

Perhaps the most remarkable feature in the two last-named writers,
is the declamatory expression of their admiration for the
discoverers of physical knowledge; and in one of them, Seneca, the
persuasion of a boundless progress in science to which man was
destined. Though this belief was no more than a vague and arbitrary
conjecture, it suggested other conjectures in detail, some of which,
having been verified, have attracted much notice. For instance, in
speaking of comets,[104\3] Seneca says, "The time will come when
those things which are now hidden shall be brought to light by time
and persevering diligence. Our posterity will wonder that we should
be ignorant of what is so obvious." "The motions of the planets," he
adds, "complex and seemingly confused, have been reduced to rule;
and some one will come hereafter, who will reveal to us the paths of
comets." Such convictions and conjectures are not to be admired for
their wisdom; for Seneca was led rather by enthusiasm, than by any
solid reasons, to entertain this opinion; nor, again, are they to be
considered as merely lucky guesses, implying no merit; they are
remarkable as showing how the persuasion of the universality of law,
and the belief of the probability of its discovery by man, grow up
in men's minds, when speculative knowledge becomes a prominent
object of attention.

[Note 104\3: Seneca, _Qu. N._ vii. 25.]

An important practical application of astronomical knowledge was
made by Julius Cæsar, in his correction of the calendar, which we
have already noticed; and this was strictly due to the Alexandrian
School: Sosigenes, an astronomer belonging to that school, came from
Egypt to Rome for the purpose. {169}


_Sect._ 5.--_Measures of the Earth._

THERE were, as we have said, few attempts made, at the period of
which we are speaking, to improve the accuracy of any of the
determinations of the early Alexandrian astronomers. One question
naturally excited much attention at all times, the _magnitude_ of
the earth, its figure being universally acknowledged to be a globe.
The Chaldeans, at an earlier period, had asserted that a man,
walking without stopping, might go round the circuit of the earth in
a year; but this might be a mere fancy, or a mere guess. The attempt
of Eratosthenes to decide this question went upon principles
entirely correct. Syene was situated on the tropic; for there, on
the day of the solstice, at noon, objects cast no shadow; and a well
was enlightened to the bottom by the sun's rays. At Alexandria, on
the same day, the sun was, at noon, distant from the zenith by a
fiftieth part of the circumference. Those two cities were north and
south from each other: and the distance had been determined, by the
royal overseers of the roads, to be 5000 stadia. This gave a
circumference of 250,000 stadia to the earth, and a radius of about
40,000. Aristotle[105\3] says that the mathematicians make the
circumference 400,000 stadia. Hipparchus conceived that the measure
of Eratosthenes ought to be increased by about one-tenth.[106\3]
Posidonius, the friend of Cicero, made another attempt of the same
kind. At Rhodes, the star Canopus but just appeared above the
horizon; at Alexandria, the same star rose to an altitude of 1/48th
of the circumference; the direct distance on the meridian was 5000
stadia, which gave 240,000 for the whole circuit. We cannot look
upon these measures as very precise; the stadium employed is not
certainly known; and no peculiar care appears to have been bestowed
on the measure of the direct distance.

[Note 105\3: _De Cœlo_, ii. ad fin.]

[Note 106\3: Plin. ii. (cviii.)]

When the Arabians, in the ninth century, came to be the principal
cultivators of astronomy, they repeated this observation in a manner
more suited to its real importance and capacity of exactness. Under
the Caliph Almamon,[107\3] the vast plain of Singiar, in
Mesopotamia, was the scene of this undertaking. The Arabian
astronomers there divided themselves into two bands, one under the
direction of Chalid ben Abdolmalic, and the other having at its head
Alis ben Isa. These two parties proceeded, the one north, the other
south, determining the distance by the actual application of their
measuring-rods to the ground, {170} till each was found, by
astronomical observation, to be a degree from the place at which
they started. It then appeared that these terrestrial degrees were
respectively 56 miles, and 56 miles and two-thirds, the mile being
4000 cubits. In order to remove all doubt concerning the scale of
this measure, we are informed that the cubit is that called the
black cubit, which consists of 27 inches, each inch being the
thickness of six grains of barley.

[Note 107\3: Montu. 357.]


_Sect._ 6.--_Ptolemy's Discovery of Evection._

BY referring, in this place, to the last-mentioned measure of the
earth, we include the labors of the Arabian as well as the
Alexandrian astronomers, in the period of mere detail, which forms
the sequel to the great astronomical revolution of the Hipparchian
epoch. And this period of verification is rightly extended to those
later times; not merely because astronomers were then still employed
in determining the magnitude of the earth, and the amount of other
elements of the theory,--for these are some of their employments to
the present day,--but because no great intervening discovery marks a
new epoch, and begins a new period;--because no great revolution in
the theory added to the objects of investigation, or presented them
in a new point of view. This being the case, it will be more
instructive for our purpose to consider the general character and
broad intellectual features of this period, than to offer a useless
catalogue of obscure and worthless writers, and of opinions either
borrowed or unsound. But before we do this, there is one writer whom
we cannot leave undistinguished in the crowd; since his name is more
celebrated even than that of Hipparchus; his works contain
ninety-nine hundredths of what we know of the Greek astronomy; and
though he was not the author of a new theory, he made some very
remarkable steps in the verification, correction, and extension of
the theory which he received. I speak of Ptolemy, whose work, "The
Mathematical Construction" (of the heavens), contains a complete
exposition of the state of astronomy in his time, the reigns of
Adrian and Antonine. This book is familiarly known to us by a term
which contains the record of our having received our first knowledge
of it from the Arabic writers. The "_Megiste_ Syntaxis," or Great
Construction, gave rise, among them, to the title _Al Magisti_, or
_Almagest_, by which the work is commonly described. As a
mathematical exposition of the Theory of Epicycles and Eccentrics,
of the observations and calculations which were employed in {171}
order to apply this theory to the sun, moon, and planets, and of the
other calculations which are requisite, in order to deduce the
consequences of this theory, the work is a splendid and lasting
monument of diligence, skill, and judgment. Indeed, all the other
astronomical works of the ancients hardly add any thing whatever to
the information we obtain from the Almagest; and the knowledge which
the student possesses of the ancient astronomy must depend mainly
upon his acquaintance with Ptolemy. Among other merits, Ptolemy has
that of giving us a very copious account of the manner in which
Hipparchus established the main points of his theories; an account
the more agreeable, in consequence of the admiration and enthusiasm
with which this author everywhere speaks of the great master of the
astronomical school.

In our present survey of the writings of Ptolemy, we are concerned
less with his exposition of what had been done before him, than with
his own original labors. In most of the branches of the subject, he
gave additional exactness to what Hipparchus had done; but our main
business, at present, is with those parts of the Almagest which
contain new steps in the application of the Hipparchian hypothesis.
There are two such cases, both very remarkable,--that of the moon's
_Evection_, and that of the _Planetary Motions_.

The law of the moon's anomaly, that is, of the leading and obvious
inequality of her motion, could be represented, as we have seen,
either by an eccentric or an epicycle; and the amount of this
inequality had been collected by observations of eclipses. But
though the hypothesis of an epicycle, for instance, would bring the
moon to her proper place, so far as eclipses could show it, that is,
at new and full moon, this hypothesis did not rightly represent her
motions at other points of her course. This appeared, when Ptolemy
set about measuring her distances from the sun at different times.
"These," he[108\3] says, "sometimes agreed, and sometimes
disagreed." But by further attention to the facts, a rule was
detected in these differences. "As my knowledge became more complete
and more connected, so as to show the order of this new inequality,
I perceived that this difference was small, or nothing, at new and
full moon; and that at both the _dichotomies_ (when the moon is half
illuminated) it was small, or nothing, if the moon was at the apogee
or perigee of the epicycle, and was greatest when she was in the
middle of the interval, and therefore when the first {172} inequality
was greatest also." He then adds some further remarks on the
circumstances according to which the moon's place, as affected by
this new inequality, is before or behind the place, as given by the
epicyclical hypothesis.

[Note 108\3: _Synth._ v. 2.]

Such is the announcement of the celebrated discovery of the moon's
second inequality, afterwards called (by Bullialdus) the _Evection_.
Ptolemy soon proceeded to represent this inequality by a combination
of circular motions, uniting, for this purpose, the hypothesis of an
epicycle, already employed to explain the first inequality, with the
hypothesis of an eccentric, in the circumference of which the centre
of the epicycle was supposed to move. The mode of combining these
was somewhat complex; more complex we may, perhaps, say, than was
absolutely requisite;[109\3] the apogee of the eccentric moved
backwards, or contrary to the order of the signs, and the centre of
the epicycle moved forwards nearly twice as fast upon the
circumference of the eccentric, so as to reach a place nearly, but
not exactly, the same, as if it had moved in a concentric instead of
an eccentric path. Thus the centre of the epicycle went twice round
the eccentric in the course of one month: and in this manner it
satisfied the condition that it should vanish at new and full moon,
and be greatest when the moon was in the quarters of her monthly
course.[110\3]

[Note 109\3: If Ptolemy had used the hypothesis of an eccentric
instead of an epicycle for the first inequality of the moon, an
epicycle would have represented the second inequality more simply
than his method did.]

[Note 110\3: I will insert here the explanation which my German
translator, the late distinguished astronomer Littrow, has given of
this point. The Rule of this Inequality, the Evection, may be most
simply expressed thus. If _a_ denote the excess of the Moon's
Longitude over the Sun's, and _b_ the Anomaly of the Moon reckoned
from her Perigee, the Evection is equal to 1°. 3. sin (2_a_ - _b_).
At New and Full Moon, _a_ is 0 or 180°, and thus the Evection is
- 1°.3.sin _b_. At both quarters, or dichotomies, _a_ is 90° or 270°,
and consequently the Evection is + 1°.3 . sin _b_. The Moon's
Elliptical Equation of the centre is at all points of her orbit
equal to 6°.3.sin _b_. The Greek Astronomers before Ptolemy observed
the moon only at the time of eclipses; and hence they necessarily
found for the sum of these two greatest inequalities of the moon's
motion the quantity 6°.3. sin _b_ - 1°.3.sin _b_, or 5°.sin _b_: and
as they took this for the moon's equation of the centre, which
depends upon the eccentricity of the moon's orbit, we obtain from
this too small equation of the centre, an eccentricity also smaller
than the truth. Ptolemy, who first observed the moon in her
quarters, found for the sum of those Inequalities at those points
the quantity 6°.3.sin _b_ + 1°.3.sin _b_, or 7°.6.sin _b_; and thus
made the eccentricity of the moon as much too great at the quarters
as the observers of eclipses had made it too small. He hence
concluded that the eccentricity of the Moon's orbit is variable,
which is not the case.]

The discovery of the Evection, and the reduction of it to the {173}
epicyclical theory, was, for several reasons, an important step in
astronomy; some of these reasons may be stated.

1. It obviously suggested, or confirmed, the suspicion that the
motions of the heavenly bodies might be subject to _many_
inequalities:--that when one set of anomalies had been discovered
and reduced to rule, another set might come into view;--that the
discovery of a rule was a step to the discovery of deviations from
the rule, which would require to be expressed in other rules;--that
in the application of theory to observation, we find, not only the
_stated phenomena_, for which the theory does account, but also
_residual phenomena_, which remain unaccounted for, and stand out
beyond the calculation;--that thus nature is not simple and regular,
by conforming to the simplicity and regularity of our hypotheses,
but leads us forwards to apparent complexity, and to an accumulation
of rules and relations. A fact like the Evection, explained by an
Hypothesis like Ptolemy's, tended altogether to discourage any
disposition to guess at the laws of nature from mere ideal views, or
from a few phenomena.

2. The discovery of Evection had an importance which did not come
into view till long afterwards, in being the first of a numerous
series of inequalities of the moon, which results from the
_Disturbing Force_ of the sun. These inequalities were successfully
discovered; and led finally to the establishment of the law of
universal gravitation. The moon's first inequality arises from a
different cause;--from the same cause as the inequality of the sun's
motion;--from the motion in an ellipse, so far as the central
attraction is undisturbed by any other. This first inequality is
called the Elliptic Inequality, or, more usually, the _Equation of
the Centre_.[111\3] All the planets have such inequalities, but the
Evection is peculiar to the moon. The discovery of other
inequalities of the moon's motion, the Variation and Annual
Equation, made an immediate sequel in the order of the subject to
{174} the discoveries of Ptolemy, although separated by a long
interval of time; for these discoveries were only made by Tycho
Brahe in the sixteenth century. The imperfection of astronomical
instruments was the great cause of this long delay.

[Note 111\3: The Equation of the Centre is the difference between
the place of the Planet in its elliptical orbit, and that place
which a Planet would have, which revolved uniformly round the Sun as
a centre in a circular orbit in the same time. An imaginary Planet
moving in the manner last described, is called the _mean_ Planet,
while the actual Planet which moves in the ellipse is called the
_true_ Planet. The Longitude of the mean Planet at a given time is
easily found, because its motion is uniform. By adding to it the
Equation of the Centre, we find the Longitude of the true Planet,
and thus, its place in its orbit.--_Littrow's Note_.

I may add that the word _Equation_, used in such cases, denotes in
general a quantity which must be added to or subtracted from a mean
quantity, to make it _equal_ to the true quantity; or rather, a
quantity which must be added to or subtracted from a variably
increasing quantity to make it increase _equably_.]

3. The Epicyclical Hypothesis was found capable of accommodating
itself to such new discoveries. These new inequalities could be
represented by new combinations of eccentrics and epicycles: all the
real and imaginary discoveries by astronomers, up to Copernicus,
were actually embodied in these hypotheses; Copernicus, as we have
said, did not reject such hypotheses; the lunar inequalities which
Tycho detected might have been similarly exhibited; and even
Newton[112\3] represents the motion of the moon's apogee by means of
an epicycle. As a mode of expressing the law of the irregularity,
and of calculating its results in particular cases, the epicyclical
theory was capable of continuing to render great service to
astronomy, however extensive the progress of the science might be.
It was, in fact, as we have already said, the modern process of
representing the motion by means of a series of circular functions.

[Note 112\3: _Principia_, lib. iii. prop. xxxv.]

4. But though the doctrine of eccentrics and epicycles was thus
admissible as an Hypothesis, and convenient as a means of expressing
the laws of the heavenly motions, the successive occasions on which it
was called into use, gave no countenance to it as a Theory; that is,
as a true view of the nature of these motions, and their causes. By
the steps of the progress of this Hypothesis, it became more and more
complex, instead of becoming more simple, which, as we shall see, was
the course of the true Theory. The notions concerning the position and
connection of the heavenly bodies, which were suggested by one set of
phenomena, were not confirmed by the indications of another set of
phenomena; for instance, those relations of the epicycles which were
adopted to account for the Motions of the heavenly bodies, were not
found to fall in with the consequences of their apparent Diameters and
Parallaxes. In reality, as we have said, if the relative distances of
the sun and moon at different times could have been accurately
determined, the Theory of Epicycles must have been forthwith
overturned. The insecurity of such measurements alone maintained the
theory to later times.[113\3] {175}

[Note 113\3: The alteration of the apparent diameter of the moon is
so great that it cannot escape us, even with very moderate
instruments. This apparent diameter contains, when the moon is
nearest the earth, 2010 seconds; when she is furthest off 1762
seconds; that is, 248 seconds, or 4 minutes 8 seconds, less than in
the former case. [The two quantities are in the proportion of 8 to
7, nearly.]--_Littrow's Note_.]


_Sect._ 7.--_Conclusion of the History of Greek Astronomy._

I MIGHT now proceed to give an account of Ptolemy's other great
step, the determination of the Planetary Orbits; but as this, though
in itself very curious, would not illustrate any point beyond those
already noticed, I shall refer to it very briefly. The planets all
move in ellipses about the sun, as the moon moves about the earth;
and as the sun apparently moves about the earth. They will therefore
each have an Elliptic Inequality or Equation of the centre, for the
same reason that the sun and moon have such inequalities. And this
inequality may be represented, in the cases of the planets, just as
in the other two, by means of an eccentric; the epicycle, it will be
recollected, had already been used in order to represent the more
obvious changes of the planetary motions. To determine the amount of
the Eccentricities and the places of the Apogees of the planetary
orbits, was the task which Ptolemy undertook; Hipparchus, as we have
seen, having been destitute of the observations which such a process
required. The determination of the Eccentricities in these cases
involved some peculiarities which might not at first sight occur to
the reader. The **elcliptical motion of the planets takes place about
the sun; but Ptolemy considered their movements as altogether
independent of the sun, and referred them to the earth alone; and
thus the apparent eccentricities which he had to account for, were
the compound result of the Eccentricity of the earth's orbit, and of
the proper eccentricity of the orbit of the Planet. He explained
this result by the received mechanism of an eccentric _Deferent_,
carrying an Epicycle; but the motion in the Deferent is uniform, not
about the centre of the circle, but about another point, the
_Equant_. Without going further into detail, it may be sufficient to
state that, by a combination of Eccentrics and Epicycles, he did
account for the leading features of these motions; and by using his
own observations, compared with more ancient ones (for instance,
those of Timocharis for Venus), he was able to determine the
Dimensions and Positions of the orbits.[114\3] {176}

[Note 114\3: Ptolemy determined the Radius and the Periodic Time of
his two circles for each Planet in the following manner: For the
_inferior_ Planets, that is, Mercury and Venus, he took the Radius of
the Deferent equal to the Radius of the Earth's orbit, and the Radius
of the Epicycle equal to that of the Planet's orbit. For these
Planets, according to his assumption, the Periodic Time of the Planet
in its Epicycle was to the Periodic Time of the Epicyclical Centre on
the Deferent, as the _synodical_ Revolution of the Planet to the
_tropical_ Revolution of the Earth above the Sun. For the three
_superior_ Planets, Mars, Jupiter, and Saturn, the Radius of the
Deferent was equal to the Radius of the Planet's orbit, and the Radius
of the Epicycle was equal to the Radius of the Earth's orbit; the
Periodic Time on the Planet in its Epicycle was to the Periodic Time
of the Epicyclical Centre on the Deferent, as the _synodical_
Revolution of the Planet to the _tropical_ Revolution of the same
Planet.

Ptolemy might obviously have made the geometrical motions of all the
Planets correspond with the observations by one of these two modes
of construction; but he appears to have adopted this double form of
the theory, in order that in the inferior, as well as in the
superior Planets, he might give the smaller of the two Radii to the
Epicycle: that is, in order that he might make the smaller circle
move round the larger, not _vice versâ_.--_Littrow's Notes._]

I shall here close my account of the astronomical progress of the
Greek School. My purpose is only to illustrate the principles on
which the progress of science depends, and therefore I have not at
all pretended to touch upon every part of the subject. Some portion
of the ancient theories, as, for instance, the mode of accounting
for the motions of the moon and planets in latitude, are
sufficiently analogous to what has been explained, not to require
any more especial notice. Other parts of Greek astronomical
knowledge, as, for instance, their acquaintance with refraction, did
not assume any clear or definite form, and can only be considered as
the prelude to modern discoveries on the same subject. And before we
can with propriety pass on to these, there is a long and remarkable,
though unproductive interval, of which some account must be given.


_Sect._ 8.--_Arabian Astronomy._

THE interval to which I have just alluded may be considered as
extending from Ptolemy to Copernicus; we have no advance in Greek
astronomy after the former; no signs of a revival of the power of
discovery till the latter. During this interval of 1350
years,[115\3] the principal cultivators of astronomy were the
Arabians, who adopted this science from the Greeks whom they
conquered, and from whom the conquerors of western Europe again
received back their treasure, when the love of science and the
capacity for it had been awakened in their minds. In the intervening
time, the precious deposit had undergone little change. The Arab
astronomer had been the scrupulous but unprofitable servant, who
kept his talent without apparent danger of loss, but also without
prospect of increase. There is little in {177} Arabic literature
which bears upon the _progress_ of astronomy; but as the little that
there is must be considered as a sequel to the Greek science, I
shall notice one or two points before I treat of the stationary
period in general.

[Note 115\3: Ptolemy died about A. D. 150. Copernicus was living
A. D. 1500.]

When the sceptre of western Asia had passed into the hands of the
Abasside caliphs,[116\3] Bagdad, "the city of peace," rose to
splendor and refinement, and became the metropolis of science under
the successors of Almansor the Victorious, as Alexandria had been
under the successors of Alexander the Great. Astronomy attracted
peculiarly the favor of the powerful as well as the learned; and
almost all the culture which was bestowed upon the science, appears
to have had its source in the patronage, often also in the personal
studies, of Saracen princes. Under such encouragement, much was
done, in those scientific labors which money and rank can command.
Translations of Greek works were made, large instruments were
erected, observers were maintained; and accordingly as observation
showed the defects and imperfection of the extant tables of the
celestial motions, new ones were constructed. Thus under Almansor,
the Grecian works of science were collected from all quarters, and
many of them translated into Arabic.[117\3] The translation of the
"Megiste Syntaxis" of Ptolemy, which thus became the Almagest, is
ascribed to Isaac ben Homain in this reign.

[Note 116\3: Gibbon, x. 31.]

[Note 117\3: Id. x. 36.]

The greatest of the Arabian Astronomers comes half a century later.
This is Albategnius, as he is commonly called; or more exactly,
Mohammed ben Geber Albatani, the last appellation indicating that he
was born at Batan, a city of Mesopotamia.[118\3] He was a Syrian
prince, whose residence was at Aracte or Racha in Mesopotamia: a
part of his observations were made at Antioch. His work still
remains to us in Latin. "After having read," he says, "the Syntaxis
of Ptolemy, and learnt the methods of calculation employed by the
Greeks, his observations led him to conceive that some improvements
might be made in their results. He found it necessary to add to
Ptolemy's observations as Ptolemy had added to those of Abrachis"
(Hipparchus). He then published Tables of the motions of the sun,
moon, and planets, which long maintained a high reputation.

[Note 118\3: Del. _Astronomie du Moyen Age_, 4.]

These, however, did not prevent the publication of others. Under the
Caliph Hakem (about A. D. 1000) Ebon Iounis published Tables of the
Sun, Moon, and Planets, which were hence called the _Hakemite
Tables_. Not long after, Arzachel of Toledo published the _Toletan_
{178} Tables. In the 13th century, Nasir Eddin published Tables of
the Stars, dedicated to Ilchan, a Tartar prince, and hence termed
the _Ilchanic_ Tables. Two centuries later, Ulugh Beigh, the
grandson of Tamerlane, and prince of the countries beyond the Oxus,
was a zealous practical astronomer; and his Tables, which were
published in Europe by Hyde in 1665, are referred to as important
authority by modern astronomers. The series of Astronomical Tables
which we have thus noticed, in which, however, many are omitted,
leads us to the _Alphonsine_ Tables, which were put forth in 1488,
and in succeeding years, under the auspices of Alphonso, king of
Castile; and thus brings us to the verge of modern astronomy.

For all these Tables, the Ptolemaic hypotheses were employed; and,
for the most part, without alteration. The Arabs sometimes felt the
extreme complexity and difficulty of the doctrine which they
studied; but their minds did not possess that kind of invention and
energy by which the philosophers of Europe, at a later period, won
their way into a simpler and better system.

Thus Alpetragius states, in the outset of his "Planetarum Theorica,"
that he was at first astonished and stupefied with this complexity,
but that afterwards "God was pleased to open to him the occult secret
in the theory of his orbs, and to make known to him the truth of their
essence and the rectitude of the quality of their motion." His system
consists, according to Delambre,[119\3] in attributing to the planets
a spiral motion from east to west, an idea already refuted by Ptolemy.
Geber of Seville criticises Ptolemy very severely,[120\3] but without
introducing any essential alteration into his system. The Arabian
observations are in many cases valuable; both because they were made
with more skill and with better instruments than those of the Greeks;
and also because they illustrate the permanence or variability of
important elements, such as the obliquity of the ecliptic and the
inclination of the moon's orbit.

[Note 119\3: Delambre, _M. A._ p. 7.]

[Note 120\3: _M. A._ p. 180, &c.]

We must, however, notice one or two peculiar Arabian doctrines. The
most important of these is the discovery of the Motion of the Son's
Apogee by Albategnius. He found the Apogee to be in longitude 82
degrees; Ptolemy had placed it in longitude 65 degrees. The
difference of 17 degrees was beyond all limit of probable error of
calculation, though the process is not capable of great precision;
and the inference of the Motion of the Apogee was so obvious, that
we cannot {179} agree with Delambre, in doubting or extenuating the
claim of Albategnius to this discovery, on the ground of his not
having expressly stated it.

In detecting this motion, the Arabian astronomers reasoned rightly
from facts well observed: they were not always so fortunate.
Arzachel, in the 11th century, found the apogee of the sun to be
less advanced than Albategnius had found it, by some degrees; he
inferred that it had receded in the intermediate time; but we now
know, from an acquaintance with its real rate of moving, that the
true inference would have been, that Albategnius, whose method was
less trustworthy than that of Arzachel, had made an error to the
amount of the difference thus arising. A curious, but utterly false
hypothesis was founded on observations thus erroneously appreciated;
namely, the _Trepidation of the fixed stars_. Arzachel conceived
that a uniform Precession of the equinoctial points would not
account for the apparent changes of position of the stars, and that
for this purpose, it was necessary to conceive two circles of about
eight degrees radius described round the equinoctial points of the
immovable sphere, and to suppose the first points of Aries and Libra
to describe the circumference of these circles in about 800 years.
This would produce, at one time a progression, and at another a
regression, of the apparent equinoxes, and would moreover change the
latitude of the stars. Such a motion is entirely visionary; but the
doctrine made a sect among astronomers, and was adopted in the first
edition of the Alphonsine Tables, though afterwards rejected.

An important exception to the general unprogressive character of
Arabian science has been pointed out recently by M. Sedillot.[121\3]
It appears that Mohammed-Aboul Wefa-al-Bouzdjani, an Arabian
astronomer of the tenth century, who resided at Cairo, and observed
at Bagdad in 975, discovered a third inequality of the moon, in
addition to the two expounded by Ptolemy, the Equation of the
Centre, and the Evection. This third inequality, the _Variation_, is
usually supposed to have been discovered by Tycho Brahe, six
centuries later. It is an inequality of the moon's motion, in virtue
of which she moves quickest when she is at new or full, and slowest
at the first and third quarter; in consequence of this, from the
first quarter to the full, she is behind her mean place; at the
full, she does not differ from her mean place; from the full to the
third quarter, she is before her true {180} place; and so on; and
the greatest effect of the inequality is in the _octants_, or points
half-way between the four quarters. In an Almagest of Aboul Wefa, a
part of which exists in the Royal Library at Paris, after describing
the two inequalities of the moon, he has a Section ix., "Of the
Third Anomaly of the moon called _Muhazal_ or _Prosneusis_." He
there says, that taking cases when the moon was in apogee or
perigee, and when, consequently, the effect of the two first
inequalities vanishes, he found, _by observation of the moon_, when
she was nearly _in trine_ and _in sextile_ with the sun, that she
was a degree and a quarter from her calculated place. "And hence,"
he adds, "I perceived that this anomaly exists independently of the
two first: and this can only take place by a declination of the
diameter of the epicycle with respect to the centre of the zodiac."

[Note 121\3: Sedillot, Nouvelles Rech. sur l'Hist. de l'Astron. chez
les Arabes. _Nouveau Journal Asiatique_. 1836.]

We may remark that we have here this inequality of the moon made out
in a really philosophical manner; a residual quantity in the moon's
longitude being detected by observation, and the cases in which it
occurs selected and grouped by an inductive effort of the mind. The
advance is not great; for Aboul Wefa appears only to have detected
the existence, and not to have fixed the law or the exact quantity
of the inequality; but still it places the scientific capacity of
the Arabs in a more favorable point of view than any circumstance
with which we were previously acquainted.

But this discovery of Aboul Wefa appears to have excited no notice
among his contemporaries and followers: at least it had been long
quite forgotten when Tycho Brahe rediscovered the same lunar
inequality. We can hardly help looking upon this circumstance as an
evidence of a servility of intellect belonging to the Arabian
period. The learned Arabians were so little in the habit of
considering science as progressive, and looking with pride and
confidence at examples of its progress, that they had not the
courage to believe in a discovery which they themselves had made,
and were dragged back by the chain of authority, even when they had
advanced beyond their Greek masters.

As the Arabians took the whole of their theory (with such slight
exceptions as we have been noticing) from the Greeks, they took from
them also the mathematical processes by which the consequences of
the theory were obtained. Arithmetic and Trigonometry, two main
branches of these processes, received considerable improvements at
their hands. In the former, especially, they rendered a service to
the world which it is difficult to estimate too highly, in
abolishing the {181} cumbrous Sexagesimal Arithmetic of the Greeks,
and introducing the notation by means of the digits 1, 2, 3, 4, 5,
6, 7, 8, 9, 0, which we now employ.[122\3] These numerals appear to
be of Indian origin, as is acknowledged by the Arabs themselves; and
thus form no exception to the sterility of the Arabian genius as to
great scientific inventions. Another improvement, of a subordinate
kind, but of great utility, was Arabian, being made by Albategnius.
He introduced into calculation the _sine_, or half-chord of the
double arc, instead of the chord of the arc itself, which had been
employed by the Greek astronomers. There have been various
conjectures concerning the origin of the word _sine_; the most
probable appears to be that _sinus_ is the Latin translation of the
Arabic word _gib_, which signifies a fold, the two halves of the
chord being conceived to be folded together.

[Note 122\3: Mont. i. 376.]

The great obligation which Science owes to the Arabians, is to have
preserved it during a period of darkness and desolation, so that
Europe might receive it back again when the evil days were past. We
shall see hereafter how differently the European intellect dealt
with this hereditary treasure when once recovered.

Before quitting the subject, we may observe that Astronomy brought
back, from her sojourn among the Arabs, a few terms which may still
be perceived in her phraseology. Such are the _zenith_, and the
opposite imaginary point, the _nadir_;--the circles of the sphere
termed _almacantars_ and _azimuth_ circles. The _alidad_ of an
instrument is its index, which possesses an angular motion. Some of
the stars still retain their Arabic names; _Aldebran_, _Rigel_,
_Fomalhaut_; many others were known by such appellations a little
while ago. Perhaps the word _almanac_ is the most familiar vestige
of the Arabian period of astronomy.

It is foreign to my purpose to note any efforts of the intellectual
faculties among other nations, which may have taken place
independently of the great system of progressive European culture,
from which all our existing science is derived. Otherwise I might
speak of the astronomy of some of the Orientals, for example, the
Chinese, who are said, by Montucla (i. 465), to have discovered the
first equation of the moon, and the proper motion of the fixed stars
(the Precession), in the third century of our era. The Greeks had
made these discoveries 500 years earlier.



{{183}}
BOOK IV.


HISTORY
OF
PHYSICAL SCIENCE IN THE MIDDLE AGES;
OR,
VIEW OF THE STATIONARY PERIOD
OF
INDUCTIVE SCIENCE.



  In vain, in vain! the all-composing hour
  Resistless falls .  .  .  .
  .  .  .  .  .
  As one by one, at dread Medea's strain,
  The sickening stars fade off th' ethereal plain;
  As Argus' eyes, by Hermes' wand opprest,
  Closed one by one to everlasting rest;
  Thus at her felt approach and secret might,
  Art after art goes out, and all is night.
  See skulking Truth to her old cavern fled,
  Mountains of casuistry heaped on her head;
  Philosophy, that reached the heavens before,
  Shrinks to her hidden cause, and is no more.
  Physic of Metaphysic begs defence,
  And Metaphysic calls for aid to Sense:
  See Mystery to Mathematics fly!
  In vain! they gaze, turn giddy, rave, and die.

           _Dunciad_, B. iv.



{{185}}
INTRODUCTION.


WE have now to consider more especially a long and barren period,
which intervened between the scientific activity of ancient Greece
and that of modern Europe; and which we may, therefore, call the
Stationary Period of Science. It would be to no purpose to enumerate
the various forms in which, during these times, men reproduced the
discoveries of the inventive ages; or to trace in them the small
successes of Art, void of any principle of genuine Philosophy. Our
object requires rather that we should point out the general and
distinguishing features of the intellect and habits of those times.
We must endeavor to delineate the character of the Stationary
Period, and, as far as possible, to analyze its defects and errors;
and thus obtain some knowledge of the causes of its barrenness and
darkness.

We have already stated, that real scientific progress requires
distinct general Ideas, applied to many special and certain Facts.
In the period of which we now have to speak, men's Ideas were
obscured; their disposition to bring their general views into
accordance with Facts was enfeebled. They were thus led to employ
themselves unprofitably, among indistinct and unreal notions. And
the evil of these tendencies was further inflamed by moral
peculiarities in the character of those times;--by an abjectness of
thought on the one hand, which could not help looking towards some
intellectual superior, and by an impatience of dissent on the other.
To this must be added an enthusiastic temper, which, when introduced
into speculation, tends to subject the mind's operations to ideas
altogether distorted and delusive.

These characteristics of the stationary period, its obscurity of
thought, its servility, its intolerant disposition, and its
enthusiastic temper, will be treated of in the four following
chapters, on the Indistinctness of Ideas, the Commentatorial Spirit,
the Dogmatism, and the Mysticism of the Middle Ages. {186}




CHAPTER I.

ON THE INDISTINCTNESS OF IDEAS OF THE MIDDLE AGES.


THAT firm and entire possession of certain clear and distinct
general ideas which is necessary to sound science, was the character
of the minds of those among the ancients who created the several
sciences which arose among them. It was indispensable that such
inventors should have a luminous and steadfast apprehension of
certain general relations, such as those of space and number, order
and cause; and should be able to apply these notions with perfect
readiness and precision to special facts and cases. It is necessary
that such scientific notions should be more definite and precise
than those which common language conveys; and in this state of
unusual clearness, they must be so familiar to the philosopher, that
they are the language in which he thinks. The discoverer is thus led
to doctrines which other men adopt and follow out, in proportion as
they seize the fundamental ideas, and become acquainted with the
leading facts. Thus Hipparchus, conceiving clearly the motions and
combinations of motion which enter into his theory, saw that the
relative lengths of the seasons were sufficient data for determining
the form of the sun's orbit; thus Archimedes, possessing a steady
notion of mechanical pressure, was able, not only to deduce the
properties of the lever and of the centre of gravity, but also to
see the truth of those principles respecting the distribution of
pressure in fluids, on which the science of hydrostatics depends.

With the progress of such distinct ideas, the inductive sciences
rise and flourish; with the decay and loss of such distinct ideas,
these sciences become stationary, languid, and retrograde. When men
merely repeat the terms of science, without attaching to them any
clear conceptions;--when their apprehensions become vague and
dim;--when they assent to scientific doctrines as a matter of
tradition, rather than of conviction, on trust rather than on
sight;--when science is considered as a collection of opinions,
rather than a record of laws by which the universe is really
governed;--it must inevitably happen, that men will lose their hold
on the knowledge which the great discoverers who preceded them have
brought to light. They are not able to push forwards the truths on
which they lay so {187} feeble and irresolute a hand; probably they
cannot even prevent their sliding back towards the obscurity from
which they had been drawn, or from being lost altogether. Such
indistinctness and vacillation of thought appear to have prevailed
in the stationary period, and to be, in fact, intimately connected
with its stationary character. I shall point out some indications of
the intellectual peculiarity of which I speak.

1. _Collections of Opinions._--The fact, that mere Collections of
the opinions of physical philosophers came to hold a prominent place
in literature, already indicated a tendency to an indistinct and
wandering apprehension of such opinions. I speak of such works as
Plutarch's five Books "on the Opinions of Philosophers," or the
physical opinions which Diogenes Laërtius gives in his "Lives of the
Philosophers." At an earlier period still, books of this kind
appear; as for instance, a large portion of Pliny's Natural History,
a work which has very appropriately been called the Encyclopædia of
Antiquity; even Aristotle himself is much in the habit of
enumerating the opinions of those who had preceded him. To present
such statements as an important part of physical philosophy, shows
an erroneous and loose apprehension of its nature. For the only
proof of which its doctrines admit, is the possibility of applying
the general theory to each particular case; the authority of great
men, which in moral and practical matters may or must have its
weight, is here of no force; and the technical precision of ideas
which the terms of a sound physical theory usually demand, renders a
mere statement of the doctrines very imperfectly intelligible to
readers familiar with common notions only. To dwell upon such
collections of opinions, therefore, both implies, and produces, in
writers and readers, an obscure and inadequate apprehension of the
full meaning of the doctrines thus collected; supposing there be
among them any which really possess such a clearness, solidity, and
reality, as to make them important in the history of science. Such
diversities of opinion convey no truth; such a multiplicity of
statements of what has been _said_, in no degree teaches us what
_is_; such accumulations of indistinct notions, however vast and
varied, do not make up one distinct idea. On the contrary, the habit
of dwelling upon the verbal expressions of the views of other
persons, and of being content with such an apprehension of doctrines
as a transient notice can give us, is fatal to firm and clear
thought: it indicates wavering and feeble conceptions, which are
inconsistent with speculation. {188}

We may, therefore, consider the prevalence of Collections of the
kind just referred to, as indicating a deficiency of philosophical
talent in the ages now under review. As evidence of the same
character, we may add the long train of publishers of Abstracts,
Epitomes, Bibliographical Notices, and similar writers. All such
writers are worthless for all purposes of _science_, and their
labors may be considered as dead works; they have in them no
principle of philosophical vitality; they draw their origin and
nutriment from the death of true physical knowledge; and resemble
the swarms of insects that are born from the perishing carcass of
some noble animal.

2. _Indistinctness of Ideas in Mechanics._--But the indistinctness
of thought which is so fatal a feature in the intellect of the
stationary period, may be traced more directly in the works, even of
the best authors, of those times. We find that they did not retain
steadily the ideas on which the scientific success of the previous
period had depended. For instance, it is a remarkable circumstance
in the history of the science of Mechanics, that it did not make any
advance from the time of Archimedes to that of Stevinus and Galileo.
Archimedes had established the doctrine of the lever; several
persons tried, in the intermediate time, to prove the property of
the inclined plane, and none of them succeeded. But let us look to
the attempts; for example, that of Pappus, in the eighth Book of his
Mathematical Collections, and we may see the reason of the failure.
His Problem shows, in the very terms in which it is propounded, the
want of a clear apprehension of the subject. "Having given the power
which will draw a given weight along the horizontal plane, to find
the additional power which will draw the same weight along a given
inclined plane." This is proposed without previously defining how
Powers, producing such effects, are to be measured; and as if the
speed with which the body were drawn, and the nature of the surface
of the plane, were of no consequence. The proper elementary Problem
is, To find the force which will _support_ a body on a smooth
inclined plane; and no doubt the solution of Pappus has more
reference to this problem than to his own. His reasoning is,
however, totally at variance with mechanical ideas on any view of
the problem. He supposes the weight to be formed into a sphere; and
this sphere being placed in contact with the inclined plane, he
assumes that the effect will be the same as if the weight were
supported on a horizontal lever, the fulcrum being the point of
contact of the sphere with the plane, and the power acting at the
circumference of the sphere. Such an assumption implies an entire
{189} absence of those distinct ideas of force and mechanical
pressure, on which our perception of the identity or difference of
different modes of action must depend;--of those ideas by the help
of which Archimedes had been able to demonstrate the properties of
the lever, and Stevinus afterwards discovered the true solution of
the problem of the inclined plane. The motive to Pappus's assumption
was probably no more than this;--he perceived that the additional
power, which he thus obtained, vanished when the plane became
horizontal, and increased as the inclination became greater. Thus
his views were vague; he had no clear conception of mechanical
action, and he tried a geometrical conjecture. This is not the way
to real knowledge.

Pappus (who lived about A. D. 400) was one of the best
mathematicians of the Alexandrian school; and, on subjects where his
ideas were so indistinct, it is not likely that any much clearer
were to be found in the minds of his contemporaries. Accordingly, on
all subjects of speculative mechanics, there appears to have been an
entire confusion and obscurity of thought till modern times. Men's
minds were busy in endeavoring to systematize the distinctions and
subtleties of the Aristotelian school, concerning Motion and Power;
and, being thus employed among doctrines in which there was involved
no definite meaning capable of real exemplification, they, of
course, could not acquire sound physical knowledge. We have already
seen that the physical opinions of Aristotle, even as they came from
him, had no proper scientific precision. His followers, in their
endeavors to perfect and develop his statements, never attempted to
introduce clearer ideas than those of their master; and as they
never referred, in any steady manner, to facts, the vagueness of
their notions was not corrected by any collision with observation.
The physical doctrines which they extracted from Aristotle were, in
the course of time, built up into a regular system; and though these
doctrines could not be followed into a practical application without
introducing distinctions and changes, such as deprived the terms of
all steady signification, the dogmas continued to be repeated, till
the world was persuaded that they were self-evident; and when, at a
later period, experimental philosophers, such as Galileo and Boyle,
ventured to contradict these current maxims, their new principles
sounded in men's ears as strange as they now sound familiar. Thus
Boyle promulgated his opinions on the mechanics of fluids, as
"Hydrostatical _Paradoxes_, proved and illustrated by experiments."
And the opinions which he there opposes, are those which the
Aristotelian philosophers habitually propounded as certain {190} and
indisputable; such, for instance, as that "in fluids the upper parts
do not gravitate on the lower;" that "a lighter fluid will not
gravitate on a heavier;" that "levity is a positive quality of
bodies as well as gravity." So long as these assertions were left
uncontested and untried, men heard and repeated them, without
perceiving the incongruities which they involved: and thus they long
evaded refutation, amid the vague notions and undoubting habits of
the stationary period. But when the controversies of Galileo's time
had made men think with more acuteness and steadiness, it was
discovered that many of these doctrines were inconsistent with
themselves, as well as with experiment. We have an example of the
confusion of thought to which the Aristotelians were liable, in
their doctrine concerning falling bodies. "Heavy bodies," said they,
"must fall quicker than light ones; for weight is the cause of their
fall, and the weight of the greater bodies is greater." They did not
perceive that, if they considered the weight of the body as a power
acting to produce motion, they must consider the body itself as
offering a resistance to motion; and that the effect must depend on
the proportion of the power to the resistance; in short, they had no
clear idea of _accelerating force_. This defect runs through all
their mechanical speculations, and renders them entirely valueless.

We may exemplify the same confusion of thought on mechanical
subjects in writers of a less technical character. Thus, if men had
any distinct idea of mechanical action, they could not have accepted
for a moment the fable of the Echineis or Remora, a little fish
which was said to be able to stop a large ship merely by sticking to
it.[1\4] Lucan refers to this legend in a poetical manner, and
notices this creature only in bringing together a collection of
monstrosities; but Pliny relates the tale gravely, and moralizes
upon it after his manner. "What," he cries,[2\4] "is more violent
than the sea and the winds? what a greater work of art than a ship?
Yet one little fish (the Echineis) can hold back all these when they
all strain the same way. The winds may {191} blow, the waves may
rage; but this small creature controls their fury, and stops a
vessel, when chains and anchors would not hold it: and this it does,
not by hard labor, but merely by adhering to it. Alas, for human
vanity! when the turreted ships which man has built, that he may
fight from castle-walls, at sea as well as at land, are held captive
and motionless by a fish a foot and a half long! Such a fish is said
to have stopped the admiral's ship at the battle of Actium, and
compelled Antony to go into another. And in our own memory, one of
these animals held fast the ship of Caius, the emperor, when he was
sailing from Astura to Antium. The stopping of this ship, when all
the rest of the fleet went on, caused surprise; but this did not
last long, for some of the men jumped into the water to look for the
fish, and found it sticking to the rudder; they showed it to Caius,
who was indignant that this animal should interpose its prohibition
to his progress, when impelled by four hundred rowers. It was like a
slug; and had no power, after it was taken into the ship."

[Note 1\4: Lucan is describing one of the poetical compounds
produced in incantations.
  Huc quicquid fœtu genuit Natura sinistro
  Miscetur: non spuma canum quibus unda timori est,
  Viscera non lyncis, non duræ nodus hyænæ
  Defuit, et cervi pasti serpente medullæ;
  In mediis _Echineis_ aquis, oculique draconum.
      Etc.               _Pharsalia_, **vi. 670.]

[Note 2\4: Plin. _Hist. N._ xxxii. 5.]

A very little advance in the power of thinking clearly on the force
which it exerted in pulling, would have enabled the Romans to see
that the ship and its rowers must pull the adhering fish by the hold
the oars had upon the water; and that, except the fish had a hold
equally strong on some external body, it could not resist this force.

3. _Indistinctness of Ideas shown in Architecture._--Perhaps it may
serve to illustrate still further the extent to which, under the
Roman empire, men's notions of mechanical relations became faint,
wavered, and disappeared, if we observe the change which took place
in architecture. All architecture, to possess genuine beauty, must
be mechanically consistent. The decorative members must represent a
structure which has in it a principle of support and stability. Thus
the Grecian colonnade was a straight horizontal beam, resting on
vertical props; and the pediment imitated a frame like a roof, where
oppositely inclined beams support each other. These forms of
building were, therefore, proper models of art, because they implied
supporting forces. But to be content with colonnades and pediments,
which, though they imitated the forms of the Grecian ones, were
destitute of their mechanical truth, belonged to the decline of art;
and showed that men had lost the idea of force, and retained only
that of shape. Yet this was what the architects of the Roman empire
did. Under their hands, the pediment was severed at its vertex, and
divided into separate halves, so that it was no longer a mechanical
possibility. The entablature no longer lay straight from pillar to
pillar, but, projecting over each {192} column, turned back to the
wall, and adhered to it in the intervening space. The splendid
remains of Palmyra, Balbec, Petra, exhibit endless examples of this
kind of perverse inventiveness; and show us, very instructively, how
the decay of art and of science alike accompany this indistinctness
of ideas which we are now endeavoring to illustrate.

4. _Indistinctness of Ideas in Astronomy._--Returning to the
sciences, it may be supposed, at first sight, that, with regard to
astronomy, we have not the same ground for charging the stationary
period with indistinctness of ideas on that subject, since they were
able to acquire and verify, and, in some measure, to apply, the
doctrines previously established. And, undoubtedly, it must be
confessed that men's notions of the relations of space and number
are never very indistinct. It appears to be impossible for these
chains of elementary perception ever to be much entangled. The later
Greeks, the Arabians, and the earliest modern astronomers, must have
conceived the hypotheses of the Ptolemaic system with tolerable
completeness. And yet, we may assert, that during the stationary
period, men did not possess the notions, even of space and number,
in that vivid and vigorous manner which enables them to discover new
truths. If they had perceived distinctly that the astronomical
theorist had merely to do with _relative_ motions, they must have
been led to see the possibility, at least, of the Copernican system;
as the Greeks, at an earlier period, had already perceived it. We
find no trace of this. Indeed, the mode in which the Arabian
mathematicians present the solutions of their problems, does not
indicate that clear apprehension of the relations of space, and that
delight in the contemplation of them, which the Greek geometrical
speculations imply. The Arabs are in the habit of giving conclusions
without demonstrations, precepts without the investigations by which
they are obtained; as if their main object were practical rather
than speculative,--the calculation of results rather than the
exposition of theory. Delambre[3\4] has been obliged to exercise
great ingenuity, in order to discover the method by which Ibn Iounis
proved his solution of certain difficult problems.

[Note 3\4: Delamb. _M. A._ p. 125-8.]

5. _Indistinctness of Ideas shown by Skeptics._--The same
unsteadiness of ideas which prevents men from obtaining clear views,
and steady and just convictions, on special subjects, may lead them
to despair of or deny the possibility of acquiring certainty at all,
and may thus make them skeptics with regard to all knowledge. Such
skeptics {193} are themselves men of indistinct views, for they
could not otherwise avoid assenting to the demonstrated truths of
science; and, so far as they may be taken as specimens of their
contemporaries, they prove that indistinct ideas prevail in the age
in which they appear. In the stationary period, moreover, the
indefinite speculations and unprofitable subtleties of the schools
might further impel a man of bold and acute mind to this universal
skepticism, because they offered nothing which could fix or satisfy
him. And thus the skeptical spirit may deserve our notice as
indicative of the defects of a system of doctrine too feeble in
demonstration to control such resistance.

The most remarkable of these philosophical skeptics is Sextus
Empiricus; so called, from his belonging to that medical sect which
was termed the _empirical_, in contradistinction to the _rational_
and _methodical_ sects. His works contain a series of treatises,
directed against all the divisions of the science of his time. He
has chapters against the Geometers, against the Arithmeticians,
against the Astrologers, against the Musicians, as well as against
Grammarians, Rhetoricians, and Logicians; and, in short, as a modern
writer has said, his skepticism is employed as a sort of frame-work
which embraces an encyclopedical view of human knowledge. It must be
stated, however, that his objections are rather to the metaphysical
grounds, than to the details of the sciences; he rather denies the
possibility of speculative truth in general, than the experimental
truths which had been then obtained. Thus his objections to geometry
and arithmetic are founded on abstract cavils concerning the nature
of points, letters, unities, &c. And when he comes to speak against
astrology, he says, "I am not going to consider that perfect science
which rests upon geometry and arithmetic; for I have already shown
the weakness of those sciences: nor that faculty of prediction (of
the motions of the heavens) which belongs to the pupils of Eudoxus,
and Hipparchus, and the rest, which some call Astronomy; for that is
an observation of phenomena, like agriculture or navigation: but
against the Art of Prediction from the time of birth, which the
Chaldeans exercise." Sextus, therefore, though a skeptic by
profession, was not insensible to the difference between
experimental knowledge and mystical dogmas, though even the former
had nothing which excited his admiration.

The skepticism which denies the evidence of the truths of which the
best established physical sciences consist, must necessarily involve
a very indistinct apprehension of those truths; for such truths,
properly exhibited, contain their own evidence, and are the best
antidote {194} to this skepticism. But an incredulity or contempt
towards the asserted truths of physical science may arise also from
the attention being mainly directed to the certainty and importance
of religious truths. A veneration for revealed religion may thus
assume the aspect of a skepticism with regard to natural knowledge.
Such appears to be the case with Algazel or Algezeli, who is adduced
by Degerando[4\4] as an example of an Arabian skeptic. He was a
celebrated teacher at Bagdad in the eleventh century, and he
declared himself the enemy, not only of the mixed Peripatetic and
Platonic philosophy of the time, but of Aristotle himself. His work
entitled _The Destructions of the Philosophers_, is known to us by
the refutation of it which Averrhoes published, under the title of
_Destruction of Algazel's Destructions of the Philosophers_. It
appears that he contested the fundamental principles both of the
Platonic and of the Aristotelian schools, and denied the possibility
of a known connection between cause and effect; thus making a
prelude, says Degerando, to the celebrated argumentation of Hume.

[Note 4\4: Degerando, _Hist. Comp. de Systèmes_, iv. 224.]

[2d Ed.] Since the publication of my first edition, an account of
Algazel or Algazzali and his works has been published under the
title of _Essai sur les Ecoles Philosophiques chez les Arabes, et
notamment sur la Doctrine d'Algazzali_, par August Schmölders.
Paris. 1842. From this book it appears that Degerando's account of
Algazzali is correct, when he says[5\4] that "his skepticism seems
to have essentially for its object to destroy all systems of merely
rational theology, in order to open an indefinite career, not only
to faith guided by revelation, but also to the free exaltation of a
mystical enthusiasm." It is remarked by Dr. Schmölders, following M.
de Hammer-Purgstall, that the title of the work referred to in the
text ought rather to be _Mutual Refutation of the Philosophers_: and
that its object is to show that Philosophy consists of a mass of
systems, each of which overturns the others. The work of Algazzali
which Dr. Schmölders has published, _On the Errors of Sects, &c._,
contains a kind of autobiographical account of the way in which the
author was led to his views. He does not reject the truths of
science, but he condemns the mental habits which are caused by
laying too much stress upon science. Religious men, he says, are, by
such a course, led to reject all science, even what relates to
eclipses of the moon and sun; and men of science are led to hate
religion.[6\4] {195}

[Note 5\4: _Hist. Comp._ iv. p. 227.]

[Note 6\4: _Essai_, p. 33.]

6. _Neglect of Physical Reasoning in Christendom._--If the Arabians,
who, during the ages of which we are speaking, were the most eminent
cultivators of science, entertained only such comparatively feeble
and servile notions of its doctrines, it will easily be supposed,
that in the Christendom of that period, where physical knowledge was
comparatively neglected, there was still less distinctness and
vividness in the prevalent ideas on such subjects. Indeed, during a
considerable period of the history of the Christian Church, and by
many of its principal authorities, the study of natural philosophy
was not only disregarded but discommended. The great practical
doctrines which were presented to men's minds, and the serious
tasks, of the regulation of the will and affections, which religion
impressed upon them, made inquiries of mere curiosity seem to be a
reprehensible misapplication of human powers; and many of the
fathers of the Church revived, in a still more peremptory form, the
opinion of Socrates, that the only valuable philosophy is that which
teaches us our moral duties and religious hopes.[7\4] Thus Eusebius
says,[8\4] "It is not through ignorance of the things admired by
them, but through contempt of their useless labor, that we think
little of these matters, turning our souls to the exercise of better
things." When the thoughts were thus intentionally averted from
those ideas which natural philosophy involves, the ideas inevitably
became very indistinct in their minds; and they could not conceive
that any other persons could find, on such subjects, grounds of
clear conviction and certainty. They held the whole of their
philosophy to be, as Lactantius[9\4] asserts it to be, "empty and
false." "To search," says he, "for the causes of natural things; to
inquire whether the sun be as large as he seems, whether the moon is
convex or concave, whether the stars are fixed in the sky or float
freely in the air; of what size and of what material are the
heavens; whether they be at rest or in motion; what is the magnitude
of the earth; on what foundations it is suspended and balanced;--to
dispute and conjecture on such matters, is just as if we chose to
discuss what we think of a city in a remote country, of which we
never heard but the name." It is impossible to express more forcibly
that absence of any definite notions on physical subjects which led
to this tone of thought.

[Note 7\4: Brucker, iii. 317.]

[Note 8\4: _Præp. Ev._ xv. 61.]

[Note 9\4: _Inst._ 1. iii. init.]

7. _Question of Antipodes._--With such habits of thought, we are not
to be surprised if the relations resulting from the best established
theories were apprehended in an imperfect and incongruous manner.
{196} We have some remarkable examples of this; and a very notable
one is the celebrated question of the existence of _Antipodes_, or
persons inhabiting the opposite side of the globe of the earth, and
consequently having the soles of their feet directly opposed to
ours. The doctrine of the globular form of the earth results, as we
have seen, by a geometrical necessity, from a clear conception of
the various points of knowledge which we obtain, bearing upon that
subject. This doctrine was held distinctly by the Greeks; it was
adopted by all astronomers, Arabian and European, who followed them;
and was, in fact, an inevitable part of every system of astronomy
which gave a consistent and intelligible representation of
phenomena. But those who did not call before their minds any
distinct representation at all, and who referred the whole question
to other relations than those of space, might still deny this
doctrine; and they did so. The existence of inhabitants on the
opposite side of the terraqueous globe, was a fact of which
experience alone could teach the truth or falsehood; but the
religious relations, which extend alike to all mankind, were
supposed to give the Christian philosopher grounds for deciding
against the possibility of such a race of men. Lactantius,[10\4] in
the fourth century, argues this matter in a way very illustrative of
that impatience of such speculations, and consequent confusion of
thought, which we have mentioned. "Is it possible," he says, "that
men can be so absurd as to believe that the crops and trees on the
other side of the earth hang downwards, and that men there have
their feet higher than their heads? If you ask of them how they
defend these monstrosities--how things do not fall away from the
earth on that side--they reply, that the nature of things is such
that heavy bodies tend towards the centre, like the spokes of a
wheel, while light bodies, as clouds, smoke, fire, tend from the
centre towards the heavens on all sides. Now I am really at a loss
what to say of those who, when they have once gone wrong, steadily
persevere in their folly, and defend one absurd opinion by another."
It is obvious that so long as the writer refused to admit into his
thoughts the fundamental conception of their theory, he must needs
be at a loss what to say to their arguments without being on that
account in any degree convinced of their doctrines.

[Note 10\4: _Inst._ 1. iii. 23.]

In the sixth century, indeed, in the reign of Justinian, we find a
writer (Cosmas Indicopleustes[11\4]) who does not rest in this
obscurity of {197} representation; but in this case, the
distinctness of the pictures only serves to show his want of any
clear conception as to what suppositions would explain the
phenomena. He describes the earth as an oblong floor, surrounded by
upright walls, and covered by a vault, below which the heavenly
bodies perform their revolutions, going round a certain high
mountain, which occupies the northern parts of the earth, and makes
night by intercepting the light of the sun. In Augustin[12\4] (who
flourished A. D. 400) the opinion is treated on other grounds; and
without denying the globular form of the earth, it is asserted that
there are no inhabitants on the opposite side, because no such race
is recorded by Scripture among the descendants of Adam.[13\4]
Considerations of the same kind operated in the well-known instance
of Virgil, Bishop of Salzburg, in the eighth century. When he was
reported to Boniface, Archbishop of Mentz, as holding the existence
of Antipodes, the prelate was shocked at the assumption, as it
seemed to him, of a world of human beings, out of the reach of the
conditions of salvation; and application was made to Pope Zachary
for a censure of the holder of this dangerous doctrine. It does not,
however, appear that this led to any severity; and the story of the
deposition of Virgil from his bishopric, which is circulated by
Kepler and by more modern writers, is undoubtedly altogether false.
The same scruples continued to prevail among Christian writers to a
later period; and Tostatus[14\4] notes the opinion of the rotundity
of the earth as an "unsafe" doctrine, only a few years before
Columbus visited the other hemisphere.

[Note 11\4: Montfaucon, _Collectio Nova Patrum_, t. ii. p. 113.
Cosmas Indicopleustes. Christianorum Opiniones de Mundo, sive
Topographia Christiana.]

[Note 12\4: _Civ. D._ xvi. 9.]

[Note 13\4: It appears, however, that scriptural arguments were
found on the other side. St. Jerome says (_Comm. in Ezech._ i. 6),
speaking of the two cherubims with four faces, seen by the prophet,
and the interpretation of the vision: "Alii vero qui philosophorum
stultam sequuntur sapientiam, duo hemispheria in duobus templi
cherubim, nos et antipodes, quasi supinos et cadentes homines
suspicantur."]

[Note 14\4: Montfauc. _Patr._ t. ii.]

8. _Intellectual Condition of the Religious Orders._--It must be
recollected, however, that though these were the views and tenets of
many religious writers, and though they may be taken as indications of
the prevalent and characteristic temper of the times of which we
speak, they never were universal. Such a confusion of thought affects
the minds of many persons, even in the most enlightened times; and in
what we call the Dark Ages, though clear views on such subjects might
be more rare, those who gave their minds to science, entertained the
true opinion of the figure of the earth. Thus Boëthius[15\4] (in the
sixth century) urges the smallness of the globe of the earth, {198}
compared with the heavens, as a reason to repress our love of glory.
This work, it will be recollected, was translated into the Anglo-Saxon
by our own Alfred. It was also commented on by Bede, who, in what he
says on this passage, assents to the doctrine, and shows an
acquaintance with Ptolemy and his commentators, both Arabian and
Greek. Gerbert, in the tenth century, went from France to Spain to
study astronomy with the Arabians, and soon surpassed his masters. He
is reported to have fabricated clocks, and an astrolabe of peculiar
construction. Gerbert afterwards (in the last year of the first
thousand from the birth of Christ) became pope, by the name of
Sylvester II. Among other cultivators of the sciences, some of whom,
from their proficiency, must have possessed with considerable
clearness and steadiness the elementary ideas on which it depends, we
may here mention, after Montucla,[16\4] Adelbold, whose work On the
Sphere was addressed to Pope Sylvester, and whose geometrical
reasonings are, according to Montucla,[17\4] vague and chimerical;
Hermann Contractus, a monk of St Gall, who, in 1050, published
astronomical works; William of Hirsaugen, who followed his example in
1080; Robert of Lorraine, who was made Bishop of Hereford by William
the Conqueror, in consequence of his astronomical knowledge. In the
next century, Adelhard Goth, an Englishman, travelled among the Arabs
for purposes of study, as Gerbert had done in the preceding age; and
on his return, translated the Elements of Euclid, which he had brought
from Spain or Egypt. Robert Grostête, Bishop of Lincoln, was the
author of an Epitome on the Sphere; Roger Bacon, in his youth the
contemporary of Robert, and of his brother Adam Marsh, praises very
highly their knowledge in mathematics.

[Note 15\4: Boëthius, _Cons._ ii. pr. 7.]

[Note 16\4: Mont. i. 502.]

[Note 17\4: Ib. i. 503.]

"And here," says the French historian of mathematics, whom I have
followed in the preceding relation, "it is impossible not to reflect
that all those men who, if they did not augment the treasure of the
sciences, at least served to transmit it, were monks, or had been
such originally. Convents were, during these stormy ages, the asylum
of sciences and letters. Without these religious men, who, in the
silence of their monasteries, occupied themselves in transcribing,
in studying, and in imitating the works of the ancients, well or
ill, those works would have perished; perhaps not one of them would
have come down to us. The thread which connects us with the Greeks
and Romans would have been snapt asunder; the precious productions
of {199} ancient literature would no more exist for us, than the
works, if any there were, published before the catastrophe that
annihilated that highly scientific nation, which, according to
Bailly, existed in remote ages in the centre of Tartary, or at the
roots of Caucasus. In the sciences we should have had all to create;
and at the moment when the human mind should have emerged from its
stupor and shaken off its slumbers, we should have been no more
advanced than the Greeks were after the taking of Troy." He adds,
that this consideration inspires feelings towards the religious
orders very different from those which, when he wrote, were
prevalent among his countrymen.

Except so far as their religious opinions interfered, it was natural
that men who lived a life of quiet and study, and were necessarily
in a great measure removed from the absorbing and blinding interests
with which practical life occupies the thoughts, should cultivate
science more successfully than others, precisely because their ideas
on speculative subjects had time and opportunity to become clear and
steady. The studies which were cultivated under the name of the
Seven Liberal Arts, necessarily tended to favor this effect. The
_Trivium_,[18\4] indeed, which consisted of Grammar, Logic, and
Rhetoric, had no direct bearing upon those ideas with which physical
science is concerned; but the _Quadrivium_, Music, Arithmetic,
Geometry, Astronomy, could not be pursued with any attention,
without a corresponding improvement of the mind for the purposes of
sound knowledge.[19\4]

[Note 18\4: Bruck. iii. 597.]

[Note 19\4: Roger Bacon, in his _Specula Mathematica_, cap. i., says
"Harum scientiarum porta et clavis est mathematica, quam sancti a
principio mundi invenerunt, etc. Cujus negligentia _jam per triginta
vel quadraginta annos_ destruxit totum studium Latinorum." I do not
know on what occasion this neglect took place.]

9. _Popular Opinions._--That, even in the best intellects, something
was wanting to fit them for scientific progress and discovery, is
obvious from the fact that science was so long absolutely
stationary. And I have endeavored to show that one part of this
deficiency was the want of the requisite clearness and vigor of the
fundamental scientific ideas. If these were wanting, even in the
most powerful and most cultivated minds, we may easily conceive that
still greater confusion and obscurity prevailed in the common class
of mankind. They actually adopted the belief, however crude and
inconsistent, that the form of the earth and heavens really is what
at any place it appears to be; that the earth is flat, and the
waters of the sky sustained above a material floor, through which in
showers they descend. Yet the true doctrines of {200} astronomy
appear to have had some popular circulation. For instance, a French
poem of the time of Edward the Second, called _Ymage du Monde_,
contains a metrical account of the earth and heavens, according to
the Ptolemaic views; and in a manuscript of this poem, preserved in
the library of the University of Cambridge, there are
representations, in accordance with the text, of a spherical earth,
with men standing upright upon it on every side; and by way of
illustrating the tendency of all things to the centre, perforations
of the earth, entirely through its mass, are described and depicted;
and figures are exhibited dropping balls down each of these holes,
so as to meet in the interior. And, as bearing upon the perplexity
which attends the motions of _up_ and _down_, when applied to the
globular earth, and the change of the direction of gravity which
would occur in passing the centre, the readers of Dante will
recollect the extraordinary manner in which the poet and his guide
emerge from the bottom of the abyss; and the explanation which
Virgil imparts to him of what he there sees. After they have crept
through the aperture in which Lucifer is placed, the poet says,
    "Io levai gli occhi e credetti vedere
  Lucifero com' io l' avea lasciato,
  E vidile le gambe in su tenere."
  . . . . . "Questi come è fitto
  Si sottasopra!" . . . . .
  "Quando mi volsi, tu passast' il punto
  Al qual si traggon d' ogni parte i pesi."
          _Inferno_, xxxiv.

  . . . . . "I raised mine eyes,
  Believing that I Lucifer should see
  Where he was lately left, but saw him now
  With legs held upward." . . . . .
  "How standeth he in posture thus reversed?"
  . . . . . . . . . . . . . .
  "Thou wast on the other side so long as I
  Descended; when I turned, thou didst o'erpass
  That point to which from every part is dragged
  All heavy substance."           CARY.

This is more philosophical than Milton's representation, in a more
scientific age, of Uriel sliding to the earth on a sunbeam, and
sliding back again, when the sun had sunk below the horizon.
  . . . . . "Uriel to his charge
  Returned on that bright beam whose point now raised,
  Bore him slope downward to the sun, now fallen
  Beneath the Azores."            _Par. Lost_, B. iv.  {201}

The philosophical notions of up and down are too much at variance
with the obvious suggestions of our senses, to be held steadily and
justly by minds undisciplined in science. Perhaps it was some
misunderstood statement of the curved surface of the ocean, which
gave rise to the tradition of there being a part of the sea directly
over the earth, from which at times an object has been known to fall
or an anchor to be let down. Even such whimsical fancies are not
without instruction, and may serve to show the reader what that
vagueness and obscurity of ideas is, of which I have been
endeavoring to trace the prevalence in the dark ages.

We now proceed to another of the features which appears to me to
mark, in a very prominent manner, the character of the stationary
period.




CHAPTER II.

THE COMMENTATORIAL SPIRIT OF THE MIDDLE AGES.


WE have already noticed, that, after the first great achievements of
the founders of sound speculation, in the different departments of
human knowledge, had attracted the interest and admiration which those
who became acquainted with them could not but give to them, there
appeared a disposition among men to lean on the authority of some of
these teachers;--to study the opinions of others as the only mode of
forming their own;--to read nature through books;--to attend to what
had been already thought and said, rather than to what really is and
happens. This tendency of men's minds requires our particular
consideration. Its manifestations were very important, and highly
characteristic of the stationary period; it gave, in a great degree, a
peculiar bias and direction to the intellectual activity of many
centuries; and the kind of labor with which speculative men were
occupied in consequence of this bias, took the place of that
examination of realities which must be their employment, in order that
real knowledge may make any decided progress.

In some subjects, indeed, as, for instance, in the domains of
morals, poetry, and the arts, whose aim is the production of beauty,
this opposition between the study of former opinion and present
reality, may not be so distinct; inasmuch as it may be said by some,
that, in these subjects, opinions are realities; that the thoughts
and feelings which {202} prevail in men's minds are the material
upon which we must work, the particulars from which we are to
generalize, the instruments which we are to use; and that,
therefore, to reject the study of antiquity, or even its authority,
would be to show ourselves ignorant of the extent and mutual bearing
of the elements with which we have to deal;--would be to cut asunder
that which we ought to unite into a vital whole. Yet even in the
provinces of history and poetry, the poverty and servility of men's
minds during the middle ages, are shown by indications so strong as
to be truly remarkable; for instance, in the efforts of the
antiquarians of almost every European country to assimilate the
early history of their own state to the poet's account of the
foundation of Rome, by bringing from the sack of Troy, Brutus to
England, Bavo to Flanders, and so on. But however this may be, our
business at present is, to trace the varying spirit of the
_physical_ philosophy of different ages; trusting that, hereafter,
this prefatory study will enable us to throw some light upon the
other parts of philosophy. And in physics the case undoubtedly was,
that the labor of observation, which is one of the two great
elements of the progress of knowledge, was in a great measure
superseded by the collection, the analysis, the explanation, of
previous authors and opinions; experimenters were replaced by
commentators; criticism took the place of induction; and instead of
great discoverers we had learned men.

1. _Natural Bias to Authority._--It is very evident that, in such a
bias of men's studies, there is something very natural; however
strained and technical this erudition may have been, the
propensities on which it depends are very general, and are easily
seen. Deference to the authority of thoughtful and sagacious men, a
disposition which men in general neither reject nor think they ought
to reject in practical matters, naturally clings to them, even in
speculation. It is a satisfaction to us to suppose that there are,
or have been, minds of transcendent powers, of wide and wise views,
superior to the common errors and blindness of our nature. The
pleasure of admiration, and the repose of confidence, are
inducements to such a belief. There are also other reasons why we
willingly believe that there are in philosophy great teachers, so
profound and sagacious, that, in order to arrive at truth, we have
only to learn their thoughts, to understand their writings. There is
a peculiar interest which men feel in dealing with the thoughts of
their fellow-men, rather than with brute matter. Matter feels and
excites no sympathies: in seeking for mere laws of nature, there is
nothing of mental intercourse with the great spirits of the past, as
there is in {203} studying Aristotle or Plato. Moreover, a large
portion of this employment is of a kind the most agreeable to most
speculative minds; it consists in tracing the consequences of
assumed principles: it is deductive like geometry: and the
principles of the teachers being known, and being undisputed, the
deduction and application of their results is an obvious,
self-satisfying, and inexhaustible exercise of ingenuity.

These causes, and probably others, make criticism and commentation
flourish, when invention begins to fail, oppressed and bewildered by
the acquisitions it has already made; and when the vigor and hope of
men's minds are enfeebled by civil and political changes.
Accordingly,[20\4] the Alexandrian school was eminently
characterized by a spirit of erudition, of literary criticism, of
interpretation, of imitation. These practices, which reigned first
in their full vigor in "the Museum," are likely to be, at all times,
the leading propensities of similar academical institutions.

[Note 20\4: Degerando, _Hist. des Syst. de Philos._ iii. p. 134.]

How natural it is to select a great writer as a paramount authority,
and to ascribe to him extraordinary profundity and sagacity, we may
see, in the manner in which the Greeks looked upon Homer; and the
fancy which detected in his poems traces of the origin of all arts
and sciences, has, as we know, found favor even in modern times. To
pass over earlier instances of this feeling, we may observe, that
Strabo begins his Geography by saying that he agrees with
Hipparchus, who had declared Homer to be the first author of our
geographical knowledge; and he does not confine the application of
this assertion to the various and curious topographical information
which the Iliad and Odyssey contain, concerning the countries
surrounding the Mediterranean; but in phrases which, to most
persons, might appear the mere play of a poetical fancy, or a casual
selection of circumstances, he finds unquestionable evidence of a
correct knowledge of general geographical truths. Thus,[21\4] when
Homer speaks of the sun "rising from the soft and deep-flowing
ocean," of his "splendid blaze plunging in the ocean;" of the
northern constellation
  "Alone unwashen by the ocean wave;"
and of Jupiter, "who goes to the ocean to feast with the blameless
Ethiopians;" Strabo is satisfied from these passages that Homer knew
the dry land to be surrounded with water: and he reasons in like
manner with respect to other points of geography. {204}

[Note 21\4: Strabo, i. p. 5.]

2. _Character of Commentators._--The spirit of commentation, as has
already been suggested, turns to questions of taste, of metaphysics,
of morals, with far more avidity than to physics. Accordingly, critics
and grammarians were peculiarly the growth of this school; and, though
the commentators sometimes chose works of mathematical or physical
science for their subject (as Proclus, who commented on Euclid's
Geometry, and Simplicius, on Aristotle's Physics), these commentaries
were, in fact, rather metaphysical than mathematical. It does not
appear that the commentators have, in any instance, illustrated the
author by bringing his assertions of facts to the test of experiment.
Thus, when Simplicius comments on the passage concerning a vacuum,
which we formerly adduced, he notices the argument which went upon the
assertion, that a vessel full of ashes would contain as much water as
an empty vessel; and he mentions various opinions of different
authors, but no trial of the fact. Eudemus had said, that the ashes
contained something hot, as quicklime does, and that by means of this,
a part of the water was evaporated; others supposed the water to be
condensed, and so on.[22\4]

[Note 22\4: Simplicius, p. 170.]

The Commentator's professed object is to explain, to enforce, to
illustrate doctrines assumed as true. He endeavors to adapt the work
on which he employs himself to the state of information and of opinion
in his own time; to elucidate obscurities and technicalities; to
supply steps omitted in the reasoning; but he does not seek to obtain
additional truths or new generalizations. He undertakes only to give
what is virtually contained in his author; to develop, but not to
create. He is a cultivator of the thoughts of others: his labor is not
spent on a field of his own; he ploughs but to enrich the granary of
another man. Thus he does not work as a freeman, but as one in a
servile condition; or rather, his is a menial, and not a productive
service: his office is to adorn the appearance of his master, not to
increase his wealth.

Yet though the Commentator's employment is thus subordinate and
dependent, he is easily led to attribute to it the greatest
importance and dignity. To elucidate good books is, indeed, a useful
task; and when those who undertake this work execute it well, it
would be most unreasonable to find fault with them for not doing
more. But the critic, long and earnestly employed on one author, may
easily underrate the relative value of other kinds of mental
exertion. He may {205} ascribe too large dimensions to that which
occupies the whole of his own field of vision. Thus he may come to
consider such study as the highest aim, and best evidence of human
genius. To understand Aristotle, or Plato, may appear to him to
comprise all that is possible of profundity and acuteness. And when
he has travelled over a portion of their domain, and satisfied
himself that of this he too is master, he may look with complacency
at the circuit he has made, and speak of it as a labor of vast
effort and difficulty. We may quote, as an expression of this
temper, the language of Sir Henry Savile, in concluding a course of
lectures on Euclid, delivered at Oxford.[23\4] "By the grace of God,
gentlemen hearers, I have performed my promise; I have redeemed my
pledge. I have explained, according to my ability, the definitions,
postulates, axioms, and _first eight propositions_ of the Elements
of Euclid. Here, sinking under the weight of years, I lay down my
art and my instruments."

[Note 23\4: Exolvi per Dei gratiam, Domini auditores, promissum;
liberavi fldem meam; explicavi pro meo modulo, definitiones,
petitiones, communes sententias, et _octo priores propositiones_
Elementorum Euclidis. Hic, annis fessus, cyclos artemque repono.]

We here speak of the peculiar province of the Commentator; for
undoubtedly, in many instances, a commentary on a received author
has been made the vehicle of conveying systems and doctrines
entirely different from those of the author himself; as, for
instance, when the New Platonists wrote, taking Plato for their
text. The labors of learned men in the stationary period, which came
under this description, belong to another class.

3. _Greek Commentators on Aristotle._--The commentators or disciples
of the great philosophers did not assume at once their servile
character. At first their object was to supply and correct, as well
as to explain their teacher. Thus among the earlier commentators of
Aristotle, Theophrastus invented five moods of syllogism in the
first figure, in addition to the four invented by Aristotle, and
stated with additional accuracy the rules of hypothetical
syllogisms. He also not only collected much information concerning
animals, and natural events, which Aristotle had omitted, but often
differed with his master; as, for instance, concerning the saltness
of the sea: this, which the Stagirite attributed to the effect of
the evaporation produced by the sun's rays, was ascribed by
Theophrastus to beds of salt at the bottom. Porphyry,[24\4] who
flourished in the third century, wrote a book on the _Predicables_,
which was found to be so suitable a complement {206} to the
_Predicaments_ or Categories of Aristotle, that it was usually
prefixed to that treatise; and the two have been used as an
elementary work together, up to modern times. The Predicables are
the five steps which the gradations of generality and particularity
introduce;--_genus_, _species_, _difference_, _individual_,
_accident_:--the Categories are the ten heads under which assertions
or predications may be arranged:--_substance_, _quantity_,
_relation_, _quality_, _place_, _time_, _position_, _habit_,
_action_, _passion_.

[Note 24\4: Buhle, Arist. i. 284.]

At a later period, the Aristotelian commentators became more
servile, and followed the author step by step, explaining, according
to their views, his expressions and doctrines; often, indeed, with
extreme prolixity, expanding his clauses into sentences, and his
sentences into paragraphs. Alexander Aphrodisiensis, who lived at
the end of the second century, is of this class; "sometimes useful,"
as one of the recent editors of Aristotle says;[25\4] "but by the
prolixity of his interpretation, by his perverse itch for himself
discussing the argument expounded by Aristotle, for defending his
opinions, and for refuting or reconciling those of others, he rather
obscures than enlightens." At various times, also, some of the
commentators, and especially those of the Alexandrian school,
endeavored to reconcile, or combined without reconciling, opposing
doctrines of the great philosophers of the earlier times.
Simplicius, for instance, and, indeed, a great number of the
Alexandrian Philosophers,[26\4] as Alexander, Ammonius, and others,
employed themselves in the futile task of reconciling the doctrines
of the Pythagoreans, of the Eleatics, of Plato, and of the Stoics,
with those of Aristotle. Boethius[27\4] entertained the design of
translating into Latin the whole of Aristotle's and Plato's works,
and of showing their agreement; a gigantic plan, which he never
executed. Others employed themselves in disentangling the confusion
which such attempts produced, as John the Grammarian, surnamed
Philoponus, "the Labor-loving;" who, towards the end of the seventh
century, maintained that Aristotle was entirely misunderstood by
Porphyry and Proclus,[28\4] who had pretended to incorporate his
doctrines into those of the New Platonic school, or even to
reconcile him with Plato himself on the subject of _ideas_. Others,
again, wrote Epitomes, Compounds, Abstracts; and endeavored to throw
the works of the philosopher into some simpler and more obviously
regular form, as John of Damascus, in {207} the middle of the eighth
century, who made abstracts of some of Aristotle's works, and
introduced the study of the author into theological education. These
two writers lived under the patronage of the Arabs; the former was
favored by Amrou, the conqueror of Egypt; the latter was at first
secretary to the Caliph, but afterwards withdrew to a
monastery.[29\4]

[Note 25\4: Ib. i. 288.]

[Note 26\4: Ib. i. 311.]

[Note 27\4: Degerando, _Hist. des Syst._ iv. 100.]

[Note 28\4: Ib. iv. 155.]

[Note 29\4: Deg. iv. 150.]

At this period the Arabians became the fosterers and patrons of
philosophy, rather than the Greeks. Justinian had, by an edict,
closed the school of Athens, the last of the schools of heathen
philosophy. Leo, the Isaurian, who was a zealous Iconoclast,
abolished also the schools where general knowledge had been taught,
in combination with Christianity,[30\4] yet the line of the
Aristotelian commentators was continued, though feebly, to the later
ages of the Greek empire. Anna Comnena[31\4] mentions a Eustratus
who employed himself upon the dialectic and moral treatises, and
whom she does not hesitate to elevate above the Stoics and
Platonists, for his talent in philosophical discussions. Nicephorus
Blemmydes wrote logical and physical epitomes for the use of John
Ducas; George Pachymerus composed an epitome of the philosophy of
Aristotle, and a compend of his logic; Theodore Metochytes, who was
famous in his time alike for his eloquence and his learning, has
left a paraphrase of the books of Aristotle on Physics, on the Soul,
the Heavens,[32\4] &c. Fabricius states that this writer has a
chapter, the object of which is to prove, that all philosophers, and
Aristotle and Plato in particular, have disdained the authority of
their predecessors. He could hardly help remarking in how different
a spirit philosophy had been pursued since their time.

[Note 30\4: Ib. iv. 163.]

[Note 31\4: Ib. 167.]

[Note 32\4: Ib. 168.]

4. _Greek Commentators of Plato and others._--I have spoken
principally of the commentators of Aristotle, for he was the great
subject of the commentators proper; and though the name of his
rival, Plato, was graced by a list of attendants, hardly less
numerous, these, the Neoplatonists, as they are called, had
introduced new elements into the doctrines of their nominal master,
to such an extent that they must be placed in a different class. We
may observe here, however, how, in this school as in the
Peripatetic, the race of commentators multiplied itself. Porphyry,
who commented on Aristotle, was commented on by Ammonius; Plotinus's
Enneads were commented on by Proclus and Dexippus. Psellus[33\4] the
elder was a paraphrast of {208} Aristotle; Psellus the younger, in
the eleventh century, attempted to restore the New Platonic school.
The former of these two writers had for his pupils two men, the
emperor Leo, surnamed the Philosopher, and Photius the patriarch,
who exerted themselves to restore the study of literature at
Constantinople. We still possess the Collection of Extracts of
Photius, which, like that of Stobæus and others, shows the tendency
of the age to compilations, abstracts, and epitomes,--the extinction
of philosophical vitality.

[Note 33\4: Deg. iv. 169.]

5. _Arabian Commentators of Aristotle._--The reader might perhaps
have expected, that when the philosophy of the Greeks was carried
among a new race of intellects, of a different national character
and condition, the train of this servile tradition would have been
broken; that some new thoughts would have started forth; that some
new direction, some new impulse, would have been given to the search
for truth. It might have been anticipated that we should have had
schools among the Arabians which should rival the Peripatetic,
Academic, and Stoic among the Greeks;--that they would preoccupy the
ground on which Copernicus and Galileo, Lavoisier and Linnæus, won
their fame;--that they would make the next great steps in the
progressive sciences. Nothing of this, however, happened. The
Arabians cannot claim, in science or philosophy, any really great
names; they produced no men and no discoveries which have materially
influenced the course and destinies of human knowledge; they tamely
adopted the intellectual servitude of the nation which they
conquered by their arms; they joined themselves at once to the
string of slaves who were dragging the car of Aristotle and
Plotinus. Nor, perhaps, on a little further reflection, shall we be
surprised at this want of vigor and productive power, in this period
of apparent national youth. The Arabians had not been duly prepared
rightly to enjoy and use the treasures of which they became
possessed. They had, like most uncivilized nations, been
passionately fond of their indigenous poetry; their imagination had
been awakened, but their rational powers and speculative tendencies
were still torpid. They received the Greek philosophy without having
passed through those gradations of ardent curiosity and keen
research, of obscurity brightening into clearness, of doubt
succeeded by the joy of discovery, by which the Greek mind had been
enlarged and exercised. Nor had the Arabians ever enjoyed, as the
Greeks had, the individual consciousness, the independent volition,
the intellectual freedom, arising from the freedom of political
institutions. They had not felt the contagious mental activity of a
small city,--the elation arising from the general {209} sympathy in
speculative pursuits diffused through an intelligent and acute
audience; in short, they had not had a national education such as
fitted the Greeks to be disciples of Plato and Hipparchus. Hence,
their new literary wealth rather encumbered and enslaved, than
enriched and strengthened them: in their want of taste for
intellectual freedom, they were glad to give themselves up to the
guidance of Aristotle and other dogmatists. Their military habits
had accustomed them to look to a leader; their reverence for the
book of their law had prepared them to accept a philosophical Koran
also. Thus the Arabians, though they never translated the Greek
poetry, translated, and merely translated, the Greek philosophy;
they followed the Greek philosophers without deviation, or, at
least, without any philosophical deviations. They became for the
most part Aristotelians;--studied not only Aristotle, but the
commentators of Aristotle; and themselves swelled the vast and
unprofitable herd.

The philosophical works of Aristotle had, in some measure, made
their way in the East, before the growth of the Saracen power. In
the sixth century, a Syrian, Uranus,[34\4] encouraged by the love of
philosophy manifested by Cosroes, had translated some of the
writings of the Stagirite; about the same time, Sergius had given
some translations in Syriac. In the seventh century, Jacob of Edessa
translated into this language the Dialectics, and added Notes to the
work. Such labors became numerous; and the first Arabic translations
of Aristotle were formed upon these Persian or Syriac texts. In this
succession of transfusions, some mistakes must inevitably have been
introduced.

[Note 34\4: Deg. iv. 196.]

The Arabian interpreters of Aristotle, like a large portion of the
Alexandrian ones, gave to the philosopher a tinge of opinions
borrowed from another source, of which I shall have to speak under
the head of _Mysticism_. But they are, for the most part,
sufficiently strong examples of the peculiar spirit of commentation,
to make it fitting to notice them here. At the head of them
stands[35\4] Alkindi, who appears to have lived at the court of
Almamon, and who wrote commentaries on the Organon of Aristotle. But
Alfarabi was the glory of the school of Bagdad; his knowledge
included mathematics, astronomy, medicine, and philosophy. Born in
an elevated rank, and possessed of a rich patrimony, he led an
austere life, and devoted himself altogether to study and
meditation. He employed himself particularly in unfolding the import
of Aristotle's treatise On the Soul.[36\4] Avicenna (Ebn Sina) {210}
was at once the Hippocrates and the Aristotle of the Arabians; and
certainly the most extraordinary man that the nation produced. In
the course of an unfortunate and stormy life, occupied by politics
and by pleasures, he produced works which were long revered as a
sort of code of science. In particular, his writings on medicine,
though they contain little besides a compilation of Hippocrates and
Galen, took the place of both, even in the universities of Europe;
and were studied as models at Paris and Montpelier, till the end of
the seventeenth century, at which period they fell into an almost
complete oblivion. Avicenna is conceived, by some modern
writers,[37\4] to have shown some power of original thinking in his
representations of the Aristotelian Logic and Metaphysics. Averroes
(Ebn Roshd) of Cordova, was the most illustrious of the Spanish
Aristotelians, and became the guide of the schoolmen,[38\4] being
placed by them on a level with Aristotle himself, or above him. He
translated Aristotle from the first Syriac version, not being able
to read the Greek text. He aspired to, and retained for centuries,
the title of the _Commentator_; and he deserves this title by the
servility with which he maintains that Aristotle[39\4] carried the
sciences to the highest possible degree, measured their whole
extent, and fixed their ultimate and permanent boundaries; although
his works are conceived to exhibit a trace of the New Platonism.
Some of his writings are directed against an Arabian skeptic, of the
name of Algazel, whom we have already noticed.

[Note 35\4: Ib. iv. 187.]

[Note 36\4: Ib. iv. 205.]

[Note 37\4: Deg. iv. 206.]

[Note 38\4: Ib. iv. 247. Averroes died A. D. 1206.]

[Note 39\4: Ib. iv. 248.]

When the schoolmen had adopted the supremacy of Aristotle to the
extent in which Averroes maintained it, their philosophy went
further than a system of mere commentation, and became a system of
dogmatism; we must, therefore, in another chapter, say a few words
more of the Aristotelians in this point of view, before we proceed
to the revival of science; but we must previously consider some
other features in the character of the Stationary Period. {211}




CHAPTER III.

OF THE MYSTICISM OF THE MIDDLE AGES.


IT has been already several times hinted, that a new and peculiar
element was introduced into the Greek philosophy which occupied the
attention of the Alexandrian school; and that this element tinged a
large portion of the speculations of succeeding ages. We may speak
of this peculiar element as _Mysticism_; for, from the notion
usually conveyed by this term, the reader will easily apprehend the
general character of the tendency now spoken of; and especially when
he sees its effect pointed out in various subjects. Thus, instead of
referring the events of the external world to space and time, to
sensible connection and causation, men attempted to reduce such
occurrences under spiritual and supersensual relations and
dependencies; they referred them to superior intelligences, to
theological conditions, to past and future events in the moral
world, to states of mind and feelings, to the creatures of an
imaginary mythology or demonology. And thus their physical Science
became Magic, their Astronomy became Astrology, the study of the
Composition of bodies became Alchemy, Mathematics became the
contemplation of the Spiritual Relations of number and figure, and
Philosophy became Theosophy.

The examination of this feature in the history of the human mind is
important for us, in consequence of its influence upon the
employments and the thoughts of the times now under our notice. This
tendency materially affected both men's speculations and their
labours in the pursuit of knowledge. By its direct operation, it
gave rise to the newer Platonic philosophy among the Greeks, and to
corresponding doctrines among the Arabians; and by calling into a
prominent place astrology, alchemy, and magic, it long occupied most
of the real observers of the material world. In this manner it
delayed and impeded the progress of true science; for we shall see
reason to believe that human knowledge lost more by the perversion
of men's minds and the misdirection of their efforts, than it gained
by any increase of zeal arising from the peculiar hopes and objects
of the mystics.

It is not our purpose to attempt any general view of the progress
and fortunes of the various forms of Mystical Philosophy; but only
to exhibit some of its characters, in so far as they illustrate
those {212} tendencies of thought which accompanied the
retrogradation of inductive science. And of these, the leading
feature which demands our notice is that already alluded to; namely,
the practice of referring things and events, not to clear and
distinct relations, obviously applicable to such cases;--not to
general rules capable of direct verification; but to notions vague,
distant, and vast, which we cannot bring into contact with facts,
because they belong to a different region from the facts; as when we
connect natural events with moral or historical causes, or seek
spiritual meanings in the properties of number and figure. Thus the
character of Mysticism is, that it refers particulars, not to
generalizations homogeneous and immediate, but to such as are
heterogeneous and remote; to which we must add, that the process of
this reference is not a calm act of the intellect, but is
accompanied with a glow of enthusiastic feeling.

1. _Neoplatonic Theosophy._--The _Newer Platonism_ is the first
example of this Mystical Philosophy which I shall consider. The main
points which here require our notice are, the doctrine of an
Intellectual World resulting from the act of the Divine Mind, as the
only reality; and the aspiration after the union of the human soul
with this Divine Mind, as the object of human existence. The "Ideas"
of Plato were Forms of our knowledge; but among the Neoplatonists
they became really existing, indeed the only really existing,
Objects; and the inaccessible scheme of the universe which these
ideas constitute, was offered as the great subject of philosophical
contemplation. The desire of the human mind to approach towards its
Creator and Preserver, and to obtain a spiritual access to Him,
leads to an employment of the thoughts which is well worth the
notice of the religious philosopher; but such an effort, even when
founded on revelation and well regulated, is not a means of advance
in physics; and when it is the mere result of natural enthusiasm, it
may easily obtain such a place in men's minds as to unfit them for
the successful prosecution of natural philosophy. The temper,
therefore, which introduces such supernatural communion into the
general course of its speculations, may be properly treated as
mystical, and as one of the causes of the decline of science in the
Stationary Period. The Neoplatonic philosophy requires our notice as
one of the most remarkable forms of this Mysticism.

Though Ammonius Saccas, who flourished at the end of the second
century, is looked upon as the beginner of the Neoplatonists, his
disciple Plotinus is, in reality, the great founder of the school,
both by his {213} works, which still remain to us, and by the
enthusiasm which his character and manners inspired among his
followers. He lived a life of meditation, gentleness, and
self-denial, and died in the second year of the reign of Claudius
(A. D. 270). His disciple, Porphyry, has given us a Life of him,
from which we may see how well his habitual manners were suited to
make his doctrines impressive. "Plotinus, the philosopher of our
time," Porphyry thus begins his biography, "appeared like a person
ashamed that he was in the body. In consequence of this disposition,
he could not bear to talk concerning his family, or his parents, or
his country. He would not allow himself to be represented by a
painter or statuary; and once, when Aurelius entreated him to permit
a likeness of him to be taken, he said, 'Is it not enough for us to
carry this image in which nature has enclosed us, but we must also
try to leave a more durable image of this image, as if it were so
great a sight?' And he retained the same temper to the last. When he
was dying, he said, 'I am trying to bring the divinity which is in
us to the divinity which is in the universe.'" He was looked upon by
his successors with extraordinary admiration and reverence; and his
disciple Porphyry collected from his lips, or from fragmental notes,
the six _Enneads_ of his doctrines (that is, parts each consisting
of _nine_ Books), which he arranged and annotated.

We have no difficulty in finding in this remarkable work examples of
mystical speculation. The Intelligible World of realities or essences
corresponds to the world of sense[40\4] in the classes of things which
it includes. To the Intelligible World, man's mind ascends, by a
triple road which Plotinus figuratively calls that of the Musician,
the Lover, the Philosopher.[41\4] The activity of the human soul is
identified by analogy with the motion of the heavens. "This activity
is about a middle point, and thus it is circular; but a middle point
is not the same in body and in the soul: in that, the middle point is
local; in this, it is that on which the rest depends. There is,
however, an analogy; for as in one case, so in the other, there must
be a middle point, and as the sphere revolves about its centre, the
soul revolves about God through its affections."

[Note 40\4: vi. Ennead, iii. 1.]

[Note 41\4: ii. E. ii. 2.]

The conclusion of the work is,[42\4] as might be supposed, upon the
approach to, union with, and fruition of God. The author refers
again to the analogy between the movements of the soul and those of
the heavens. "We move round him like a choral dance; even when we
{214} look from him we revolve about him: we do not always look at
him, but when we do, we have satisfaction and rest, and the harmony
which belongs to that divine movement. In this movement, the mind
beholds the fountain of life, the fountain of mind, the origin of
being, the cause of good, the root of the soul."[43\4] "There will
be a time when this vision shall be continual; the mind being no
more interrupted, nor suffering any perturbation from the body. Yet
that which beholds is not that which is disturbed; and when this
vision becomes dim, it does not obscure the knowledge which resides
in demonstration, and faith, and reasoning; but the vision itself is
not reason, but greater than reason, and before reason."[44\4]

[Note 42\4: vi. Enn. ix. 8.]

[Note 43\4: vi. Enn. ix. 9.]

[Note 44\4: vi. Enn. ix. 10.]

The fifth book of the third Ennead has for its subject the Dæmon
which belongs to each man. It is entitled "Concerning Love;" and the
doctrine appears to be, that the Love, or common source of the
passions which is in each man's mind, is "the Dæmon which they say
accompanies each man."[45\4] These dæmons were, however (at least by
later writers), invested with a visible aspect and with a personal
character, including a resemblance of human passions and motives. It
is curious thus to see an untenable and visionary generalization
falling back into the domain of the senses and the fancy, after a
vain attempt to support itself in the region of the reason. This
imagination soon produced pretensions to the power of making these
dæmons or genii visible; and the Treatise on the Mysteries of the
Egyptians, which is attributed to Iamblichus, gives an account of
the secret ceremonies, the mysterious words, the sacrifices and
expiations, by which this was to be done.

[Note 45\4: Ficinus, _Comm._ in v. Enn. iii.]

It is unnecessary for us to dwell on the progress of this school; to
point out the growth of the Theurgy which thus arose; or to describe
the attempts to claim a high antiquity for this system, and to make
Orpheus, the poet, the first promulgator of its doctrines. The
system, like all mystical systems, assumed the character rather of
religion than of a theory. The opinions of its disciples materially
influenced their lives. It gave the world the spectacle of an
austere morality, a devotional exaltation, combined with the
grossest superstitions of Paganism. The successors of Iamblichus
appeared rather to hold a priesthood, than the chair of a
philosophical school.[46\4] They were persecuted by Constantine and
Constantius, as opponents of Christianity. Sopater, a {215} Syrian
philosopher of this school, was beheaded by the former emperor on a
charge that he had bound the winds by the power of magic.[47\4] But
Julian, who shortly after succeeded to the purple, embraced with
ardor the opinions of Iamblichus. Proclus (who died A. D. 487) was
one of the greatest of the teachers of this school;[48\4] and was,
both in his life and doctrines, a worthy successor of Plotinus,
Porphyry, and Iamblichus. We possess a biography, or rather a
panegyric of him, by his disciple Marinus, in which he is exhibited
as a representation of the ideal perfection of the philosophic
character, according to the views of the Neoplatonists. His virtues
are arranged as physical, moral, purificatory, theoretic, and
theurgic. Even in his boyhood, Apollo and Minerva visited him in his
dreams: he studied oratory at Alexandria, but it was at Athens that
Plutarch and Lysianus initiated him in the mysteries of the New
Platonists. He received a kind of consecration at the hands of the
daughter of Plutarch, the celebrated Asclepigenia, who introduced
him to the traditions of the Chaldeans, and the practices of
theurgy; he was also admitted to the mysteries of Eleusis. He became
celebrated for his knowledge and eloquence; but especially for his
skill in the supernatural arts which were connected with the
doctrines of his sect. He appears before us rather as a hierophant
than a philosopher. A large portion of his life was spent in
evocations, purifications, fastings, prayers, hymns, intercourse
with apparitions, and with the gods, and in the celebration of the
festivals of Paganism, especially those which were held in honor of
the Mother of the Gods. His religious admiration extended to all
forms of mythology. The philosopher, said he, is not the priest of a
single religion, but of all the religions of the world. Accordingly,
he composed hymns in honor of all the divinities of Greece, Rome,
Egypt, Arabia;--Christianity alone was excluded from his favor.

[Note 46\4: Deg. iii. 407]

[Note 47\4: Gibbon, iii. 352.]

[Note 48\4: Deg. iii. 419.]

The reader will find an interesting view of the _School of
Alexandria_, in M. Barthelemy Saint-Hilaire's _Rapport_ on the
_Mémoires_ sent to the Academy of Moral and Political Sciences at
Paris, in consequence of its having, in 1841, proposed this as the
subject of a prize, which was awarded in 1844. M. Saint-Hilaire has
prefixed to this _Rapport_ a dissertation on the Mysticism of that
school. He, however, uses the term _Mysticism_ in a wider sense than
my purpose, which regarded mainly the bearing of the doctrines of
this school upon the progress of the Inductive Sciences, has led me
to do. Although he finds much to {216} admire in the Alexandrian
philosophy, he declares that they were incapable of treating
scientific questions. The extent to which this is true is well
illustrated by the extract which he gives from Plotinus, on the
question, "Why objects appear smaller in proportion as they are more
distant." Plotinus denies that the reason of this is that the angles
of vision become smaller. His reason for this denial is curious
enough. If it were so, he says, how could the heaven appear smaller
than it is, since it occupies the whole of the visual angle?

2. _Mystical Arithmetic._--It is unnecessary further to exemplify,
from Proclus, the general mystical character of the school and time
to which he belonged; but we may notice more specially one of the
forms of this mysticism, which very frequently offers itself to our
notice, especially in him; and which we may call _Mystical
Arithmetic_. Like all the kinds of Mysticism, this consists in the
attempt to connect our conceptions of external objects by general
and inappropriate notions of goodness, perfection, and relation to
the divine essence and government; instead of referring such
conceptions to those appropriate ideas, which, by due attention,
become perfectly distinct, and capable of being positively applied
and verified. The subject which is thus dealt with, in the doctrines
of which we now speak, is Number; a notion which tempts men into
these visionary speculations more naturally than any other. For
number is really applicable to moral notions--to emotions and
feelings, and to their objects--as well as to the things of the
material world. Moreover, by the discovery of the principle of
musical concords, it had been found, probably most unexpectedly,
that numerical relations were closely connected with sounds which
could hardly be distinguished from the expression of thought and
feeling; and a suspicion might easily arise, that the universe, both
of matter and of thought, might contain many general and abstract
truths of some analogous kind. The relations of number have so wide
a bearing, that the ramifications of such a suspicion could not
easily be exhausted, supposing men willing to follow them into
darkness and vagueness; which it is precisely the mystical tendency
to do. Accordingly, this kind of speculation appeared very early,
and showed itself first among the Pythagoreans, as we might have
expected, from the attention which they gave to the theory of
harmony: and this, as well as some other of the doctrines of the
Pythagorean philosophy, was adopted by the later Platonists, and,
indeed, by Plato himself, whose speculations concerning number have
decidedly a mystical character. The mere mathematical relations of
numbers,--as odd and even, perfect and imperfect, {217} abundant and
defective,--were, by a willing submission to an enthusiastic bias,
connected with the notions of good and beauty, which were suggested
by the terms expressing their relations; and principles resulting
from such a connection were woven into a wide and complex system. It
is not necessary to dwell long on this subject; the mere titles of
the works which treated of it show its nature. Archytas[49\4] is
said to have written a treatise on the number _ten_: Telaugé, the
daughter of Pythagoras, wrote on the number _four_. This number,
indeed, which was known by the name of the _Tetractys_, was very
celebrated in the school of Pythagoras. It is mentioned in the
"Golden Verses," which are ascribed to him: the pupil is conjured to
be virtuous,
  Ναὶ μὰ τὸν ἁμετέρᾳ ψυχᾷ παραδόντα τετρακτὺν
  Παγὰν ἀεννάου φύσεως . . . .
  By him who stampt _The Four_ upon the mind,--
  _The Four_, the fount of nature's endless stream.

[Note 49\4: Mont. ii. 123.]

In Plato's works, we have evidence of a similar belief in religious
relations of Number; and in the new Platonists, this doctrine was
established as a system. Proclus, of whom we have been speaking,
founds his philosophy, in a great measure, on the relation of Unity
and Multiple; from this, he is led to represent the causality of the
Divine Mind by three Triads of abstractions; and in the development
of one part of this system, the number seven is introduced.[50\4]
"The intelligible and intellectual gods produce all things
triadically; for the monads in these latter are divided according to
number; and what the monad was in the former, the number is in these
latter. And the intellectual gods produce all things hebdomically;
for they evolve the intelligible, and at the same time intellectual
triads, into intellectual hebdomads, and expand their contracted
powers into intellectual variety." Seven is what is called by
arithmeticians a _prime_ number, that is, it cannot be produced by
the multiplication of other numbers. In the language of the New
Platonists, the number seven is said to be a virgin, and without a
mother, and it is therefore sacred to Minerva. The number six is a
perfect number, and is consecrated to Venus.

[Note 50\4: Procl. v. 3, Taylor's translation.]

The relations of space were dealt with in like manner, the
Geometrical properties being associated with such physical and
metaphysical notions as vague thought and lively feeling could
anyhow connect with them. We may consider, as an example of
this,[51\4] Plato's opinion {218} concerning the particles of the
four elements. He gave to each kind of particle one of the five
regular solids, about which the geometrical speculations of himself
and his pupils had been employed. The particles of fire were
pyramids, because they are sharp, and tend upwards; those of earth
are cubes, because they are stable, and fill space; the particles of
air are octahedral, as most nearly resembling those of fire; those
of water are the icositetrahedron, as most nearly spherical. The
dodecahedron is the figure of the element of the heavens, and shows
its influence in other things, as in the twelve signs of the zodiac.
In such examples we see how loosely space and number are combined or
confounded by these mystical visionaries.

[Note 51\4: Stanley, _Hist. Phil._]

These numerical dreams of ancient philosophers have been imitated by
modern writers; for instance, by Peter Bungo and Kircher, who have
written De Mysteriis Numerorum. Bungo treats of the mystical
properties of each of the numbers in order, at great length. And
such speculations have influenced astronomical theories. In the
first edition of the Alphonsine Tables,[52\4] the precession was
represented by making the first point of Aries move, in a period of
7000 years, through a circle of which the radius was 18 degrees,
while the circle moved round the ecliptic in 49,000 years; and these
numbers, 7000 and 49,000, were chosen probably by Jewish
calculators, or with reference to Jewish Sabbatarian notions.

[Note 52\4: Montucla, i. 511.]

3. _Astrology._--Of all the forms which mysticism assumed, none was
cultivated more assiduously than astrology. Although this art
prevailed most universally and powerfully during the stationary
period, its existence, even as a detailed technical system, goes
back to a very early age. It probably had its origin in the East; it
is universally ascribed to the Babylonians and Chaldeans; the name
_Chaldean_ was, at Rome, synonymous with _mathematicus_, or
astrologer; and we read repeatedly that this class of persons were
expelled from Italy by a decree of the senate, both during the times
of the republic and of the empire.[53\4] The recurrence of this act
of legislation shows that it was not effectual: "It is a class of
men," says Tacitus, "which, in our city, will always be prohibited,
and will always exist." In Greece, it does not appear that the state
showed any hostility to the professors of this art. They undertook,
it would seem, then, as at a later period, to determine the course
of a man's character and life from the configuration of the stars at
the moment of his birth. We do not possess any of the {219}
speculations of the early astrologers; and we cannot therefore be
certain that the notions which operated in men's minds when the art
had its birth, agreed with the views on which it was afterwards
defended, when it became a matter of controversy. But it appears
probable, that, though it was at later periods supported by physical
analogies, it was originally suggested by mythological belief. The
Greeks spoke of the _influences_ or _effluxes_ (ἀπόῤῥοιας) which
proceeded from the stars; but the Chaldeans had probably thought
rather of the powers which they exercised as _deities_. In whatever
manner the sun, moon, and planets came to be identified with gods
and goddesses, it is clear that the characters ascribed to these
gods and goddesses regulate the virtues and powers of the stars
which bear their names. This association, so manifestly visionary,
was retained, amplified, and pursued, in an enthusiastic spirit,
instead of being rejected for more distinct and substantial
connections; and a pretended science was thus formed, which bears
the obvious stamp of mysticism.

[Note 53\4: Tacit. _Ann._ ii. 32. xii. 52. _Hist._ I. 22, II. 62.]

That common sense of mankind which teaches them that theoretical
opinions are to be calmly tried by their consequences and their
accordance with facts, appears to have counteracted the prevalence
of astrology in the better times of the human mind. Eudoxus, as we
are informed by Cicero,[54\4] rejected the pretensions of the
Chaldeans; and Cicero himself reasons against them with arguments as
sensible and intelligent as could be adduced by a writer of the
present day; such as the different fortunes and characters of
persons born at the same time; and the failure of the predictions,
in the case of Pompey, Crassus, Cæsar, to whom the astrologers had
foretold glorious old age and peaceful death. He also employs an
argument which the reader would perhaps not expect from him,--the
very great remoteness of the planets as compared with the distance
of the moon. "What contagion can reach us," he asks, "from a
distance almost infinite?"

[Note 54\4: Cic. _de Div._ ii. 42.]

Pliny argues on the same side, and with some of the same
arguments.[55\4] "Homer," he says, "tells us that Hector and
Polydamus were born the same night;--men of such different fortune.
And every hour, in every part of the world, are born lords and
slaves, kings and beggars."

[Note 55\4: _Hist. Nat._ vii. 49.]

The impression made by these arguments is marked in an anecdote told
concerning Publius Nigidius Figulus, a Roman of the time of Julius
Cæsar, whom Lucan mentions as a celebrated astrologer. It is {220}
said, that when an opponent of the art urged as an objection the
different fates of persons born in two successive instants, Nigidius
bade him make two contiguous marks on a potter's wheel, which was
revolving rapidly near them. On stopping the wheel, the two marks were
found to be really far removed from each other; and Nigidius is said
to have received the name of Figulus (the potter), in remembrance of
this story, His argument, says St. Augustine, who gives us the
narrative, was as fragile as the ware which the wheel manufactured.

As the darkening times of the Roman empire advanced, even the
stronger minds seem to have lost the clear energy which was
requisite to throw off this delusion. Seneca appears to take the
influence of the planets for granted; and even Tacitus[56\4] seems
to hesitate. "For my own part," says he, "I doubt; but certainly the
majority of mankind cannot be weaned from the opinion, that, at the
birth of each man, his future destiny is fixed; though some things
may fall out differently from the predictions, by the ignorance of
those who profess the art; and that thus the art is unjustly blamed,
confirmed as it is by noted examples in all ages." The occasion
which gives rise to these reflections of the historian is the
mention of Thrasyllus, the favorite astrologer of the Emperor
Tiberius, whose skill is exemplified in the following narrative.
Those who were brought to Tiberius on any important matter, were
admitted to an interview in an apartment situated on a lofty cliff
in the island of Capreæ. They reached this place by a narrow path,
accompanied by a single freedman of great bodily strength; and on
their return, if the emperor had conceived any doubts of their
trustworthiness, a single blow buried the secret and its victim in
the ocean below. After Thrasyllus had, in this retreat, stated the
results of his art as they concerned the emperor, Tiberius asked him
whether he had calculated how long he himself had to live. The
astrologer examined the aspect of the stars, and while he did this,
as the narrative states, showed hesitation, alarm, increasing
terror, and at last declared that, "the present hour was for him
critical, perhaps fatal." Tiberius embraced him, and told him "he
was right in supposing he had been in danger, but that he should
escape it;" and made him thenceforth his confidential counsellor.

[Note 56\4: _Ann._ vi. 22.]

The belief in the power of astrological prediction which thus obtained
dominion over the minds of men of literary cultivation and practical
energy, naturally had a more complete sway among the speculative {221}
but unstable minds of the later philosophical schools of Alexandria,
Athens, and Rome. We have a treatise on astrology by Proclus, which
will serve to exemplify the mystical principle in this form. It
appears as a commentary on a work on the same subject called
"Tetrabiblos," ascribed to Ptolemy; though we may reasonably doubt
whether the author of the "Megale Syntaxis" was also the writer of the
astrological work. A few notices of the commentary of Proclus will
suffice.[57\4] The science is defended by urging how powerful we know
the physical effects of the heavenly bodies to be. "The sun regulates
all things on earth;--the birth of animals, the growth of fruits, the
flowing of waters, the change of health, according to the seasons: he
produces heat, moisture, dryness, cold, according to his approach to
our zenith. The moon, which is the nearest of all bodies to the earth,
gives out much _influence_; and all things, animate and inanimate,
sympathize with her: rivers increase and diminish according to her
light; the advance of the sea, and its recess, are regulated by her
rising and setting; and along with her, fruits and animals wax and
wane, either wholly or in part." It is easy to see that by pursuing
this train of associations (some real and some imaginary) very vaguely
and very enthusiastically, the connections which astrology supposes
would receive a kind of countenance. Proclus then proceeds to
state[58\4] the doctrines of the science. "The sun," he says, "is
productive of heat and dryness; this power is moderate in its nature,
but is more perceived than that of the other luminaries, from his
magnitude, and from the change of seasons. The nature of the moon is
for the most part moist; for being the nearest to the earth, she
receives the vapors which rise from moist bodies, and thus she causes
bodies to soften and rot. But by the illumination she receives from
the sun, she partakes in a moderate degree of heat. Saturn is cold and
dry, being most distant both from the heating power of the sun, and
the moist vapors of the earth. His cold, however, is most prevalent,
his dryness is more moderate. Both he and the rest receive additional
powers from the configurations which they make with respect to the sun
and moon." In the same manner it is remarked that Mars is dry and
caustic, from his fiery nature, which, indeed, his color shows.
Jupiter is well compounded of warm and moist, as is Venus. Mercury is
variable in his character. From these notions were derived others
concerning the beneficial or hurtful effect of these stars. Heat and
{222} moisture are generative and creative elements; hence the
ancients, says Proclus, deemed Jupiter, and Venus, and the Moon to
have a good power; Saturn and Mercury, on the other hand, had an evil
nature.

[Note 57\4: I. 2.]

[Note 58\4: I. 4.]

Other distinctions of the character of the stars are enumerated,
equally visionary, and suggested by the most fanciful connections.
Some are masculine, and some feminine: the Moon and Venus are of the
latter kind. This appears to be merely a mythological or
etymological association. Some are diurnal, some nocturnal: the Moon
and Venus are of the latter kind, the Sun and Jupiter of the former;
Saturn and Mars are both.

The fixed stars, also, and especially those of the zodiac, had
especial influences and subjects assigned to them. In particular, each
sign was supposed to preside over a particular part of the body; thus
Aries had the head assigned to it, Taurus the neck, and so on.

The most important part of the sky in the astrologer's consideration,
was that sign of the zodiac which rose at the moment of the child's
birth; this was, properly speaking, the _horoscope_, the _ascendant_,
or the _first house_; the whole circuit of the heavens being divided
into twelve _houses_, in which life and death, marriage and children,
riches and honors, friends and enemies, were distributed.

We need not attempt to trace the progress of this science. It
prevailed extensively among the Arabians, as we might expect from the
character of that nation. Albumasar, of Balkh in Khorasan, who
flourished in the ninth century, who was one of their greatest
astronomers, was also a great astrologer; and his work on the latter
subject, "De Magnis Conjunctionibus, Annorum Revolutionibus ac eorum
Perfectionibus," was long celebrated in Europe. Aboazen Haly (the
writer of a treatise "De Judiciis Astrorum"), who lived in Spain in
the thirteenth century, was one of the classical authors on this
subject.

It will easily be supposed that when this _apotelesmatic_ or
_judicial_ astrology obtained firm possession of men's minds, it
would be pursued into innumerable subtle distinctions and
extravagant conceits; and the more so, as experience could offer
little or no check to such exercises of fancy and subtlety. For the
correction of rules of astrological divination by comparison with
known events, though pretended to by many professors of the art, was
far too vague and fallible a guidance to be of any real advantage.
Even in what has been called Natural Astrology, the dependence of
the weather on the heavenly bodies, it is easy to see what a vast
accumulation of well-observed facts is requisite to establish {223}
any true rule; and it is well known how long, in spite of facts,
false and groundless rules (as the dependence of the weather on the
moon) may keep their hold on men's minds. When the facts are such
loose and many-sided things as human characters, passions, and
happiness, it was hardly to be expected that even the most powerful
minds should be able to find a footing sufficiently firm, to enable
them to resist the impression of a theory constructed of sweeping
and bold assertions, and filled out into a complete system of
details. Accordingly, the connection of the stars with human persons
and actions was, for a long period, undisputed. The vague, obscure,
and heterogeneous character of such a connection, and its unfitness
for any really scientific reasoning, could, of course, never be got
rid of; and the bewildering feeling of earnestness and solemnity,
with which the connection of the heavens with man was contemplated,
never died away. In other respects, however, the astrologers fell
into a servile commentatorial spirit; and employed themselves in
annotating and illustrating the works of their predecessors to a
considerable extent, before the revival of true science.

It may be mentioned, that astrology has long been, and probably is,
an art held in great esteem and admiration among other eastern
nations besides the Mohammedans; for instance, the Jews, the
Indians, the Siamese, and the Chinese. The prevalence of vague,
visionary, and barren notions among these nations, cannot surprise
us; for with regard to them we have no evidence, as with regard to
Europeans we have, that they are capable, on subjects of physical
speculation, of originating sound and rational general principles.
The Arts may have had their birth in all parts of the globe; but it
is only Europe, at particular favored periods of its history, which
has ever produced Sciences.

We are, however, now speaking of a long period, during which this
productive energy was interrupted and suspended. During this period
Europe descended, in intellectual character, to the level at which
the other parts of the world have always stood. Her Science was then
a mixture of Art and Mysticism; we have considered several forms of
this Mysticism, but there are two others which must not pass
unnoticed, Alchemy and Magic.

We may observe, before we proceed, that the deep and settled
influence which Astrology had obtained among them, appears perhaps
most strongly in the circumstance, that the most vigorous and
clear-sighted minds which were concerned in the revival of science,
did not, for a long period, shake off the persuasion that there was,
in this art, some element of truth. Roger Bacon, Cardan, Kepler,
Tycho Brahe, {224} Francis Bacon, are examples of this. These, or
most of them, rejected all the more obvious and extravagant
absurdities with which the subject had been loaded; but still
conceived that some real and valuable truth remained when all these
were removed. Thus Campanella,[59\4] whom we shall have to speak of
as one of the first opponents of Aristotle, wrote an "Astrology
purified from all the Superstitions of the Jews and Arabians, and
treated physiologically."

[Note 59\4: Bacon, _De Aug._ iii. 4.]

4. _Alchemy._--Like other kinds of Mysticism, Alchemy seems to have
grown out of the notions of moral, personal, and mythological
qualities, which men associated with terms, of which the primary
application was to physical properties. This is the form in which
the subject is presented to us in the earliest writings which we
possess on the subject of chemistry;--those of Geber[60\4] of
Seville, who is supposed to have lived in the eighth or ninth
century. The very titles of Geber's works show the notions on which
this pretended science proceeds. They are, "Of the Search of
Perfection;" "Of the Sum of Perfection, or of the Perfect
Magistery;" "Of the Invention of Verity, or Perfection." The basis
of this phraseology is the distinction of metals into more or less
_perfect_; gold being the most perfect, as being the most valuable,
most beautiful, most pure, most durable; silver the next; and so on.
The "Search of Perfection" was, therefore, the attempt to convert
other metals into gold; and doctrines were adopted which represented
the metals as all compounded of the same elements, so that this was
theoretically possible. But the mystical trains of association were
pursued much further than this; gold and silver were held to be the
most noble of metals; gold was their King, and silver their Queen.
Mythological associations were called in aid of these fancies, as
had been done in astrology. Gold was Sol, silver was Luna, the moon;
copper, iron, tin, lead, were assigned to Venus, Mars, Jupiter,
Saturn. The processes of mixture and heat were spoken of as personal
actions and relations, struggles and victories. Some elements were
conquerors, some conquered; there existed preparations which
possessed the power of changing the whole of a body into a substance
of another kind: these were called _magisteries_.[61\4] When gold
and quicksilver are combined, the king and the queen are married, to
produce children of their own kind. It will easily be conceived,
that when chemical operations were described in phraseology of this
sort, the enthusiasm of the {225} fancy would be added to that of
the hopes, and observation would not be permitted to correct the
delusion, or to suggest sounder and more rational views.

[Note 60\4: Thomson's _Hist. of Chem._ i. 117.]

[Note 61\4: Boyle, Thomson's _Hist. Ch._ i. 25. Carolus Musitanus.]

The exaggeration of the vague notion of perfection and power in the
object of the alchemist's search, was carried further still. The
same preparation which possessed the faculty of turning baser metals
into gold, was imagined to be also a universal medicine, to have the
gift of curing or preventing diseases, prolonging life, producing
bodily strength and beauty: the _philosophers' stone_ was finally
invested with every desirable efficacy which the fancy of the
"philosophers" could devise.

It has been usual to say that Alchemy was the mother of Chemistry;
and that men would never have made the experiments on which the real
science is founded, if they had not been animated by the hopes and
the energy which the delusive art inspired. To judge whether this is
truly said, we must be able to estimate the degree of interest which
men feel in purely speculative truth, and in the real and
substantial improvement of art to which it leads. Since the fall of
Alchemy, and the progress of real Chemistry, these motives have been
powerful enough to engage in the study of the science, a body far
larger than the Alchemists ever were, and no less zealous. There is
no apparent reason why the result should not have been the same, if
the progress of true science had begun sooner. Astronomy was long
cultivated without the bribe of Astrology. But, perhaps, we may
justly say this;--that, in the stationary period, men's minds were
so far enfeebled and degraded, that pure speculative truth had not
its full effect upon them; and the mystical pursuits in which some
dim and disfigured images of truth were sought with avidity, were
among the provisions by which the human soul, even when sunk below
its best condition, is perpetually directed to something above the
mere objects of sense and appetite;--a contrivance of compensation,
as it were, in the intellectual and spiritual constitution of man.

5. _Magic._--Magical Arts, so far as they were believed in by those
who professed to practise them, and so far as they have a bearing in
science, stand on the same footing as astrology; and, indeed, a
close alliance has generally been maintained between the two
pursuits. Incapacity and indisposition to perceive natural and
philosophical causation, an enthusiastic imagination, and such a
faith as can devise and maintain supernatural and spiritual
connexions, are the elements of this, as of other forms of
Mysticism. And thus, that temper which led men to aim at the
magician's supposed authority over the elements, {226} is an
additional exemplification of those habits of thought which
prevented the progress of real science, and the acquisition of that
command over nature which is founded on science, during the interval
now before us.

But there is another aspect under which the opinions connected with
this pursuit may serve to illustrate the mental character of the
Stationary Period.

The tendency, during the middle ages, to attribute the character of
Magician to almost all persons eminent for great speculative or
practical knowledge, is a feature of those times, which shows how
extensive and complete was the inability to apprehend the nature of
real science. In cultivated and enlightened periods, such as those of
ancient Greece, or modern Europe, knowledge is wished for and admired,
even by those who least possess it: but in dark and degraded periods,
superior knowledge is a butt for hatred and fear. In the one case,
men's eyes are open; their thoughts are clear; and, however high the
philosopher may be raised above the multitude, they can catch glimpses
of the intervening path, and see that it is free to all, and that
elevation is the reward of energy and labor. In the other case, the
crowd are not only ignorant, but spiritless; they have lost the
pleasure in knowledge, the appetite for it, and the feeling of dignity
which it gives: there is no sympathy which connects them with the
learned man: they see him above them, but know not how he is raised or
supported: he becomes an object of aversion and envy, of vague
suspicion and terror; and these emotions are embodied and confirmed by
association with the fancies and dogmas of superstition. To consider
superior knowledge as Magic, and Magic as a detestable and criminal
employment, was the form which these feelings of dislike assumed; and
at one period in the history of Europe, almost every one who had
gained any eminent literary fame, was spoken of as a magician.
Naudæus, a learned Frenchman, in the seventeenth century, wrote "An
Apology for all the Wise Men who have been unjustly reported
Magicians, from the Creation to the present Age." The list of persons
whom he thus thinks it necessary to protect, are of various classes
and ages. Alkindi, Geber, Artephius, Thebit, Raymund Lully, Arnold de
Villâ Novâ, Peter of Apono, and Paracelsus, had incurred the black
suspicion as physicians or alchemists. Thomas Aquinas, Roger Bacon,
Michael Scott, Picus of Mirandula, and Trithemius, had not escaped it,
though ministers of religion. Even dignitaries, such as Robert
Grosteste, Bishop of Lincoln, Albertus Magnus, Bishop of Ratisbon,
{227} Popes Sylvester the Second, and Gregory the Seventh, had been
involved in the wide calumny. In the same way in which the vulgar
confounded the eminent learning and knowledge which had appeared in
recent times, with skill in dark and supernatural arts, they converted
into wizards all the best-known names in the rolls of fame; as
Aristotle, Solomon, Joseph, Pythagoras; and, finally, the poet Virgil
was a powerful and skilful necromancer, and this fancy was exemplified
by many strange stories of his achievements and practices.

The various results of the tendency of the human mind to mysticism,
which we have here noticed, form prominent features in the
intellectual character of the world, for a long course of centuries.
The theosophy and theurgy of the Neoplatonists, the mystical
arithmetic of the Pythagoreans and their successors, the predictions
of the astrologers, the pretences of alchemy and magic, represent,
not unfairly, the general character and disposition of men's
thoughts, with reference to philosophy and science. That there were
stronger minds, which threw off in a greater or less degree this
train of delusive and unsubstantial ideas, is true; as, on the other
hand, Mysticism, among the vulgar or the foolish, often went to an
extent of extravagance and superstition, of which I have not
attempted to convey any conception. The lesson which the preceding
survey teaches us is, that during the Stationary Period, Mysticism,
in its various forms, was a leading character, both of the common
mind, and of the speculations of the most intelligent and profound
reasoners; and that this Mysticism was the opposite of that habit of
thought which we have stated Science to require; namely, clear
Ideas, distinctly employed to connect well-ascertained Facts;
inasmuch as the Ideas in which it dealt were vague and unstable, and
the temper in which they were contemplated was an urgent and
aspiring enthusiasm, which could not submit to a calm conference
with experience upon even terms. The fervor of thought in some
degree supplied the place of reason in producing belief; but
opinions so obtained had no enduring value; they did not exhibit a
permanent record of old truths, nor a firm foundation for new.
Experience collected her stores in vain, or ceased to collect them,
when she had only to pour them into the flimsy folds of the lap of
Mysticism; who was, in truth, so much absorbed in looking for the
treasures which were to fall from the skies, that she heeded little
how scantily she obtained, or how loosely she held, such riches as
might be found near her. {228}




CHAPTER IV.

OF THE DOGMATISM OF THE STATIONARY PERIOD.


IN speaking of the character of the age of commentators, we noticed
principally the ingenious servility which it displays;--the
acuteness with which it finds ground for speculation in the
expression of other men's thoughts;--the want of all vigor and
fertility in acquiring any real and new truths. Such was the
character of the reasoners of the stationary period from the first;
but, at a later day, this character, from various causes, was
modified by new features. The servility which had yielded itself to
the yoke, insisted upon forcing it on the necks of others: the
subtlety which found all the truth it needed in certain accredited
writings, resolved that no one should find there, or in any other
region, any other truths; speculative men became tyrants without
ceasing to be slaves; to their character of Commentators they added
that of Dogmatists.

1. _Origin of the Scholastic Philosophy._--The causes of this change
have been very happily analyzed and described by several modern
writers.[62\4] The general nature of the process may be briefly
stated to have been the following.

[Note 62\4:  Dr. Hampden, in the Life of Thomas Aquinas, in the
_Encyc. Metrop._ Degerando, _Hist. Comparée_, vol. iv. Also
Tennemann, _Hist. of Phil._ vol. viii. Introduction.]

The tendencies of the later times of the Roman empire to a
commenting literature, and a second-hand philosophy, have already
been noticed. The loss of the dignity of political freedom, the want
of the cheerfulness of advancing prosperity, and the substitution of
the less philosophical structure of the Latin language for the
delicate intellectual mechanism of the Greek, fixed and augmented
the prevalent feebleness and barrenness of intellect. Men forgot, or
feared, to consult nature, to seek for new truths, to do what the
great discoverers of other times had done; they were content to
consult libraries, to study and defend old opinions, to talk of what
great geniuses had said. They sought their philosophy in accredited
treatises, and dared not question such doctrines as they there found.

The character of the philosophy to which they were thus led, was
determined by this want of courage and originality. There are various
{229} antagonist principles of opinion, which seem alike to have their
root in the intellectual constitution of man, and which are maintained
and developed by opposing sects, when the intellect is in vigorous
action. Such principles are, for instance,--the claims of Authority
and of Reason to our assent;--the source of our knowledge in
Experience or in Ideas;--the superiority of a Mystical or of a
Skeptical turn of thought. Such oppositions of doctrine were found in
writers of the greatest fame; and two of those, who most occupied the
attention of students, Plato and Aristotle, were, on several points of
this nature, very diverse from each other in their tendency. The
attempt to reconcile these philosophers by Boëthius and others, we
have already noticed; and the attempt was so far successful, that it
left on men's minds the belief in the possibility of a great
philosophical system which should be based on both these writers, and
have a claim to the assent of all sober speculators.

But, in the mean time, the Christian Religion had become the leading
subject of men's thoughts; and divines had put forward its claims to
be, not merely the guide of men's lives, and the means of
reconciling them to their heavenly Master, but also to be a
Philosophy in the widest sense in which the term had been used;--a
consistent speculative view of man's condition and nature, and of
the world in which he is placed.

These claims had been acknowledged; and, unfortunately, from the
intellectual condition of the times, with no due apprehension of the
necessary ministry of Observation, and Reason dealing with
observation, by which alone such a system can be embodied. It was
held without any regulating principle, that the philosophy which had
been bequeathed to the world by the great geniuses of heathen
antiquity, and the Philosophy which was deduced from, and implied
by, the Revelations made by God to man, must be identical; and,
therefore, that Theology is the only true philosophy. Indeed, the
Neoplatonists had already arrived, by other roads, at the same
conviction. John Scot Erigena, in the reign of Alfred, and
consequently before the existence of the Scholastic Philosophy,
properly so called, had reasserted this doctrine.[63\4] Anselm, in
the eleventh century, again brought it forward;[64\4] and Bernard de
Chartres, in the thirteenth.[65\4]

[Note 63\4: Deg. iv. 351.]

[Note 64\4: Ib. iv. 388.]

[Note 65\4: Ib. iv. 418.]

This view was confirmed by the opinion which prevailed, concerning
the nature of philosophical truth; a view supported by the theory
{230} of Plato, the practice of Aristotle, and the general
propensities of the human mind: I mean the opinion that all science
may be obtained by the use of reasoning alone;--that by analysing
and combining the notions which common language brings before us, we
may learn all that we can know. Thus Logic came to include the whole
of Science; and accordingly this Abelard expressly maintained.[66\4]
I have already explained, in some measure, the fallacy of this
belief, which consists, as has been well said,[67\4] "in mistaking
the universality of the theory of language for the generalization of
facts." But on all accounts this opinion is readily accepted; and it
led at once to the conclusion, that the Theological Philosophy which
we have described, is complete as well as true.

[Note 66\4: Deg. iv. 407.]

[Note 67\4: _Enc. Met._ 807.]

Thus a Universal Science was established, with the authority of a
Religious Creed. Its universality rested on erroneous views of the
relation of words and truths; its pretensions as a science were
admitted by the servile temper of men's intellects; and its
religious authority was assigned it, by making all truth part of
religion. And as Religion claimed assent within her own jurisdiction
under the most solemn and imperative sanctions, Philosophy shared in
her imperial power, and dissent from their doctrines was no longer
blameless or allowable. Error became wicked, dissent became heresy;
to reject the received human doctrines, was nearly the same as to
doubt the Divine declarations. The _Scholastic Philosophy_ claimed
the assent of all believers.

The external form, the details, and the text of this philosophy,
were taken, in a great measure, from Aristotle; though, in the
spirit, the general notions, and the style of interpretation, Plato
and the Platonists had no inconsiderable share. Various causes
contributed to the elevation of Aristotle to this distinction. His
Logic had early been adopted as an instrument of theological
disputation; and his spirit of systematization, of subtle
distinction, and of analysis of words, as well as his disposition to
argumentation, afforded the most natural and grateful employment to
the commentating propensities. Those principles which we before
noted as the leading points of his physical philosophy, were
selected and adopted; and these, presented in a most technical form,
and applied in a systematic manner, constitute a large portion of
the philosophy of which we now speak, so far as it pretends to deal
with physics.

2. _Scholastic Dogmas._--But before the complete ascendancy of
Aristotle was thus established, when something of an intellectual
waking {231} took place after the darkness and sleep of the ninth
and tenth centuries, the Platonic doctrines seem to have had, at
first, a strong attraction for men's minds, as better falling in
with the mystical speculations and contemplative piety which
belonged to the times. John Scot Erigena[68\4] may be looked upon as
the reviver of the New Platonism in the tenth century. Towards the
end of the eleventh, Peter Damien,[69\4] in Italy, reproduced,
involved in a theological discussion, some Neoplatonic ideas.
Godefroy[70\4] also, censor of St. Victor, has left a treatise,
entitled _Microcosmus_; this is founded on a mystical analogy, often
afterwards again brought forward, between Man and the Universe.
"Philosophers and theologians," says the writer, "agree in
considering man as a little world; and as the world is composed of
four elements, man is endowed with four faculties, the senses, the
imagination, reason, and understanding." Bernard of Chartres,[71\4]
in his _Megascosmus_ and _Microcosmus_, took up the same notions.
Hugo, abbot of St. Victor, made a contemplative life the main point
and crown of his philosophy; and is said to have been the first of
the scholastic writers who made psychology his special study.[72\4]
He says the faculties of the mind are "the senses, the imagination,
the reason, the memory, the understanding, and the intelligence."

[Note 68\4: Deg. iv. 35.]

[Note 69\4: Ib. iv. 367.]

[Note 70\4: Ib. iv. 413.]

[Note 71\4: Ib. iv. 419.]

[Note 72\4: Ib. iv. 415.]

Physics does not originally and properly form any prominent part of
the Scholastic Philosophy, which consists mainly of a series of
questions and determinations upon the various points of a certain
technical divinity. Of this kind is the _Book of Sentences_ of Peter
the Lombard (bishop of Paris), who is, on that account, usually
called "Magister Sententiarum;" a work which was published in the
twelfth century, and was long the text and standard of such
discussions. The questions are decided by the authority of Scripture
and of the Fathers of the Church, and are divided into four Books,
of which the first contains questions concerning God and the
doctrine of the Trinity in particular; the second is concerning the
Creation; the third, concerning Christ and the Christian Religion;
and the fourth treats of Religious and Moral Duties. In the second
book, as in many of the writers of this time, the nature of Angels
is considered in detail, and the Orders of their Hierarchy, of which
there were held to be nine. The physical discussions enter only as
bearing upon the scriptural history of the creation, and cannot be
taken as a specimen of the work; but I may observe, that in speaking
of the division of the waters above the {232} firmament, he gives
one opinion, that of Bede, that the former waters are the solid
crystalline heavens in which the stars are fixed,[73\4] "for
crystal, which is so hard and transparent, is made of water." But he
mentions also the opinion of St. Augustine, that the waters above
the heavens are in a state of vapor, (_vaporaliter_) and in minute
drops; "if, then, water can, as we see in clouds, be so minutely
divided that it may be thus supported as vapor on air, which is
naturally lighter than water; why may we not believe that it floats
above that lighter celestial element in still minuter drops and
still lighter vapors? But in whatever manner the waters are there,
we do not doubt that they are there."

[Note 73\4: Lib. ii. Distinct. xiv. _De opere secundæ diei_.]

The celebrated _Summa Theologicæ_ of Thomas Aquinas is a work of the
same kind; and anything which has a physical bearing forms an
equally small part of it. Thus, of the 512 Questions of the _Summa_,
there is only one (Part I., Quest. 115), "on Corporeal Action," or
on any part of the material world; though there are several
concerning the celestial Hierarchies, as "on the Act of Angels,"
"on the Speaking of Angels," "on the Subordination of Angels,"
"on Guardian Angels," and the like. This, of course, would not be
remarkable in a treatise on Theology, except this Theology were
intended to constitute the whole of Philosophy.

We may observe, that in this work, though Plato, Avecibron, and many
other heathen as well as Christian philosophers, are adduced as
authority, Aristotle is referred to in a peculiar manner as "the
philosopher." This is noticed by John of Salisbury, as attracting
attention in his time (he died A.D. 1182). "The various Masters of
Dialectic," says he,[74\4] "shine each with his peculiar merit; but
all are proud to worship the footsteps of Aristotle; so much so,
indeed, that the name of _philosopher_, which belongs to them all, has
been pre-eminently appropriated to him. He is called the philosopher
_autonomatice_, that is, by excellence."

[Note 74\4: _Metalogicus_, lib. ii. cap. 16.]

The Question concerning Corporeal Action, in Aquinas, is divided
into six Articles; and the conclusion delivered upon the first
is,[75\4] that "Body being compounded of power and act, is active as
well as passive." Against this it is urged, that quantity is an
attribute of body, and that quantity prevents action; that this
appears in fact, since a larger body is more difficult to move. The
author replies, that {233} "quantity does not prevent corporeal form
from action altogether, but prevents it from being a universal
agent, inasmuch as the form is individualized, which, in matter
subject to quantity, it is. Moreover, the illustration deduced from
the ponderousness of bodies is not to the purpose; first, because
the addition of quantity is not the cause of gravity, as is proved
in the fourth book, De Cœlo and De Mundo" (we see that he quotes
familiarly the physical treatises of Aristotle); "second, because it
is false that ponderousness makes motion slower; on the contrary, in
proportion as any thing is heavier, the more does it move with its
proper motion; thirdly, because action does not take place by local
motion, as Democritus asserted; but by this, that something is drawn
from power into act."

[Note 75\4: _**Summa_, P. i. Q. 115. Art. 1.]

It does not belong to our purpose to consider either the theological
or the metaphysical doctrines which form so large a portion of the
treatises of the schoolmen. Perhaps it may hereafter appear, that
some light is thrown on some of the questions which have occupied
metaphysicians in all ages, by that examination of the history of
the Progressive Sciences in which we are now engaged; but till we
are able to analyze the leading controversies of this kind, it would
be of little service to speak of them in detail. It may be noticed,
however, that many of the most prominent of them refer to the great
question, "What is the relation between actual things and general
terms?" Perhaps in modern times, the actual things would be more
commonly taken as the point to start from; and men would begin by
considering how classes and universals are obtained from
individuals. But the schoolmen, founding their speculations on the
received modes of considering such subjects, to which both Aristotle
and Plato had contributed, travelled in the opposite direction, and
endeavored to discover how individuals were deduced from genera and
species;--what was "the Principle of Individuation." This was
variously stated by different reasoners. Thus Bonaventura[76\4]
solves the difficulty by the aid of the Aristotelian distinction of
Matter and Form. The individual derives from the Form the property
of _being something_, and from the Matter the property of being that
_particular thing_. Duns Scotus,[77\4] the great adversary of Thomas
Aquinas in theology, placed the principle of Individuation in "a
certain determining positive entity," which his school called
_Hæcceity_ or _thisness_. "Thus an individual man is Peter, because
his _humanity_ is combined with_ Petreity_." The force {234} of
abstract terms is a curious question, and some remarkable
experiments in their use had been made by the Latin Aristotelians
before this time. In the same way in which we talk of the _quantity_
and _quality_ of a thing, they spoke of its _quiddity_.[78\4]

[Note 76\4: Deg. iv. 573.]

[Note 77\4: Ib. iv. 523.]

[Note 78\4: Deg. iv. 494.]

We may consider the reign of mere disputation as fully established
at the time of which we are now speaking; and the only kind of
philosophy henceforth studied was one in which no sound physical
science had or could have a place. The wavering abstractions,
indistinct generalizations, and loose classifications of common
language, which we have already noted as the fountain of the physics
of the Greek Schools of philosophy, were also the only source from
which the Schoolmen of the middle ages drew their views, or rather
their arguments: and though these notional and verbal relations were
invested with a most complex and pedantic technicality, they did
not, on that account, become at all more precise as notions, or more
likely to lead to a single real truth. Instead of acquiring distinct
ideas, they multiplied abstract terms; instead of real
generalizations, they had recourse to verbal distinctions. The whole
course of their employments tended to make them, not only ignorant
of physical truth, but incapable of conceiving its nature.

Having thus taken upon themselves the task of raising and discussing
questions by means of abstract terms, verbal distinctions, and
logical rules alone, there was no tendency in their activity to come
to an end, as there was no progress. The same questions, the same
answers, the same difficulties, the same solutions, the same verbal
subtleties,--sought for, admired, cavilled at, abandoned,
reproduced, and again admired,--might recur without limit. John of
Salisbury[79\4] observes of the Parisian teachers, that, after
several years' absence, he found them not a step advanced, and still
employed in urging and parrying the same arguments; and this, as Mr.
Hallam remarks,[80\4] "was equally applicable to the period of
centuries." The same knots were tied and {235} untied; the same
clouds were formed and dissipated. The poet's censure of "the Sons
of Aristotle," is just as happily expressed:
               They stand
    Locked up together hand in hand
    Every one leads as he is led,
    The same bare path they tread,
  And dance like Fairies a fantastic round,
  But neither change their motion nor their ground.

[Note 79\4: He studied logic at Paris, at St. Geneviève, and then
left them. "Duodecennium mihi elapsum est diversis studiis
occupatum. Jucundum itaque visum est veteres quos reliqueram, et
quos adhuc Dialectica detinebat in monte, (Sanctæ Genovefæ) revisere
socios, conferre cum eis super ambiguitatibus pristinis; ut nostrûm
invicem collatione mutuâ commetiremur profectum. Inventi sunt, qui
fuerant, et ubi; neque enim ad palmam visi sunt processisse ad
quæstiones pristinis dirimendas, neque propositiunculam unam
adjecerant. Quibus urgebant stimulis eisdem et ipsi urgebantur," &c.
_Metalogicus_, lib. ii. cap. 10.]

[Note 80\4: _Middle Ages_, iii. 537.]

It will therefore be unnecessary to go into any detail respecting
the history of the School Philosophy of the thirteenth, fourteenth,
and fifteenth centuries. We may suppose it to have been, during the
intermediate time, such as it was at first and at last. An occasion
to consider its later days will be brought before us by the course
of our subject. But, even during the most entire ascendency of the
scholastic doctrines, the elements of change were at work. While the
doctors and the philosophers received all the ostensible homage of
men, a doctrine and a philosophy of another kind were gradually
forming: the practical instincts of man, their impatience of
tyranny, the progress of the useful arts, the promises of alchemy,
were all disposing men to reject the authority and deny the
pretensions of the received philosophical creed. Two antagonist
forms of opinion were in existence, which for some time went on
detached, and almost independent of each other; but, finally, these
came into conflict, at the time of Galileo; and the war speedily
extended to every part of civilized Europe.

3. _Scholastic Physics._--It is difficult to give briefly any
appropriate examples of the nature of the Aristotelian physics which
are to be found in the works of this time. As the gravity of bodies
was one of the first subjects of dispute when the struggle of the
rival methods began, we may notice the mode in which it was
treated.[81\4] "Zabarella maintains that the proximate cause of the
motion of elements is the _form_, in the Aristotelian sense of the
term: but to this sentence we," says Keckerman, "cannot agree; for
in all other things the _form_ is the proximate cause, not of the
_act_, but of the power or faculty from which the act flows. Thus in
man, the rational soul is not the cause of the act of laughing, but
of the risible faculty or power." Keckerman's system was at one time
a work of considerable authority: it was published in 1614. By
comparing and systematizing what he finds in Aristotle, he is led to
state his results in the form of definitions {236} and theorems.
Thus, "gravity is a motive quality, arising from cold, density, and
bulk, by which the elements are carried downwards." "Water is the
lower, intermediate element, cold and moist." The first theorem
concerning water is, "The moistness of the water is controlled by
its coldness, so that it is less than the moistness of the air;
though, according to the sense of the vulgar, water appears to
moisten more than air." It is obvious that the two properties of
fluids, to have their parts easily moved, and to wet other bodies,
are here confounded. I may, as a concluding specimen of this kind,
mention those propositions or maxims concerning fluids, which were
so firmly established, that, when Boyle propounded the true
mechanical principles of fluid action, he was obliged to state his
opinions as "hydrostatical _paradoxes_." These were,--that fluids do
not gravitate _in proprio loco_; that is, that water has no gravity
in or on water, since it is in its own place;--that air has no
gravity on water, since it is above water, which is its proper
place;--that earth in water tends to descend, since its place is
below water;--that the water rises in a pump or siphon, because
nature abhors a vacuum;--that some bodies have a positive levity in
others, as oil in water; and the like.

[Note 81\4: Keckerman, p. 1428.]

4. _Authority of Aristotle among the Schoolmen._--The authority of
Aristotle, and the practice of making him the text and basis of the
system, especially as it regarded physics, prevailed during the period
of which we speak. This authority was not, however, without its
fluctuations. Launoy has traced one part of its history in a book _On
the various Fortune of Aristotle in the University of Paris_. The most
material turns of this fortune depend on the bearing which the works
of Aristotle were supposed to have upon theology. Several of
Aristotle's works, and more especially his metaphysical writings, had
been translated into Latin, and were explained in the schools of the
University of Paris, as early as the beginning of the thirteenth
century.[82\4] At a council held at Paris in 1209, they were
prohibited, as having given occasion to the heresy of Almeric (or
Amauri), and because "they might give occasion to other heresies not
yet invented." The Logic of Aristotle recovered its credit some years
after this, and was publicly taught in the University of Paris in the
year 1215; but the Natural Philosophy and Metaphysics were prohibited
by a decree of Gregory the Ninth, in 1231. The Emperor Frederic the
Second employed a number of learned men to translate into Latin, from
the Greek and {237} Arabic, certain books of Aristotle, and of other
ancient sages; and we have a letter of Peter de Vineis, in which they
are recommended to the attention of the University of Bologna:
probably the same recommendation was addressed to other Universities.
Both Albertus Magnus and Thomas Aquinas wrote commentaries on
Aristotle's works; and as this was done soon after the decree of
Gregory the Ninth, Launoy is much perplexed to reconcile the fact with
the orthodoxy of the two doctors. Campanella, who was one of the first
to cast off the authority of Aristotle, says, "We are by no means to
think that St. Thomas _aristotelized_; he only expounded Aristotle,
that he might correct his errors; and I should conceive he did this
with the license of the Pope." This statement, however, by no means
gives a just view of the nature of Albertus's and Aquinas's
commentaries. Both have followed their author with profound
deference.[83\4] For instance, Aquinas[84\4] attempts to defend
Aristotle's assertion, that if there were no resistance, a body would
move through a space in no time; and the same defence is given by
Scotus.

[Note 82\4: Mosheim, iii. 157.]

[Note 83\4: Deg. N. 475.]

[Note 84\4: F. Piccolomini, ii. 835.]

We may imagine the extent of authority and admiration which
Aristotle would attain, when thus countenanced, both by the powerful
and the learned. In universities, no degree could be taken without a
knowledge of the philosopher. In 1452, Cardinal Totaril established
this rule in the University of Paris.[85\4] When Ramus, in 1543,
published an attack upon Aristotle, it was repelled by the power of
the court, and the severity of the law. Francis the First published
an edict, in which he states that he had appointed certain judges,
who had been of opinion,[86\4] "que le dit Ramus avoit été
téméraire, arrogant et impudent; et que parcequ'en son livre des
animadversions il reprenait Aristotle, estait évidemment connue et
manifeste son ignorance." The books are then declared to be
suppressed. It was often a complaint of pious men, that theology was
corrupted by the influence of Aristotle and his commentators.
Petrarch says,[87\4] that one of the Italian learned men conversing
with him, after expressing much contempt for the apostles and
fathers, exclaimed, "Utinam tu Averroen pati posses, ut videres
quanto ille tuis his nugatoribus major sit!"

[Note 85\4: Launoy, pp. 108, 128.]

[Note 86\4: Launoy, p. 132.]

[Note 87\4: Hallam, _M. A._ iii. 536.]

When the revival of letters began to take place, and a number of men
of ardent and elegant minds, susceptible to the impressions of
beauty of style and dignity of thought, were brought into contact
with Greek literature, Plato had naturally greater charms for them.
A {238} powerful school of Platonists (not Neoplatonists) was formed
in Italy, including some of the principal scholars and men of genius
of the time; as Picus of Mirandula in the middle, Marsilius Ficinus
at the end, of the fifteenth century. At one time, it appeared as if
the ascendency of Aristotle was about to be overturned; but, in
physics at least, his authority passed unshaken through this trial.
It was not by disputation that Aristotle could be overthrown; and
the Platonists were not persons whose doctrines led them to use the
only decisive method in such cases, the observation and unfettered
interpretation of facts.

The history of their controversies, therefore, does not belong to
our design. For like reasons we do not here speak of other authors,
who opposed the scholastic philosophy on general theoretical grounds
of various kinds. Such examples of insurrection against the
dogmatism which we have been reviewing, are extremely interesting
events in the history of the philosophy of science. But, in the
present work, we are to confine ourselves to the history of science
itself; in the hope that we may thus be able, hereafter, to throw a
steadier light upon that philosophy by which the succession of
stationary and progressive periods, which we are here tracing, may be
in some measure explained. We are now to close our account of the
stationary period, and to enter upon the great subject of the
progress of physical science in modern times.

5. _Subjects omitted. Civil Law, Medicine._--My object has been to
make my way, as rapidly as possible, to this period of progress; and
in doing this, I have had to pass over a long and barren track,
where almost all traces of the right road disappear. In exploring
this region, it is not without some difficulty that he who is
travelling with objects such as mine, continues a steady progress in
the proper direction; for many curious and attractive subjects of
research come in his way: he crosses the track of many a
controversy, which in its time divided the world of speculators, and
of which the results may be traced, even now, in the conduct of
moral, or political, or metaphysical discussions; or in the common
associations of thought, and forms of language. The wars of the
Nominalists and Realists; the disputes concerning the foundations of
morals, and the motives of human actions; the controversies
concerning predestination, free will, grace, and the many other
points of metaphysical divinity; the influence of theology and
metaphysics upon each other, and upon other subjects of human
curiosity; the effects of opinion upon politics, and of political
condition upon opinion; the influence of literature and philosophy
{239} upon each other, and upon society; and many other
subjects;--might be well worth examination, if our hope of success
did not reside in pursuing, steadily and directly, those inquiries
in which we can look for a definite and certain reply. We must even
neglect two of the leading studies of those times, which occupied
much of men's time and thoughts, and had a very great influence on
society; the one dealing with Notions, the other with Things; the
one employed about moral rules, the other about material causes, but
both for practical ends; I mean, the study of the _Civil Law_, and
of _Medicine_. The second of these studies will hereafter come
before us, as one of the principal occasions which led to the
cultivation of chemistry; but, in itself, its progress is of too
complex and indefinite a nature to be advantageously compared with
that of the more exact sciences. The Roman Law is held, by its
admirers, to be a system of deductive science, as exact as the
mathematical sciences themselves; and it may, therefore, be useful
to consider it, if we should, in the sequel, have to examine how far
there can exist an analogy between moral and physical science. But,
after a few more words on the middle ages, we must return to our
task of tracing the progress of the latter.




CHAPTER V.

PROGRESS OF THE ARTS IN THE MIDDLE AGES.


ART AND SCIENCE.--I shall, before I resume the history of science, say
a few words on the subject described in the title of this chapter,
both because I might otherwise be accused of doing injustice to the
period now treated of; and also, because we shall by this means bring
under our notice some circumstances which were important as being the
harbingers of the revival of progressive knowledge.

The accusation of injustice towards the state of science in the
middle ages, if we were to terminate our survey of them with what
has hitherto been said, might be urged from obvious topics. How do
we recognize, it might be asked, in a picture of mere confusion and
mysticism of thought, of servility and dogmatism of character, the
powers and acquirements to which we owe so many of the most
important inventions which we now enjoy? Parchment and paper,
printing and engraving, improved glass and steel, gunpowder, clocks,
telescopes, {240} the mariner's compass, the reformed calendar, the
decimal notation, algebra, trigonometry, chemistry, counterpoint, an
invention equivalent to a new creation of music;--these are all
possessions which we inherit from that which has been so
disparagingly termed the Stationary Period. Above all, let us look
at the monuments of architecture of this period;--the admiration and
the despair of modern architects, not only for their beauty, but for
the skill disclosed in their construction. With all these evidences
before us, how can we avoid allowing that the masters of the middle
ages not only made some small progress in Astronomy, which has,
grudgingly as it would seem, been admitted in a former Book; but
also that they were no small proficients in other sciences, in
Optics, in Harmonics, in Physics, and, above all, in Mechanics?

If, it may be added, we are allowed, in the present day, to refer to
the perfection of our arts as evidence of the advanced state of our
physical philosophy;--if our steam-engines, our gas-illumination, our
buildings, our navigation, our manufactures, are cited as triumphs of
science;--shall not prior inventions, made under far heavier
disadvantages,--shall not greater works, produced in an earlier state
of knowledge, also be admitted as witnesses that the middle ages had
their share, and that not a small or doubtful one, of science?

To these questions I answer, by distinguishing between Art, and
Science in that sense of general Inductive Systematic Truth, which
it bears in this work. To separate and compare, with precision,
these two processes, belongs to the Philosophy of Induction; and the
attempt must be reserved for another place: but the leading
differences are sufficiently obvious. Art is practical, Science is
speculative: the former is seen in doing; the latter rests in the
contemplation of what is known. The Art of the builder appears in
his edifice, though he may never have meditated on the abstract
propositions on which its stability and strength depends. The
Science of the mathematical mechanician consists in his seeing that,
under certain conditions, bodies must sustain each other's pressure,
though he may never have applied his knowledge in a single case.

Now the remark which I have to make is this:--in all cases the Arts
are prior to the related Sciences. Art is the parent, not the
progeny, of Science; the realization of principles in practice forms
part of the prelude, as well as of the sequel, of theoretical
discovery. And thus the inventions of the middle ages, which have
been above enumerated, though at the present day they may be
portions of our sciences, are no evidence that the sciences then
existed; but only that {241} those powers of practical observation
and practical skill were at work, which prepare the way for
theoretical views and scientific discoveries.

It may be urged, that the great works of art do virtually take for
granted principles of science; and that, therefore, it is unreasonable
to deny science to great artists. It may be said, that the grand
structures of Cologne, or Amiens, or Canterbury, could not have been
erected without a profound knowledge of mechanical principles.

To this we reply, that _such_ knowledge is manifestly not of the
nature of that which we call _science_. If the beautiful and skilful
structures of the middle ages prove that mechanics then existed as a
science, mechanics must have existed as a science also among the
builders of the Cyclopean walls of Greece and Italy, or of our own
Stonehenge; for the masses which are there piled on each other, could
not be raised without considerable mechanical skill. But we may go
much further. The actions of every man who raises and balances
weights, or walks along a pole, take for granted the laws of
equilibrium; and even animals constantly avail themselves of such
principles. Are these, then, acquainted with mechanics as a science?
Again, if actions which are performed by taking advantage of
mechanical properties prove a knowledge of the science of mechanics,
they must also be allowed to prove a knowledge of the science of
geometry, when they proceed on geometrical properties. But the most
familiar actions of men and animals proceed upon geometrical truths.
The Epicureans held, as Proclus informs us, that even asses knew that
two sides of a triangle are greater than the third. And animals may
truly be said to have a practical knowledge of this truth; but they
have not, therefore, a science of geometry. And in like manner among
men, if we consider the matter strictly, a practical assumption of a
principle does not imply a speculative knowledge of it.

We may, in another way also, show how inadmissible are the works of
the Master Artists of the middle ages into the series of events which
mark the advance of Science. The following maxim is applicable to a
history, such as we are here endeavoring to write. We are employed in
tracing the progress of such general principles as constitute each of
the sciences which we are reviewing; and no facts or subordinate
truths belong to our scheme, except so far as they tend to or are
included in these higher principles; nor are they important to us, any
further than as they prove such principles. Now with regard to
processes of art like those which we have referred to, namely, the
inventions of the middle ages, let us ask, _what_ principle each of
them {242} illustrates? What chemical doctrine rests for its support
on the phenomena of gunpowder, or glass, or steel? What new harmonical
truth was illustrated in the Gregorian chant? What mechanical
principle unknown to Archimedes was displayed in the printing-press?
The practical value and use, the ingenuity and skill of these
inventions is not questioned; but what is their place in the history
of speculative knowledge? Even in those cases in which they enter into
such a history, how minute a figure do they make! how great is the
contrast between their practical and theoretical importance! They may
in their operation have changed the face of the world; but in the
history of the principles of the sciences to which they belong, they
may be omitted without being missed.

As to that part of the objection which was stated by asking, why, if
the arts of our age prove its scientific eminence, the arts of the
middle ages should not be received as proof of theirs; we must reply
to it, by giving up some of the pretensions which are often put
forwards on behalf of the science of our times. The perfection of
the mechanical and other arts among us proves the advanced condition
of our sciences, only in so far as these arts have been perfected by
the application of some great scientific truth, with a clear insight
into its nature. The greatest improvement of the steam-engine was
due to the steady apprehension of an atmological doctrine by Watt;
but what distinct theoretical principle is illustrated by the
beautiful manufactures of porcelain, or steel, or glass? A chemical
view of these compounds, which would explain the conditions of
success and failure in their manufacture, would be of great value in
art; and it would also be a novelty in chemical theory; so little is
the present condition of those processes a triumph of science,
shedding intellectual glory on our age. And the same might be said
of many, or of most, of the processes of the arts as now practised.

2. _Arabian Science._--Having, I trust, established the view I have
stated, respecting the relation of Art and Science, we shall be able
very rapidly to dispose of a number of subjects which otherwise
might seem to require a detailed notice. Though this distinction has
been recognized by others, it has hardly been rigorously adhered to,
in consequence of the indistinct notion of _science_ which has
commonly prevailed. Thus Gibbon, in speaking of the knowledge of the
period now under our notice, says,[88\4] "Much useful experience had
been acquired in {243} the practice of arts and manufactures; but
the _science_ of chemistry owes its origin and improvement to the
industry of the Saracens. They," he adds, "first invented and named
the alembic for the purposes of distillation, analyzed the
substances of the three kingdoms of nature, tried the distinction
and affinities of alkalies and acids, and converted the poisonous
minerals into soft and salutary medicines." The formation and
realization of the notions of _analysis_ and of _affinity_, were
important steps in chemical science, which, as I shall hereafter
endeavor to show, it remained for the chemists of Europe to make at
a much later period. If the Arabians had done this, they might with
justice have been called the authors of the science of chemistry;
but no doctrines can be adduced from their works which give them any
title to this eminent distinction. Their claims are dissipated at
once by the application of the maxim above stated. _What_ analysis
of theirs tended to establish any received principle of chemistry?
_What_ true doctrine concerning the differences and affinities of
acids and alkalies did they teach? We need not wonder if Gibbon,
whose views of the boundaries of scientific chemistry were probably
very wide and indistinct, could include the arts of the Arabians
within its domain; but they cannot pass the frontier of science if
philosophically defined, and steadily guarded.

[Note 88\4: _Decline and Fall_, vol. x. p. 43.]

The judgment which we are thus led to form respecting the chemical
knowledge of the middle ages, and of the Arabians in particular, may
serve to measure the condition of science in other departments; for
chemistry has justly been considered one of their strongest points.
In botany, anatomy, zoology, optics, acoustics, we have still the
same observations to make, that the steps in science which, in the
order of progress, next followed what the Greeks had done, were left
for the Europeans of the sixteenth and seventeenth centuries. The
merits and advances of the Arabian philosophers in astronomy and
pure mathematics, we have already described.

3. _Experimental Philosophy of the Arabians._--The estimate to which
we have thus been led, of the scientific merits of the learned men
of the middle ages, is much less exalted than that which has been
formed by many writers; and, among the rest, by some of our own
time. But I am persuaded that any attempt to answer the questions
just asked, will expose the untenable nature of the higher claims
which have been advanced in favor of the Arabians. We can deliver no
just decision, except we will consent to use the terms of science in
a strict and precise sense: and if we do this, we shall find little,
either in the {244} particular discoveries or general processes of
the Arabians, which is important in the history of the Inductive
Sciences.[89\4]

[Note 89\4: If I might take the liberty of criticising an author who
has given a very interesting view of the period in question
(_Mahometanism Unveiled_, by the Rev. Charles Forster, 1829), I
would remark, that in his work this caution is perhaps too little
observed. Thus, he says, in speaking of Alhazen (vol. ii. p. 270),
"the theory of the telescope may be found in the work of this
astronomer;" and of another, "the uses of magnifying glasses and
telescopes, and the principle of their construction, are explained
in the Great Work of (Roger) Bacon, with a truth and clearness which
have commanded universal admiration." Such phrases would be much too
strong, even if used respecting the optical doctrines of Kepler,
which were yet incomparably more true and clear than those of Bacon.
To employ such language, in such cases, is to deprive such terms as
_theory_ and _principle_ of all meaning.]

The credit due to the Arabians for improvements in the general
methods of philosophizing, is a more difficult question; and cannot
be discussed at length by us, till we examine the history of such
methods in the abstract, which, in the present work, it is not our
intention to do.  But we may observe, that we cannot agree with
those who rank their merits high in this respect. We have already
seen, that their minds were completely devoured by the worst habits
of the stationary period,--Mysticism and Commentation. They followed
their Greek leaders, for the most part, with abject servility, and
with only that kind of acuteness and independent speculation which
the Commentator's vocation implies. And in their choice of the
standard subjects of their studies, they fixed upon those works, the
Physical Books of Aristotle, which have never promoted the progress
of science, except in so far as they incited men to refute them; an
effect which they never produced on the Arabians. That the Arabian
astronomers made some advances beyond the Greeks, we have already
stated: the two great instances are, the discovery of the Motion of
the Sun's Apogee by Albategnius, and the discovery (recently brought
to light) of the existence of the Moon's Second Inequality, by Aboul
Wefa. But we cannot but observe in how different a manner they
treated these discoveries, from that with which Hipparchus or
Ptolemy would have done. The Variation of the Moon, in particular,
instead of being incorporated into the system by means of an
Epicycle, as Ptolemy had done with the Evection, was allowed, almost
immediately, so far as we can judge, to fall into neglect and
oblivion: so little were the learned Arabians prepared to take their
lessons from observation as well as from books. That in many
subjects they made experiments, may easily be allowed: there never
was a period of the earth's history, and least of all a period of
commerce {245} and manufactures, luxury and art, medicine and
engineering, in which there were not going on innumerable processes,
which may be termed Experiments; and, in addition to these, the
Arabians adopted the pursuit of alchemy, and the love of exotic
plants and animals. But so far from their being, as has been
maintained,[90\4] a people whose "experimental intellect" fitted
them to form sciences which the "abstract intellect" of the Greeks
failed in producing, it rather appears, that several of the sciences
which the Greeks had founded, were never even comprehended by the
Arabians. I do not know any evidence that these pupils ever attained
to understand the real principles of Mechanics, Hydrostatics, and
Harmonics, which their masters had established. At any rate, when
these sciences again became progressive, Europe had to start where
Europe had stopped. There is no Arabian name which any one has
thought of interposing between Archimedes the ancient, and Stevinus
and Galileo the moderns.

[Note 90\4: _Mahometanism Unveiled_, ii. 271.]

4. _Roger Bacon._--There is one writer of the middle ages, on whom
much stress has been laid, and who was certainly a most remarkable
person. Roger Bacon's works are not only so far beyond his age in
the knowledge which they contain, but so different from the temper
of the times, in his assertion of the supremacy of experiment, and
in his contemplation of the future progress of knowledge, that it is
difficult to conceive how such a character could then exist. That he
received much of his knowledge from Arabic writers, there can be no
doubt; for they were in his time the repositories of all
traditionary knowledge. But that he derived from them his
disposition to shake off the authority of Aristotle, to maintain the
importance of experiment, and to look upon knowledge as in its
infancy, I cannot believe, because I have not myself hit upon, nor
seen quoted by others, any passages in which Arabian writers express
such a disposition. On the other hand, we do find in European
writers, in the authors of Greece and Rome, the solid sense, the
bold and hopeful spirit, which suggest such tendencies. We have
already seen that Aristotle asserts, as distinctly as words can
express, that all knowledge must depend on observation, and that
science must be collected from facts by induction. We have seen,
too, that the Roman writers, and Seneca in particular, speak with an
enthusiastic confidence of the progress which science must make in
the course of ages. When Roger Bacon holds similar language in the
thirteenth century, the resemblance is probably rather a sympathy of
character, than a matter of direct derivation; but I know of nothing
{246} which proves even so much as this sympathy in the case of
Arabian philosophers.

A good deal has been said of late of the coincidences between his
views, and those of his great namesake in later times, Francis
Bacon.[91\4] The resemblances consist mainly in such points as I
have just noticed; and we cannot but acknowledge, that many of the
expressions of the Franciscan Friar remind us of the large thoughts
and lofty phrases of the Philosophical Chancellor. How far the one
can be considered as having anticipated the method of the other, we
shall examine more advantageously, when we come to consider what the
character and effect of Francis Bacon's works really are.[92\4]

[Note 91\4: Hallam's _Middle Ages_, iii. 549. Forster's _Mahom. U._
ii. 313.]

[Note 92\4: In the _Philosophy of the Inductive Sciences_, I have
given an account at considerable length of Roger Bacon's mode of
treating Arts and Sciences; and have also compared more fully his
philosophy with that of Francis Bacon; and I have given a view of
the bearing of this latter upon the progress of Science in modern
times. See _Phil. Ind. Sc._ book xii. chaps. 7 and 11. See also the
Appendix to this volume.]

5. _Architecture of the Middle Ages._--But though we are thus
compelled to disallow several of the claims which have been put
forwards in support of the scientific character of the middle ages,
there are two points in which we may, I conceive, really trace the
progress of scientific ideas among them; and which, therefore, may
be considered as the prelude to the period of discovery. I mean
their practical architecture, and their architectural treatises.

In a previous chapter of this book, we have endeavored to explain how
the indistinctness of ideas, which attended the decline of the Roman
empire, appears in the forms of their architecture;--in the disregard,
which the decorative construction exhibits, of the necessary
mechanical conditions of support. The original scheme of Greek
ornamental architecture had been horizontal masses resting on vertical
columns: when the arch was introduced by the Romans, it was concealed,
or kept in a state of subordination: and the lateral support which it
required was supplied latently, marked by some artifice. But the
struggle between the _mechanical_ and the _decorative
construction_[93\4] ended in the complete disorganization of the
classical style. The {247} inconsistencies and extravagances of which
we have noticed the occurrence, were results and indications of the
fall of good architecture. The elements of the ancient system had lost
all principle of connection and regard to rule. Building became not
only a mere art, but an art exercised by masters without skill, and
without feeling for real beauty.

[Note 93\4: See Mr. Willis's admirable _Remarks on the Architecture
of the Middle Ages_, chap. ii.

Since the publication of my first edition, Mr. Willis has shown that
much of the "mason-craft" of the middle ages consisted in the
geometrical methods by which the artists wrought out of the blocks
the complex forms of their decorative system.

To the general indistinctness of speculative notions on mechanical
subjects prevalent in the middle ages, there may have been some
exceptions, and especially so long as there were readers of
Archimedes. Boëthius had translated the mechanical works of
Archimedes into Latin, as we learn from the enumeration of his works
by his friend Cassiodorus (_Variar._ lib i. cap. 45), "_Mechanicum_
etiam Archimedem latialem siculis reddidisti." But _Mechanicus_ was
used in those times rather for one skilled in the art of
constructing wonderful machines than in the speculative theory of
them. The letter from which the quotation is taken is sent by King
Theodoric to Boëthius, to urge him to send the king a water-clock.]

When, after this deep decline, architecture rose again, as it did in
the twelfth and succeeding centuries, in the exquisitely beautiful
and skilful forms of the Gothic style, what was the nature of the
change which had taken place, so far as it bears upon the progress
of science? It was this:--the idea of true mechanical relations in
an edifice had been revived in men's minds, as far as was requisite
for the purposes of art and beauty: and this, though a very
different thing from the possession of the idea as an element of
speculative science, was the proper preparation for that
acquisition. The notion of support and stability again became
conspicuous in the decorative construction, and universal in the
forms of building. The eye which, looking for beauty in definite and
significant relations of parts, is never satisfied except the
weights appear to be duly supported,[94\4] was again gratified.
Architecture threw off its barbarous characters: a new decorative
construction was matured, not thwarting and controlling, but
assisting and harmonizing with the mechanical construction. All the
ornamental parts were made to enter into the apparent construction.
Every member, almost every moulding, became a sustainer of weight;
and by the multiplicity of props assisting each other, and the
consequent subdivision of weight, the eye was satisfied of the
stability of the structure, notwithstanding the curiously-slender
forms of the separate parts. The arch and the vault, no longer
trammelled by an incompatible system of decoration, but favoured by
more tractable forms, were only limited by the skill of the
builders. Everything showed that, practically at least, men
possessed and applied, with steadiness and pleasure, the idea of
mechanical pressure and support.

[Note 94\4: Willis, pp. 15-21. I have throughout this description of
the formation of the Gothic style availed myself of Mr. Willis's
well-chosen expressions.]

The possession of this idea, as a principle of art, led, in the
course of time, to its speculative development as the foundation of
a science; {248} and thus Architecture prepared the way for
Mechanics. But this advance required several centuries. The interval
between the admirable cathedrals of Salisbury, Amiens, Cologne, and
the mechanical treatises of Stevinus, is not less than three hundred
years. During this time, men were advancing towards science; but in
the mean time, and perhaps from the very beginning of the time, art
had begun to decline. The buildings of the fifteenth century,
erected when the principles of mechanical support were just on the
verge of being enunciated in general terms, exhibit those principles
with a far less impressive simplicity and elegance than those of the
thirteenth. We may hereafter inquire whether we find any other
examples to countenance the belief, that the formation of Science is
commonly accompanied by the decline of Art.

The leading principle of the style of the Gothic edifices was, not
merely that the weights were supported, but that they were seen to
be so; and that not only the mechanical relations of the larger
masses, but of the smaller members also, were displayed. Hence we
cannot admit, as an origin or anticipation of the Gothic, a style in
which this principle is not manifested. I do not see, in any of the
representations of the early Arabic buildings, that distribution of
weights to supports, and that mechanical consistency of parts, which
would elevate them above the character of barbarous architecture.
Their masses are broken into innumerable members, without
subordination or meaning, in a manner suggested apparently by
caprice and the love of the marvellous. "In the construction of
their mosques, it was a favorite artifice of the Arabs to sustain
immense and ponderous masses of stone by the support of pillars so
slender, that the incumbent weight seemed, as it were, suspended in
the air by an invisible hand."[95\4] This pleasure in the
contemplation of apparent impossibilities is a very general
disposition among mankind; but it appears to belong to the infancy,
rather than the maturity of intellect. On the other hand, the
pleasure in the contemplation of what is clear, the craving for a
thorough insight into the reasons of things, which marks the
European mind, is the temper which leads to science.

[Note 95\4: _Mahometanism Unveiled_, ii. 255.]

6. _Treatises on Architecture._--No one who has attended to the
architecture which prevailed in England, France, and Germany, from
the twelfth to the fifteenth century, so far as to comprehend its
beauty, harmony, consistency, and uniformity, even in the minutest
parts and most obscure relations, can look upon it otherwise than as
a {249} remarkably connected and definite artificial system. Nor can
we doubt that it was exercised by a class of artists who formed
themselves by laborious study and practice, and by communication
with each other. There must have been bodies of masters and of
scholars, discipline, traditions, precepts of art. How these
associated artists diffused themselves over Europe, and whether
history enables us to trace them in a distinct form, I shall not
here discuss. But the existence of a course of instruction, and of a
body of rules of practice, is proved beyond dispute by the great
series of European cathedrals and churches, so nearly identical in
their general arrangements, and in their particular details. The
question then occurs, have these rules and this system of
instruction anywhere been committed to writing? Can we, by such
evidence, trace the progress of the scientific idea, of which we see
the working in these buildings?

We are not to be surprised, if, during the most flourishing and
vigorous period of the art of the middle ages, we find none of its
precepts in books. Art has, in all ages and countries, been taught
and transmitted by practice and verbal tradition, not by writing. It
is only in our own times, that the thought occurs as familiar, of
committing to books all that we wish to preserve and convey. And,
even in our own times, most of the Arts are learned far more by
practice, and by intercourse with practitioners, than by reading.
Such is the case, not only with Manufactures and Handicrafts, but
with the Fine Arts, with Engineering, and even yet, with that art,
Building, of which we are now speaking.

We are not, therefore, to wonder, if we have no treatises on
Architecture belonging to the great period of the Gothic
masters;--or if it appears to have required some other incitement
and some other help, besides their own possession of their practical
skill, to lead them to shape into a literary form the precepts of
the art which they knew so well how to exercise:--or if, when they
did write on such subjects, they seem, instead of delivering their
own sound practical principles, to satisfy themselves with pursuing
some of the frivolous notions and speculations which were then
current in the world of letters.

Such appears to be the case. The earliest treatises on Architecture
come before us under the form which the commentatorial spirit of the
middle ages inspired. They are Translations of Vitruvius, with
Annotations. In some of these, particularly that of Cesare
Cesariano, published at Como, in 1521, we see, in a very curious
manner, how the habit of assuming that, in every department of
literature, the ancients {250} must needs be their masters, led
these writers to subordinate the members of their own architecture
to the precepts of the Roman author. We have Gothic shafts,
mouldings, and arrangements, given as parallelisms to others, which
profess to represent the Roman style, but which are, in fact,
examples of that mixed manner which is called the style of the
_Cinque cento_ by the Italians, of the _Renaissance_ by the French,
and which is commonly included in our _Elizabethan_. But in the
early architectural works, besides the superstitions and mistaken
erudition which thus choked the growth of real architectural
doctrines, another of the peculiar elements of the middle ages comes
into view;--its mysticism. The dimensions and positions of the
various parts of edifices and of their members, are determined by
drawing triangles, squares, circles, and other figures, in such a
manner as to bound them; and to these geometrical figures were
assigned many abstruse significations. The plan and the front of the
Cathedral at Milan are thus represented in Cesariano's work, bounded
and subdivided by various equilateral triangles; and it is easy to
see, in the earnestness with which he points out these relations,
the evidence of a fanciful and mystical turn of thought.[96\4]

[Note 96\4: The plan which he has given, fol. 14, he has entitled
"Ichnographia Fundamenti sacræ Ædis baricephalæ, Germanico more, à
Trigono ac Pariquadrato perstructa, uti etiam ea quæ nunc Milani
videtur."

The work of Cesariano was translated into German by Gualter Rivius,
and published at Nuremberg, in 1548, under the title of _Vitruvius
Teutsch_, with copies of the Italian diagrams. A few years ago, in an
article in the _Wiener Jahrbücher_ (Oct.-Dec., 1821), the reviewer
maintained, on the authority of the diagrams in Rivius's book, that
Gothic architecture had its origin in Germany and not in England.]

We thus find erudition and mysticism take the place of much of that
development of the architectural principles of the middle ages which
would be so interesting to us. Still, however, these works are by no
means without their value. Indeed many of the arts appear to
flourish not at all the worse, for being treated in a manner
somewhat mystical; and it may easily be, that the relations of
geometrical figures, for which fantastical reasons are given, may
really involve principles of beauty or stability. But independently
of this, we find, in the best works of the architects of all ages
(including engineers), evidence that the true idea of mechanical
pressure exists among them more distinctly than among men in
general, although it may not be developed in a scientific form. This
is true up to our own time, and the arts which such persons
cultivate could not be successfully {251} exercised if it were not
so. Hence the writings of architects and engineers during the middle
ages do really form a prelude to the works on scientific mechanics.
Vitruvius, in his _Architecture_, and Julius Frontinus, who, under
Vespasian, wrote _On Aqueducts_, of which he was superintendent,
have transmitted to us the principal part of what we know respecting
the practical mechanics and hydraulics of the Romans. In modern
times the series is resumed. The early writers on architecture are
also writers on engineering, and often on hydrostatics: for example,
Leonardo da Vinci wrote on the equilibrium of water. And thus we are
led up to Stevinus of Bruges, who was engineer to Prince Maurice of
Nassau, and inspector of the dykes in Holland; and in whose work, on
the processes of his art, is contained the first clear modern
statement of the scientific principles of hydrostatics.

Having thus explained both the obstacles and the prospects which the
middle ages offered to the progress of science, I now proceed to the
history of the progress, when that progress was once again resumed.



{{253}}
BOOK V.



HISTORY
OF
FORMAL ASTRONOMY
AFTER THE STATIONARY PERIOD.


  .  .  . Cyclopum educta caminis
  Mœnia conspicio, atque adverso fornice portas.
    .   .   .   .   .
  His demum exactis, perfecto munere Divæ,
  Devenere locos lætos et amœna vireta
  Fortunatorum nemorum sedesque beatas.
  Largior hic campos æther et lumine vestit
  Purpureo: solemque suum, sua sidera norunt.
          VIRGIL, _Æn._ vi. 630.


  They leave at length the nether gloom, and stand
  Before the portals of a better land:
  To happier plains they come, and fairer groves,
  The seats of those whom heaven, benignant, loves;
  A brighter day, a bluer ether, spreads
  Its lucid depths above their favored heads;
  And, purged from mists that veil our earthly skies,
  Shine suns and stars unseen by mortal eyes.



{{255}}
INTRODUCTION.


_Of Formal and Physical Astronomy._

WE have thus rapidly traced the causes of the almost complete blank
which the history of physical science offers, from the decline of
the Roman empire, for a thousand years. Along with the breaking up
of the ancient forms of society, were broken up the ancient energy
of thinking, the clearness of idea, and steadiness of intellectual
action. This mental declension produced a servile admiration for the
genius of the better periods, and thus, the spirit of Commentation:
Christianity established the claim of truth to govern the world; and
this principle, misinterpreted and combined with the ignorance and
servility of the times, gave rise to the Dogmatic System: and the
love of speculation, finding no secure and permitted path on solid
ground, went off into the regions of Mysticism.

The causes which produced the inertness and blindness of the
stationary period of human knowledge, began at last to yield to the
influence of the principles which tended to progression. The
indistinctness of thought, which was the original feature in the
decline of sound knowledge, was in a measure remedied by the steady
cultivation of Pure Mathematics and Astronomy, and by the progress of
inventions in the Arts, which call out and fix the distinctness of our
conceptions of the relations of natural phenomena. As men's minds
became clear, they became less servile: the perception of the nature
of truth drew men away from controversies about mere opinion; when
they saw distinctly the relations of _things_, they ceased to give
their whole attention to what had been _said_ concerning them; and
thus, as science rose into view, the spirit of commentation lost its
way. And when men came to feel what it was to think for themselves on
subjects of science, they soon rebelled against the right of others to
impose opinions upon them. When they threw off their blind admiration
for the ancients, they were disposed to cast away also their passive
obedience to the ancient system of doctrines. When they were no longer
inspired by the spirit of commentation, they were no longer submissive
to the dogmatism of the schools. When they began to feel that they
could {256} discover truths, they felt also a persuasion of a right
and a growing will so to do.

Thus the revived clearness of ideas, which made its appearance at
the revival of letters, brought on a struggle with the authority,
intellectual and civil, of the established schools of philosophy.
This clearness of idea showed itself, in the first instance, in
Astronomy, and was embodied in the system of Copernicus; but the
contest did not come to a crisis till a century later, in the time
of Galileo and other disciples of the new doctrine. It is our
present business to trace the principles of this series of events in
the history of philosophy.

I do not profess to write a history of Astronomy, any further than
is necessary in order to exhibit the principles on which the
progression of science proceeds; and, therefore, I neglect
subordinate persons and occurrences, in order to bring into view the
leading features of great changes. Now in the introduction of the
Copernican system into general acceptation, two leading views
operated upon men's minds; the consideration of the system as
exhibiting the apparent motions of the universe, and the
consideration of this system with reference to its causes;--the
_formal_ and the _physical_ aspect of the Theory;--the relations of
Space and Time, and the relations of Force and Matter. These two
divisions of the subject were at first not clearly separated; the
second was long mixed, in a manner very dim and obscure, with the
first, without appearing as a distinct subject of attention; but at
last it was extricated and treated in a manner suitable to its
nature. The views of Copernicus rested mainly on the formal
condition of the universe, the relations of space and time; but
Kepler, Galileo, and others, were led, by controversies and other
causes, to give a gradually increasing attention to the physical
relations of the heavenly bodies; an impulse was given to the study
of Mechanics (the Doctrine of Motion), which became very soon an
important and extensive science; and in no long period, the
discoveries of Kepler, suggested by a vague but intense belief in
the physical connection of the parts of the universe, led to the
decisive and sublime generalizations of Newton.

The distinction of _formal_ and _physical_ Astronomy thus becomes
necessary, in order to treat clearly of the discussions which the
propounding of the Copernican theory occasioned. But it may be
observed that, besides this great change, Astronomy made very great
advances in the same path which we have already been tracing,
namely, the determination of the quantities and laws of the
celestial motions, in so far as they were exhibited by the ancient
theories, or {257} might be represented by obvious modifications of
those theories. I speak of new Inequalities, new Phenomena, such as
Copernicus, Galileo, and Tycho Brahe discovered. As, however, these
were very soon referred to the Copernican rather than the Ptolemaic
hypothesis, they may be considered as developments rather of the new
than of the old Theory; and I shall, therefore, treat of them,
agreeably to the plan of the former part, as the sequel of the
Copernican Induction.




CHAPTER I.

PRELUDE TO THE INDUCTIVE EPOCH OF COPERNICUS.


THE Doctrine of Copernicus, that the Sun is the true centre of the
celestial motions, depends primarily upon the consideration that
such a supposition explains very simply and completely all the
obvious appearances of the heavens. In order to see that it does
this, nothing more is requisite than a distinct conception of the
nature of Relative Motion, and a knowledge of the principal
Astronomical Phenomena. There was, therefore, no reason why such a
doctrine might not be _discovered_, that is, suggested as a theory
plausible at first sight, long before the time of Copernicus; or
rather, it was impossible that this guess, among others, should not
be propounded as a solution of the appearances of the heavens. We
are not, therefore, to be surprised if we find, in the earliest
times of Astronomy, and at various succeeding periods, such a system
spoken of by astronomers, and maintained by some as true, though
rejected by the majority, and by the principal writers.

When we look back at such a difference of opinion, having in our
minds, as we unavoidably have, the clear and irresistible
considerations by which the Copernican Doctrine is established _for
us_, it is difficult for us not to attribute superior sagacity and
candor to those who held that side of the question, and to imagine
those who clung to the Ptolemaic Hypothesis to have been blind and
prejudiced; incapable of seeing the beauty of simplicity and
symmetry, or indisposed to resign established errors, and to accept
novel and comprehensive truths. Yet in judging thus, we are probably
ourselves influenced by prejudices arising from the knowledge and
received opinions of our own times. For is it, in reality, clear
that, before the time of Copernicus, the {258} _Heliocentric_ Theory
(that which places the centre of the celestial motions in the Sun)
had a claim to assent so decidedly superior to the Geocentric
Theory, which places the Earth in the centre? What is the basis of
the heliocentric theory?--That the _relative_ motions are _the
same_, on that and on the other supposition. So far, therefore, the
two hypotheses are exactly on the same footing. But, it is urged, on
the heliocentric side we have the advantage of simplicity:--true;
but we have, on the other side, the testimony of our senses; that
is, the geocentric doctrine (which asserts that the Earth rests and
the heavenly bodies move) is the obvious and spontaneous
interpretation of the appearances. Both these arguments,
_simplicity_ on the one side, and _obviousness_ on the other, are
vague, and we may venture to say, both indecisive. We cannot
establish any strong preponderance of probability in favor of the
former doctrine, without going much further into the arguments of
the question.

Nor, when we speak of the superior _simplicity_ of the Copernican
theory, must we forget, that though this theory has undoubtedly, in
this respect, a great advantage over the Ptolemaic, yet that the
Copernican system itself is very complex, when it undertakes to
account, as the Ptolemaic did, for the _Inequalities_ of the Motions
of the sun, moon, and planets; and, that in the hands of Copernicus,
it retained a large share of the eccentrics and epicycles of its
predecessor, and, in some parts, with increased machinery. The
heliocentric theory, without these appendages, would not approach
the Ptolemaic, in the accurate explanation of facts; and as those
who had placed the sun in the centre had never, till the time of
Copernicus, shown how the inequalities were to be explained on that
supposition, we may assert that after the promulgation of the theory
of eccentrics and epicycles on the geocentric hypothesis, there was
no _published_ heliocentric theory which could bear a comparison
with that hypothesis.

It is true, that all the contrivances of epicycles, and the like, by
which the geocentric hypothesis was made to represent the phenomena,
were susceptible of an easy adaptation to a heliocentric method, _when
a good mathematician had once proposed to himself the problem_: and
this was precisely what Copernicus undertook and executed. But, till
the appearance of his work, the heliocentric system had never come
before the world except as a hasty and imperfect hypothesis; which
bore a favorable comparison with the phenomena, so long as their
general features only were known; but which had been completely thrown
into the shade by the labor and intelligence bestowed upon {259} the
Hipparchian or Ptolemaic theories by a long series of great
astronomers of all civilized countries.

But, though the astronomers who, before Copernicus, held the
heliocentric opinion, cannot, on any good grounds, be considered as
much more enlightened than their opponents, it is curious to trace the
early and repeated manifestations of this view of the universe. The
distinct assertion of the heliocentric theory among the Greeks is an
evidence of the clearness of their thoughts, and the vigour of their
minds; and it is a proof of the feebleness and servility of intellect
in the stationary period, that, till the period of Copernicus, no one
was found to try the fortune of this hypothesis, modified according to
the improved astronomical knowledge of the time.

The most ancient of the Greek philosophers to whom the ancients
ascribe the heliocentric doctrine, is Pythagoras; but Diogenes
Laertius makes Philolaus, one of the followers of Pythagoras, the
first author of this doctrine. We learn from Archimedes, that it was
held by his contemporary, Aristarchus. "Aristarchus of Samos," says
he,[1\5] "makes this supposition,--that the fixed stars and the sun
remain at rest, and that the earth revolves round the sun in a
circle." Plutarch[2\5] asserts that this, which was only a
hypothesis in the hands of Aristarchus, was _proved_ by Seleucus;
but we may venture to say that, at that time, no such proof was
possible. Aristotle had recognized the existence of this doctrine by
arguing against it. "All things," says he,[3\5] "tend to the centre
of the earth, and rest there, and therefore the whole mass of the
earth cannot rest except there." Ptolemy had in like manner argued
against the diurnal motion of the earth: such a revolution would, he
urged, disperse into surrounding space all the loose parts of the
earth. Yet he allowed that such a supposition would facilitate the
explanation of some phenomena. Cicero appears to make Mercury and
Venus revolve about the sun, as does Martianus Capella at a later
period; and Seneca says[4\5] it is a worthy subject of
contemplation, whether the earth be at rest or in motion: but at
this period, as we may see from Seneca himself, that habit of
intellect which was requisite for the solution of such a question,
had been succeeded by indistinct views, and rhetorical forms of
speech. If there were any good mathematicians and good observers at
this period, they were employed in cultivating and verifying the
Hipparchian theory.

[Note 1\5: Archim. _Arenarius._]

[Note 2\5: _Quest. Plat._ Delamb. _A. A._ vi.]

[Note 3\5: Quoted by Copernic. i. 7.]

[Note 4\5: _Quest. Nat._ vii. 2.]

Next to the Greeks, the Indians appear to have possessed that {260}
original vigor and clearness of thought, from which true science
springs. It is remarkable that the Indians, also, had their
heliocentric theorists. Aryabatta[5\5] (A. D. 1322), and other
astronomers of that country, are said to have advocated the doctrine
of the earth's revolution on its axis; which opinion, however, was
rejected by subsequent philosophers among the Hindoos.

[Note 5\5: Lib. U. K. _Hist. Ast._ p. 11.]

Some writers have thought that the heliocentric doctrine was
_derived_ by Pythagoras and other European philosophers, from some
of the oriental nations. This opinion, however, will appear to have
little weight, if we consider that the heliocentric hypothesis, in
the only shape in which the ancients knew it, was too obvious to
require much teaching; that it did not and could not, so far as we
know, receive any additional strength from any thing which the
oriental nations could teach; and that each astronomer was induced
to adopt or reject it, not by any information which a master could
give him, but by his love of geometrical simplicity on the one hand,
or the prejudices of sense on the other. Real science, depending on
a clear view of the relation of phenomena to general theoretical
ideas, cannot be communicated in the way of secret and exclusive
traditions, like the mysteries of certain arts and crafts. If the
philosopher do not _see_ that the theory is true, he is little the
better for having heard or read the words which assert its truth.

It is impossible, therefore, for us to assent to those views which
would discover in the heliocentric doctrines of the ancients, traces
of a more profound astronomy than any which they have transmitted to
us. Those doctrines were merely the plausible conjectures of men
with sound geometrical notions; but they were never extended so as
to embrace the details of the existing astronomical knowledge; and
perhaps we may say, that the analysis of the phenomena into the
arrangements of the Ptolemaic system, was so much more obvious than
any other, that it must necessarily come first, in order to form an
introduction to the Copernican.

The true foundation of the heliocentric theory for the ancients was,
as we have intimated, its perfect geometrical consistency with the
general features of the phenomena, and its simplicity. But it was
unlikely that the human mind would be content to consider the
subject under this strict and limited aspect alone. In its eagerness
for wide speculative views, it naturally looked out for other and
vaguer principles of connection and relation. Thus, as it had been
urged in {261} favor of the geocentric doctrine, that the heaviest
body must be in the centre, it was maintained, as a leading
recommendation of the opposite opinion, that it placed the Fire, the
noblest element, in the Centre of the Universe. The authority of
mythological ideas was called in on both sides to support these
views. Numa, as Plutarch[6\5] informs us, built a circular temple
over the ever-burning Fire of Vesta; typifying, not the earth, but
the Universe, which, according to the Pythagoreans, has the Fire
seated at its Centre. The same writer, in another of his works,
makes one of his interlocutors say, "Only, my friend, do not bring
me before a court of law on a charge of impiety; as Cleanthes said,
that Aristarchus the Samian ought to be tried for impiety, because
he removed the Hearth of the Universe." This, however, seems to have
been intended as a pleasantry.

[Note 6\5: _De Facie in Orbe Lunæ_, 6.]

The prevalent physical views, and the opinions concerning the causes
of the motions of the parts of the universe, were scarcely more
definite than the ancient opinions concerning the relations of the
four elements, till Galileo had founded the true Doctrine of Motion.
Though, therefore, arguments on this part of the subject were the
most important part of the controversy after Copernicus, the force
of such arguments was at his time almost balanced. Even if more had
been known on such subjects, the arguments would not have been
conclusive: for instance, the vast mass of the heavens, which is
commonly urged as a reason why the heavens do not move round the
earth, would not make such a motion impossible; and, on the other
hand, the motions of bodies at the earth's surface, which were
alleged as inconsistent with its motion, did not really disprove
such an opinion. But according to the state of the science of motion
before Copernicus, all reasonings from such principles were utterly
vague and obscure.

We must not omit to mention a modern who preceded Copernicus, in the
assertion at least of the heliocentric doctrine. This was Nicholas
of Cusa (a village near Treves), a cardinal and bishop, who, in the
first half of the fifteenth century, was very eminent as a divine
and mathematician; and who in a work, _De Doctâ Ignorantiâ_,
propounded the doctrine of the motion of the earth; more, however,
as a paradox than as a reality. We cannot consider this as any
distinct anticipation of a profound and consistent view of the truth.

We shall now examine further the promulgation of the Heliocentric
System by Copernicus, and its consequences. {262}




CHAPTER II.

INDUCTION OF COPERNICUS.--THE HELIOCENTRIC THEORY ASSERTED ON FORMAL
GROUNDS.


IT will be recollected that the _formal_ are opposed to the
_physical_ grounds of a theory; the former term indicating that it
gives a satisfactory account of the relations of the phenomena in
Space and Time, that is, of the Motions themselves; while the latter
expression implies further that we include in our explanation the
Causes of the motions, the laws of Force and Matter. The strongest
of the considerations by which Copernicus was led to invent and
adopt his system of the universe were of the former kind. He was
dissatisfied, he says, in his Preface addressed to the Pope, with
the want of symmetry in the Eccentric Theory, as it prevailed in his
days; and weary of the uncertainty of the mathematical traditions.
He then sought through all the works of philosophers, whether any
had held opinions concerning the motions of the world, different
from those received in the established mathematical schools. He
found, in ancient authors, accounts of Philolaus and others, who had
asserted the motion of the earth. "Then," he adds, "I, too, began to
meditate concerning the motion of the earth; and though it appeared
an absurd opinion, yet since I knew that, in previous times, others
had been allowed the privilege of feigning what circles they chose,
in order to explain the phenomena, I conceived that I also might
take the liberty of trying whether, on the supposition of the
earth's motion, it was possible to find better explanations than the
ancient ones, of the revolutions of the celestial orbs.

"Having then assumed the motions of the earth, which are hereafter
explained, by laborious and long observation I at length found, that
if the motions of the other planets be compared with the revolution of
the earth, not only their phenomena follow from the suppositions, but
also that the several orbs, and the whole system, are so connected in
order and magnitude, that no one part can be transposed without
disturbing the rest, and introducing confusion into the whole
universe."

Thus the satisfactory explanation of the apparent motions of the
planets, and the simplicity and symmetry of the system, were the
{263} grounds on which Copernicus adopted his theory; as the craving
for these qualities was the feeling which led him to seek for a new
theory. It is manifest that in this, as in other cases of discovery,
a clear and steady possession of abstract Ideas, and an aptitude in
comprehending real Facts under these general conceptions, must have
been leading characters in the discoverer's mind. He must have had a
good geometrical head, and great astronomical knowledge. He must
have seen, with peculiar distinctness, the consequences which flowed
from his suppositions as to the relations of space and time,--the
apparent motions which resulted from the assumed real ones; and he
must also have known well all the irregularities of the apparent
motions for which he had to account. We find indications of these
qualities in his expressions. A steady and calm contemplation of the
theory is what he asks for, as the main requisite to its reception.
If you suppose the earth to revolve and the heaven to be at rest,
you will find, he says, "_si serio animadvertas_," if you think
steadily, that the apparent diurnal motion will follow. And after
alleging his reasons for his system, he says,[7\5] "We are,
therefore, not ashamed to confess, that the whole of the space
within the orbit of the moon, along with the centre of the earth,
moves round the sun in a year among the other planets; the magnitude
of the world being so great, that the distance of the earth from the
sun has no apparent magnitude when compared with the sphere of the
fixed stars." "All which things, though they be difficult and almost
inconceivable, and against the opinion of the majority, yet, in the
sequel, by God's favor, we will make clearer than the sun, at least
to those who are not ignorant of mathematics."

[Note 7\5: Nicolai Copernici Torinensis _de Revolutionibus Orbium
Cœlestium Libri VI_. Norimbergæ, M.D.XLIII. p. 9.]

It will easily be understood, that since the ancient geocentric
hypothesis ascribed to the planets those motions which were apparent
only, and which really arose from the motion of the earth round the
sun in the new hypothesis, the latter scheme must much simplify the
planetary theory. Kepler[8\5] enumerates eleven motions of the
Ptolemaic system, which are at once exterminated and rendered
unnecessary by the new system. Still, as the real motions, both of
the earth and the planets, are unequable, it was requisite to have
some mode of representing their inequalities; and, accordingly, the
ancient theory of eccentrics and epicycles was retained, so far as
was requisite for this purpose. The planets revolved round the sun
by means of a Deferent, and a {264} great and small Epicycle; or
else by means of an Eccentric and Epicycle, modified from Ptolemy's,
for reasons which we shall shortly mention. This mode of
representing the motions of the planets continued in use, until it
was expelled by the discoveries of Kepler.

[Note 8\5: _Myst. Cosm._ cap. 1.]

Besides the daily rotation of the earth on its axis, and its annual
circuit about the sun, Copernicus attributed to the axis a "motion
of declination," by which, during the whole annual revolution, the
pole was constantly directed towards the same part of the heavens.
This constancy in the absolute direction of the axis, or its moving
parallel to itself, may be more correctly viewed as not indicating
any separate motion. The axis continues in the same direction,
because there is nothing to make it change its direction; just as a
straw, lying on the surface of a cup of water, continues to point
nearly in the same direction when the cup is carried round a room.
And this was noticed by Copernicus's adherent, Rothman,[9\5] a few
years after the publication of the work _De Revolutionibus_. "There
is no occasion," he says, in a letter to Tycho Brahe, "for the
triple motion of the earth: the annual and diurnal motions suffice."
This error of Copernicus, if it be looked upon as an error, arose
from his referring the position of the axis to a limited space,
which he conceived to be carried round the sun along with the earth,
instead of referring it to fixed or absolute space. When, in a
Planetarium (a machine in which the motions of the planets are
imitated), the earth is carried round the sun by being fastened to a
material radius, it is requisite to give a motion to the axis by
_additional_ machinery, in order to enable it to _preserve_ its
parallelism. A similar confusion of geometrical conception, produced
by a double reference to absolute space and to the centre of
revolution, often leads persons to dispute whether the moon, which
revolves about the earth, always turning to it the same face,
revolves about her axis or not.

[Note 9\5: Tycho. Epist. i. p. 184, A. D. 1590.]

It is also to be noticed that the precession of the equinoxes made
it necessary to suppose the axis of the earth to be not _exactly_
parallel to itself, but to deviate from that position by a slight
annual difference. Copernicus erroneously supposes the precession to
be unequable; and his method of explaining this change, which is
simpler than that of the ancients, becomes more simple still, when
applied to the true state of the facts.

The tendencies of our speculative nature, which carry us onwards in
{265} pursuit of symmetry and rule, and which thus produced the
theory of Copernicus, as they produce all theories, perpetually show
their vigor by overshooting their mark. They obtain something by
aiming at much more. They detect the order and connection which
exist, by imagining relations of order and connection which have no
existence. Real discoveries are thus mixed with baseless
assumptions; profound sagacity is combined with fanciful conjecture;
not rarely, or in peculiar instances, but commonly, and in most
cases; probably in all, if we could read the thoughts of the
discoverers as we read the books of Kepler. To try wrong guesses is
apparently the only way to hit upon right ones. The character of the
true philosopher is, not that he never conjectures hazardously, but
that his conjectures are clearly conceived and brought into rigid
contact with facts. He sees and compares distinctly the ideas and
the things,--the relations of his notions to each other and to
phenomena. Under these conditions it is not only excusable, but
necessary for him, to snatch at every semblance of general rule;--to
try all promising forms of simplicity and symmetry.

Copernicus is not exempt from giving us, in his work, an example of
this character of the inventive spirit. The axiom that the celestial
motions must be _circular_ and _uniform_, appeared to him to have
strong claims to acceptation; and his theory of the inequalities of
the planetary motions is fashioned upon it. His great desire was to
apply it more rigidly than Ptolemy had done. The time did not come
for rejecting this axiom, till the observations of Tycho Brahe and
the calculations of Kepler had been made.

I shall not attempt to explain, in detail, Copernicus's system of
the planetary inequalities. He retained epicycles and eccentrics,
altering their centres of motion; that is, he retained what was
_true_ in the old system, _translating_ it into his own. The
peculiarities of his method consisted in making such a combination
of epicycles as to supply the place of the _equant_,[10\5] and to
make all the motions equable about the centres of motion. This
device was admired for a time, till Kepler's elliptic theory
expelled it, with all other forms of the theory of epicycles: but we
must observe that Copernicus was aware of some of the discrepancies
which belonged to that theory as it had, up to that time, been
propounded. In the case of Mercury's orbit, which is more eccentric
than that of the other planets, he makes suppositions which are
complex indeed, but which show his perception of the imperfection of
{266} the common theory; and he proposes a new theory of the moon,
for the very reason which did at last overturn the doctrine of
epicycles, namely, that the ratio of their distances from the earth
at different times was inconsistent with the circular
hypothesis.[11\5]

[Note 10\5: See B. iii. Chap. **iv. Sect. 7.]

[Note 11\5: _De Rev._ iv. c. 2.]

It is obvious, that, along with his mathematical clearness of view,
and his astronomical knowledge, Copernicus must have had great
intellectual boldness and vigor, to conceive and fully develop a
theory so different as his was from all received doctrines. His pupil
and expositor, Rheticus, says to Schener, "I beg you to have this
opinion concerning that learned man, my Preceptor; that he was an
ardent admirer and follower of Ptolemy; but when he was compelled by
phenomena and demonstration, he thought he did well to aim at the same
mark at which Ptolemy had aimed, though with a bow and shafts of a
very different material from his. We must recollect what Ptolemy says,
Δεῖ δ' ἐλευθέρον εἶναι τῇ γνώμῃ τὸν μέλλοντα φιλοσοφεῖν. 'He who is to
follow philosophy must be a freeman in mind.'" Rheticus then goes on
to defend his master from the charge of disrespect to the ancients:
"That temper," he says, "is alien from the disposition of every good
man, and most especially from the spirit of philosophy, and from no
one more utterly than from my Preceptor. He was very far from rashly
rejecting the opinions of ancient philosophers, except for weighty
reasons and irresistible facts, through any love of novelty. His
years, his gravity of character, his excellent learning, his
magnanimity and nobleness of spirit, are very far from having any
liability to such a temper, which belongs either to youth, or to
ardent and light minds, or to those τῶν μέγα φρονούντων ἐπὶ θεωρίᾳ
μικρῂ, 'who think much of themselves and know little,' as Aristotle
says." Undoubtedly this deference for the great men of the past,
joined with the talent of seizing the spirit of their methods when the
letter of their theories is no longer tenable, _is_ the true mental
constitution of discoverers.

Besides the intellectual energy which was requisite in order to
construct a system of doctrines so novel as those of Copernicus, some
courage was necessary to the publication of such opinions; certain, as
they were, to be met, to a great extent, by rejection and dispute, and
perhaps by charges of heresy and mischievous tendency. This last
danger, however, must not be judged so great as we might infer from
the angry controversies and acts of authority which occurred in {267}
Galileo's time. The Dogmatism of the stationary period, which
identified the cause of philosophical and religious truth, had not yet
distinctly felt itself attacked by the advance of physical knowledge;
and therefore had not begun to look with alarm on such movements.
Still, the claims of Scripture and of ecclesiastical authority were
asserted as paramount on all subjects; and it was obvious that many
persons would be disquieted or offended with the new interpretation of
many scriptural expressions, which the true theory would make
necessary. This evil Copernicus appears to have foreseen; and this and
other causes long withheld him from publication. He was himself an
ecclesiastic; and, by the patronage of his maternal uncle, was
prebendary of the church of St. John at Thorn, and a canon of the
church of Frauenburg, in the diocese of Ermeland.[12\5] He had been a
student at Bologna, and had taught mathematics at Rome in the year
1500; and he afterwards pursued his studies and observations at his
residence near the mouth of the Vistula.[13\5] His discovery of his
system must have occurred before 1507, for in 1543 he informs Pope
Paulus the Third, in his dedication, that he had kept his book by him
for four times the nine years recommended by Horace, and then only
published it at the earnest entreaty of his friend Cardinal Schomberg,
whose letter is prefixed to the work. "Though I know," he says, "that
the thoughts of a philosopher do not depend on the judgment of the
many, his study being to seek out truth in all things as far as that
is permitted by God to human reason: yet when I considered," he adds,
"how absurd my doctrine would appear, I long hesitated whether I
should publish my book, or whether it were not better to follow the
example of the Pythagoreans and others, who delivered their doctrines
only by tradition and to friends." It will be observed that he speaks
here of the opposition of the established school of Astronomers, not
of Divines. The latter, indeed, he appears to consider as a less
formidable danger. "If perchance," he says at the end of his preface,
"there be ματαιολόγοι, vain babblers, who knowing nothing of
mathematics, yet assume the right of judging on account of some place
of Scripture perversely wrested to their purpose, and who blame and
attack my undertaking; I heed them not, and look upon their judgments
as rash and contemptible." He then goes on to show that the globular
figure of the earth (which was, of course, at that time, an undisputed
point among astronomers), had been opposed on similar grounds by
Lactantius, who, {268} though a writer of credit in other respects,
had spoken very childishly in that matter. In another epistle prefixed
to the work (by Andreas Osiander), the reader is reminded that the
hypotheses of astronomers are not necessarily asserted to be true, by
those who propose them, but only to be a way of _representing_ facts.
We may observe that, in the time of Copernicus, when the motion of the
earth had not been connected with the physical laws of matter and
motion, it could not be considered so distinctly real as it
necessarily was held to be in after times.

[Note 12\5: Rheticus, _Nar._ p. 94.]

[Note 13\5: Riccioli.]

The delay of the publication of Copernicus's work brought it to the
end of his life; he died in the year 1543, in which it was
published. It was entitled _De Revolutionibus Orbium Cœlestium Libri
VI_. He received the only copy he ever saw on the day of his death,
and never opened it: he had then, says Gassendi, his biographer,
other cares. His system was, however, to a certain extent,
promulgated, and his fame diffused before that time. Cardinal
Schomberg, in his letter of 1536, which has been already mentioned,
says, "Some years ago, when I heard tidings of your merit by the
constant report of all persons, my affection for you was augmented,
and I congratulated the men of our time, among whom you flourish in
so much honor. For I had understood that you were not only
acquainted with the discoveries of ancient mathematicians, but also
had formed a new system of the world, in which you teach that the
Earth moves, the Sun occupies the lowest, and consequently, the
middle place, the sphere of the fixed stars remains immovable and
fixed, and the Moon, along with the elements included in her sphere,
placed between the orbits (_cœlum_) of Mars and Venus, travels round
the sun in a yearly revolution."[14\5] The writer goes on to say
that he has heard that Copernicus has written a book
(_Commentarios_), in which this system is applied to the
construction of Tables of the Planetary Motions (_erraticarum
stellarum_). He then proceeds to entreat him earnestly to publish
his lucubrations. {269}

[Note 14\5: This passage has so important a place in the history, that
I will give it in the original:--"Intellexeram te non modo veterum
mathematicorum inventa egregie callere sed etiam novam mundi rationem
constituisse: Qua doceas terram moveri: solem imum mundi, atque medium
locum obtinere: cœlum octavum immotum atque fixum perpetuo manere:
Lunam se una cum inclusis suæ spheræ elementis, inter Martis et
Veneris cœlum sitam, anniversario cursu circum solem convertere. Atque
de hac tota astronomiæ ratione commentarios a te confectos esse, ac
erraticarum stellarum motus calculis subductos tabulis te contulisse,
maxima omnium cum admiratione. Quamobrem vir doctissime, nisi tibi
molestus sum, te etiam atque etiam oro vehementer ut hoc tuum inventum
studiosis communices, et tuas de mundi sphæra lucubrationes, una cum
Tabulis et si quid habes præterea quod ad eandem rem pertineat primo
quoque tempore ad me mittas."]

This letter is dated 1536, and implies that the work of Copernicus
was then written, and known to persons who studied astronomy.
Delambre says that Achilles Gassarus of Lindau, in a letter dated
1540, sends to his friend George Vogelin of Constance, the book _De
Revolutionibus_. But Mr. De Morgan[15\5] has pointed out that the
printed work which Gassarus sent to Vogelin was the _Narratio_ by
Rheticus of Feldkirch, a eulogium of Copernicus and his system
prefixed to the second edition of the _De Revolutionibus_, which
appeared in 1566. In this Narration, Rheticus speaks of the work of
Copernicus as a Palingenesia, or New Birth of astronomy. Rheticus,
it appears, had gone to Copernicus for the purpose of getting
knowledge about triangles and trigonometrical tables, and had had
his attention called to the heliocentric theory, of which he became
an ardent admirer. He speaks of his "Preceptor" with strong
admiration, as we have seen. "He appears to me," says he, "more to
resemble Ptolemy than any other astronomers." This, it must be
recollected, was selecting the highest known subject of comparison.

[Note 15\5: _Ast. Mod._ i. p. 138. I owe this and many other
corrections to the personal kindness of Mr. De Morgan.]




CHAPTER III.

SEQUEL TO COPERNICUS.--THE RECEPTION AND DEVELOPMENT OF THE
COPERNICAN THEORY.


_Sect._ 1.--_First Reception of the Copernican Theory._

THE theories of Copernicus made their way among astronomers, in the
manner in which true astronomical theories always obtain the assent
of competent judges. They led to the construction of Tables of the
motion of the sun, moon, and planets, as the theories of Hipparchus
and Ptolemy had done; and the verification of the doctrines was to
be looked for, from the agreement of these Tables with observation,
through a sufficient course of time. The work _De Revolutionibus_
contains such Tables. In 1551 Reinhold improved and republished
Tables founded on the principles of Copernicus. "We owe," he says in
his preface, "great obligations to Copernicus, both for his
laborious {270} observations, and for restoring the doctrine of the
Motions. But though his geometry is perfect, the good old man
appears to have been, at times, careless in his numerical
calculations. I have, therefore, recalculated the whole, from a
comparison of his observations with those of Ptolemy and others,
following nothing but the general plan of Copernicus's
demonstrations." These "Prutenic Tables" were republished in 1571
and 1585, and continued in repute for some time; till superseded by
the Rudolphine Tables of Kepler in 1627. The name _Prutenic_, or
Prussian, was employed by the author as a mark of gratitude to his
benefactor Albert, Markgrave of Brandenbourg. The discoveries of
Copernicus had inspired neighboring nations with the ambition of
claiming a place in the literary community of Europe. In something
of the same spirit, Rheticus wrote an _Encomium Borussiæ_, which was
published along with his _Narratio_.

The Tables founded upon the Copernican system were, at first, much
more generally adopted than the heliocentric doctrine on which they
were founded. Thus Magini published at Venice, in 1587, _New
Theories of the Celestial Orbits, agreeing with the Observations of
Nicholas Copernicus_. But in the preface, after praising Copernicus,
he says, "Since, however, he, either for the sake of showing his
talents, or induced by his own reasons, has revived the opinion of
Nicetas, Aristarchus, and others, concerning the motion of the
earth, and has disturbed the established constitution of the world,
which was a reason why many rejected, or received with dislike, his
hypothesis, I have thought it worth while, that, rejecting the
suppositions of Copernicus, I should accommodate other causes to his
observations, and to the Prutenic Tables."

This doctrine, however, was, as we have shown, received with favor
by many persons, even before its general publication. The doctrine
of the motion of the earth was first publicly maintained at Rome by
Widmanstadt,[16\5] who professed to have received it from
Copernicus, and explained the System before the Pope and the
Cardinals, but did not teach it to the public.

[Note 16\5:  See Venturi, _Essai sur les Ouvrages
Physico-Mathématiques de Leonard da Vinci, avec des Fragmens tirés
de ses Manuscrits apportés d'Italie_. Paris, 1797; and, as there
quoted, _Marini Archiatri Pontificii_, tom. ii. p. 251.]

Leonardo da Vinci, who was an eminent mathematician, as well as
painter, about 1510, explained how a body, by describing a kind of
spiral, might descend towards a revolving globe, so that its
apparent motion relative to a point in the surface of the globe,
might be in a {271} straight line leading to the centre. He thus
showed that he had entertained in his thoughts the hypothesis of the
earth's rotation, and was employed in removing the difficulties
which accompanied this supposition, by means of the consideration of
the composition of motions.

In like manner we find the question stirred by other eminent men.
Thus John Muller of Konigsberg, a celebrated astronomer who died in
1476, better known by the name of Regiomontanus, wrote a
dissertation on the subject "Whether the earth be in motion or at
rest," in which he decides _ex professo_[17\5] against the motion.
Yet such discussions must have made generally known the arguments
for the heliocentric theory.

[Note 17\5: Schoneri _Opera_, part ii. p. 129.]

We have already seen the enthusiasm with which Rheticus, who was
Copernicus's pupil in the latter years of his life, speaks of him.
"Thus," says he, "God has given to my excellent preceptor a reign
without end; which may He vouchsafe to guide, govern, and increase,
to the restoration of astronomical truth. Amen."

Of the immediate converts of the Copernican system, who adopted it
before the controversy on the subject had attracted attention, I
shall only add **Mæstlin, and his pupil, Kepler. **Mæstlin published
in 1588 an _Epitome Astronomiæ_, in which the immobility of the
earth is asserted; but in 1596 he edited Kepler's _Mysterium
Cosmographicum_, and the _Narratio_ of Rheticus: and in an epistle
of his own, which he inserts, he defends the Copernican system by
those physical reasonings which we shall shortly have to mention, as
the usual arguments in this dispute. Kepler himself, in the outset
of the work just named, says, "When I was at Tübingen, attending to
Michael Mæstlin, being disturbed by the manifold inconveniences of
the usual opinion concerning the world, I was so delighted with
Copernicus, of whom he made great mention in his lectures, that I
not only defended his opinions in our disputations of the candidates,
but wrote a thesis concerning the First Motion which is produced by
the revolution of the earth." This must have been in 1590.

The differences of opinion respecting the Copernican system, of which
we thus see traces, led to a controversy of some length and extent.
This controversy turned principally upon physical considerations,
which were much more distinctly dealt with by Kepler, and others of
the followers of Copernicus, than they had been by the {272}
discoverer himself. I shall, therefore, give a separate consideration
to this part of the subject. It may be proper, however, in the first
place, to make a few observations on the progress of the doctrine,
independently of these physical speculations.


_Sect._ 2.--_Diffusion of the Copernican Theory._

THE diffusion of the Copernican opinions in the world did not take
place rapidly at first. Indeed, it was necessarily some time before
the progress of observation and of theoretical mechanics gave the
heliocentric doctrine that superiority in argument, which now makes us
wonder that men should have hesitated when it was presented to them.
Yet there were some speculators of this kind, who were attracted at
once by the enlarged views of the universe which it opened to them.
Among these was the unfortunate Giordano Bruno of Nola, who was burnt
as a heretic at Rome in 1600. The heresies which led to his unhappy
fate were, however, not his astronomical opinions, but a work which he
published in England, and dedicated to Sir Philip Sydney, under the
title of _Spaccio della Bestia Trionfante_, and which is understood to
contain a bitter satire of religion and the papal government. Montucla
conceives that, by his rashness in visiting Italy after putting forth
such a work, he compelled the government to act against him. Bruno
embraced the Copernican opinions at an early period, and connected
with them the belief in innumerable worlds besides that which we
inhabit; as also certain metaphysical or theological doctrines which
he called the Nolan philosophy. In 1591 he published _De
innumerabilibus, immenso, et infigurabili, seu de Universo et Mundis_,
in which he maintains that each star is a sun, about which revolve
planets like our earth; but this opinion is mixed up with a large mass
of baseless verbal speculations.

Giordano Bruno is a disciple of Copernicus on whom we may look with
peculiar interest, since he probably had a considerable share in
introducing the new opinions into England;[18\5] although other
persons, as Recorde, Field, Dee, had adopted it nearly thirty years
earlier; and Thomas Digges ten years before, much more expressly.
Bruno visited this country in the reign of Queen Elizabeth, and
speaks of her and of her councillors in terms of praise, which
appear to show that {273} his book was intended for English readers;
though he describes the mob which was usually to be met with in the
streets of London with expressions of great disgust: "Una plebe la
quale in essere irrespettevole, incivile, rozza, rustica, selvatica,
et male allevata, non cede ad altra che pascer possa la terra nel
suo seno."[19\5] The work to which I refer is _La Cena de le
Cenere_, and narrates what took place at a supper held on the
evening of Ash Wednesday (about 1583, see p. 145 of the book), at
the house of Sir Fulk Greville, in order to give "Il Nolano" an
opportunity of defending his peculiar opinions. His principal
antagonists are two "Dottori d' Oxonia," whom Bruno calls Nundinio
and Torquato. The subject is not treated in any very masterly manner
on either side; but the author makes himself have greatly the
advantage not only in argument, but in temper and courtesy: and in
support of his representations of "pedantesca, ostinatissima
ignoranza et presunzione, mista con una rustica incivilità, che
farebbe prevaricar la pazienza di Giobbe," in his opponents, he
refers to a public disputation which he had held at Oxford with
these doctors of theology, in presence of Prince Alasco, and many of
the English nobility.[20\5]

[Note 18\5: See Burton's _Anat. Mel._ Pref. "Some prodigious tenet
or paradox of the earth's motion," &c. "Bruno," &c.]

[Note 19\5: _Opere di Giordano Bruno_, vol. i. p. 146.]

[Note 20\5: Ib. vol. i. p. 179.]

Among the evidences of the difficulties which still lay in the way
of the reception of the Copernican system, we may notice Bacon, who,
as is well known, never gave a full assent to it. It is to be
observed, however, that he does not reject the opinion of the
earth's motion in so peremptory and dogmatical a manner as he is
sometimes accused of doing: thus in the _Thema Cœli_ he says, "The
earth, then, being supposed to be at rest (for that now appears to
us the _more true_ opinion)." And in his tract _On the Cause of the
Tides_, he says, "If the tide of the sea be the extreme and
diminished limit of the diurnal motion of the heavens, it will
follow that the earth is immovable; or at least that it moves with a
much slower motion than the water." In the _Descriptio Globi
Intellectualis_ he gives his reasons for not accepting the
heliocentric theory. "In the system of Copernicus there are many and
grave difficulties: for the threefold motion with which he encumbers
the earth is a serious inconvenience; and the separation of the sun
from the planets, with which he has so many affections in common, is
likewise a harsh step; and the introduction of so many immovable
bodies into nature, as when he makes the sun and the stars
immovable, the bodies which are peculiarly lucid and radiant; and
his making the moon adhere to the earth in a sort of epicycle; and
some {274} other things which he assumes, are proceedings which mark
a man who thinks nothing of introducing fictions of any kind into
nature, provided his calculations turn out well." We have already
explained that, in attributing _three_ motions to the earth,
Copernicus had presented his system encumbered with a complexity not
really belonging to it. But it will be seen shortly, that Bacon's
fundamental objection to this system was his wish for a system which
could be supported by sound physical considerations; and it must be
allowed, that at the period of which we are speaking, this had not
yet been done in favor of the Copernican hypothesis. We may add,
however, that it is not quite clear that Bacon was in full
possession of the details of the astronomical systems which that of
Copernicus was intended to supersede; and that thus he, perhaps, did
not see how much less harsh were these fictions, as he called them,
than those which were the inevitable alternatives. Perhaps he might
even be liable to a little of that indistinctness, with respect to
strictly geometrical conceptions, which we have remarked in
Aristotle. We can hardly otherwise account for his not seeing any
use in resolving the apparently irregular motion of a planet into
separate regular motions. Yet he speaks slightingly of this
important step.[21\5] "The motion of planets, which is constantly
talked of as the motion of regression, or renitency, from west to
east, and which is ascribed to the planets as a proper motion, is
not true; but only arises from appearance, from the greater advance
of the starry heavens towards the west, by which the planets are
left behind to the east." Undoubtedly those who spoke of such a
motion of _regression_ were aware of this; but they saw how the
motion was simplified by this way of conceiving it, which Bacon
seems not to have seen. Though, therefore, we may admire Bacon for
the steadfastness with which he looked forward to physical astronomy
as the great and proper object of philosophical interest, we cannot
give him credit for seeing the full value and meaning of what had
been done, up to his time, in Formal Astronomy.

[Note 21\5: _Thema Cœli_, p. 246.]

Bacon's contemporary, Gilbert, whom he frequently praises as a
philosopher, was much more disposed to adopt the Copernican
opinions, though even he does not appear to have made up his mind to
assent to the whole of the system. In his work. _De Magnete_
(printed 1600), he gives the principal arguments in favor of the
Copernican system, and decides that the earth revolves on its
axis.[22\5] He connects {275} this opinion with his magnetic
doctrines; and especially endeavors by that means to account for the
precession of the equinoxes. But he does not seem to have been
equally confident of its annual motion. In a posthumous work,
published in 1661 (_De Mundo Nostra Sublunari Philosophia Nova_) he
appears to hesitate between the systems of Tycho and
Copernicus.[23\5] Indeed, it is probable that at this period many
persons were in a state of doubt on such subjects. Milton, at a
period somewhat later, appears to have been still undecided. In the
opening of the eighth book of the _Paradise Lost_, he makes Adam
state the difficulties of the Ptolemaic hypothesis, to which the
archangel Raphael opposes the usual answers; but afterwards suggests
to his pupil the newer system:
  . . . . What if seventh to these
  The planet earth, so steadfast though she seem,
  Insensibly three different motions move?
          _Par. Lost_, b. viii.

[Note 22\5: Lib. vi. cap. 3, 4.]

[Note 23\5: Lib. ii. cap. 20.]

Milton's leaning, however, seems to have been for the new system; we
can hardly believe that he would otherwise have conceived so
distinctly, and described with such obvious pleasure, the motion of
the earth:
  Or she from west her silent course advance
  With inoffensive pace, that spinning sleeps
  On her soft axle, while she paces even,
  And bears thee soft with the smooth air along.
          _Par. Lost_, b. viii.

Perhaps the works of the celebrated Bishop Wilkins tended more than
any others to the diffusion of the Copernican system in England,
since even their extravagances drew a stronger attention to them. In
1638, when he was only twenty-four years old, he published a book
entitled _The Discovery of a New World; or a Discourse tending to
prove that it is probable there may be another habitable World in
the Moon; with a Discourse concerning_ the possibility of a passage
thither. The latter part of his subject was, of course, an obvious
mark for the sneers and witticisms of critics. Two years afterwards,
in 1640, appeared his _Discourse concerning a new Planet; tending to
prove that it is probable our Earth is one of the Planets_: in which
he urged the reasons in favor of the heliocentric system; and
explained away the opposite arguments, especially those drawn from
the {276} supposed declarations of Scripture. Probably a good deal
was done for the establishment of those opinions by Thomas
Salusbury, who was a warm admirer of Galileo, and published, in
1661, a translation of several of his works bearing upon this
subject. The mathematicians of this country, in the seventeenth
century, as Napier and Briggs, Horrox and Crabtree, Oughtred and
Seth Ward, Wallis and Wren, were probably all decided Copernicans.
Kepler dedicates one of his works to Napier, and Ward invented an
approximate method of solving Kepler's problem, still known as "the
simple elliptical hypothesis." Horrox wrote, and wrote well, in
defence of the Copernican opinion, in his _Keplerian Astronomy
defended and promoted_, composed (in Latin) probably about 1635, but
not published till 1673, the author having died at the age of
twenty-two, and his papers having been lost. But Salusbury's work
was calculated for another circle of readers. "The book," he says in
the introductory address, "being, for subject and design, intended
chiefly for gentlemen, I have been as careless of using a studied
pedantry in my style, as careful in contriving a pleasant and
beautiful impression." In order, however, to judge of the advantage
under which the Copernican system now came forward, we must consider
the additional evidence for it which was brought to light by
Galileo's astronomical discoveries.


_Sect._ 3.--_The Heliocentric Theory confirmed by Facts.--Galileo's
Astronomical Discoveries._

THE long interval which elapsed between the last great discoveries
made by the ancients and the first made by the moderns, had afforded
ample time for the development of all the important consequences of
the ancient doctrines. But when the human mind had been thoroughly
roused again into activity, this was no longer the course of events.
Discoveries crowded on each other; one wide field of speculation was
only just opened, when a richer promise tempted the laborers away into
another quarter. Hence the history of this period contains the
beginnings of many sciences, but exhibits none fully worked out into a
complete or final form. Thus the science of Statics, soon after its
revival, was eclipsed and overlaid by that of Dynamics; and the
Copernican system, considered merely with reference to the views of
its author, was absorbed in the commanding interest of Physical
Astronomy.

Still, advances were made which had an important bearing on the {277}
heliocentric theory, in other ways than by throwing light upon its
physical principles. I speak of the new views of the heavens which the
Telescope gave; the visible inequalities of the moon's surface; the
moon-like phases of the planet Venus; the discovery of the Satellites
of Jupiter, and of the Ring of Saturn. These discoveries excited at
the time the strongest interest; both from the novelty and beauty of
the objects they presented to the sense; from the way in which they
seemed to gratify man's curiosity with regard to the remote parts of
the universe; and also from that of which we have here to speak, their
bearing upon the conflict of the old and the new philosophy, the
heliocentric and geocentric theories. It may be true, as Lagrange and
Montucla say, that the laws which Galileo discovered in Mechanics
implied a profounder genius than the novelties he detected in the sky:
but the latter naturally attracted the greater share of the attention
of the world, and were matter of keener discussion.

It is not to our purpose to speak here of the details and of the
occasion of the invention of the Telescope; it is well known that
Galileo constructed his about 1609, and proceeded immediately to apply
it to the heavens. The discovery of the Satellites of Jupiter was
almost immediately the reward of his activity; and these were
announced in his _Nuncius Sidereus_, published at Venice in 1610. The
title of this work will best convey an idea of the claim it made to
public notice: "The _Sidereal Messenger_, announcing great and very
wonderful spectacles, and offering them to the consideration of every
one, but especially of philosophers and astronomers; which have been
observed by _Galileo Galilei_, &c. &c., by the assistance of a
perspective glass lately invented by him; namely, in the face of the
moon, in innumerable fixed stars in the milky-way, in nebulous stars,
but especially in four planets which revolve round Jupiter at
different intervals and periods with a wonderful celerity; which,
hitherto not known to any one, the author has recently been the first
to detect, and has decreed to call the _Medicean stars_."

The interest this discovery excited was intense: and men were at this
period so little habituated to accommodate their convictions on
matters of science to newly observed facts, that several of the
"paper-philosophers," as Galileo termed them, appear to have thought
they could get rid of these new objects by writing books against them.
The effect which the discovery had upon the reception of the
Copernican system was immediately very considerable. It showed that
the real universe was very different from that which ancient
philosophers had imagined, {278} and suggested at once the thought
that it contained mechanism more various and more vast than had yet
been conjectured. And when the system of the planet Jupiter thus
offered to the bodily eye a model or image of the solar system
according to the views of Copernicus, it supported the belief of such
an arrangement of the planets, by an analogy all but irresistible. It
thus, as a writer[24\5] of our own times has said, "gave the _holding
turn_ to the opinions of mankind respecting the Copernican system." We
may trace this effect in Bacon, even though he does not assent to the
motion of the earth. "We affirm," he says,[25\5] "the _sun-following
arrangement_ (solisequium) of Venus and Mercury; since it has been
found by Galileo that Jupiter also has attendants."

[Note 24\5: Sir J. Herschel.]

[Note 25\5: _Thema Cœli_, ix. p. 253.]

The _Nuncius Sidereus_ contained other discoveries which had the
same tendency in other ways. The examination of the moon showed, or
at least seemed to show, that she was a solid body, with a surface
extremely rugged and irregular. This, though perhaps not bearing
directly upon the question of the heliocentric theory, was yet a
blow to the Aristotelians, who had, in their philosophy, made the
moon a body of a kind altogether different from this, and had given
an abundant quantity of reasons for the visible marks on her
surface, all proceeding on these preconceived views. Others of his
discoveries produced the same effect; for instance, the new stars
invisible to the naked eye, and those extraordinary appearances
called Nebulæ.

But before the end of the year, Galileo had new information to
communicate, bearing more decidedly on the Copernican controversy.
This intelligence was indeed decisive with regard to the motion of
Venus about the sun; for he found that that planet, in the course of
her revolution, assumes the same succession of phases which the moon
exhibits in the course of a month. This he expressed by a Latin
verse:
  Cynthiæ figuras æmulatur mater amorum:
  The Queen of Love like Cynthia shapes her forms:
transposing the letters of this line in the published account,
according to the practice of the age; which thus showed the ancient
love for combining verbal puzzles with scientific discoveries, while
it betrayed the newer feeling, of jealousy respecting the priority
of discovery of physical facts.

It had always been a formidable objection to the Copernican theory
that this appearance of the planets had not been observed. The
author {279} of that theory had endeavored to account for this, by
supposing that the rays of the sun passed freely through the body of
the planet; and Galileo takes occasion to praise him for not being
deterred from adopting the system which, on the whole, appeared to
agree best with the phenomena, by meeting with some appearances
which it did not enable him to explain.[26\5] Yet while the fate of
the theory was yet undecided, this could not but be looked upon as a
weak point in its defences.

[Note 26\5: Drinkwater-Bethune, _Life of Galileo_, p. 35.]

The objection, in another form also, was embarrassing alike to the
Ptolemaic and Copernican systems. Why, it was asked, did not Venus
appear four times as large when nearest to the earth, as when
furthest from it? The author of the Epistle prefixed to Copernicus's
work had taken refuge in this argument from the danger of being
supposed to believe in the reality of the system; and Bruno had
attempted to answer it by saying, that luminous bodies were not
governed by the same laws of perspective as opake ones. But a more
satisfactory answer now readily offered itself. Venus does not
appear four times as large when she is four times as near, because
her _bright part_ is _not_ four times as large, though her visible
diameter is; and as she is too small for us to see her shape with
the naked eye, we judge of her size only by the quantity of light.

The other great discoveries made in the heavens by means of
telescopes, as that of Saturn's ring and his satellites, the spots
in the sun, and others, belong to the further progress of astronomy.
But we may here observe, that this doctrine of the motion of Mercury
and Venus about the sun was further confirmed by Kepler's
observation of the transit of the former planet over the sun in
1631. Our countryman Horrox was the first person who, in 1639, had
the satisfaction of seeing a transit of Venus.

These events are a remarkable instance of the way in which a
discovery in art (for at this period, the making of telescopes must
be mainly so considered) may influence the progress of science. We
shall soon have to notice a still more remarkable example of the way
in which two sciences (Astronomy and Mechanics) may influence and
promote the progress of each other. {280}


_Sect._ 4.--_The Copernican System opposed on Theological Grounds._

THE doctrine of the Earth's motion round the Sun, when it was
asserted and promulgated by Copernicus, soon after 1500, excited no
visible alarm among the theologians of his own time. Indeed, it was
received with favor by the most intelligent ecclesiastics; and
lectures in support of the heliocentric doctrine were delivered in
the ecclesiastical colleges. But the assertion and confirmation of
this doctrine by Galileo, about a century later, excited a storm of
controversy, and was visited with severe condemnation. Galileo's own
behavior appears to have provoked the interference of the
ecclesiastical authorities; but there must have been a great change
in the temper of the times to make it possible for his adversaries
to bring down the sentence of the Inquisition upon opinions which
had been so long current without giving any serious offence.

[2d Ed.] [It appears to me that the different degree of toleration
accorded to the heliocentric theory in the time of Copernicus and of
Galileo, must be ascribed in a great measure to the controversies
and alarms which had in the mean time arisen out of the Reformation
in religion, and which had rendered the Romish Church more jealous
of innovations in received opinions than it had previously been. It
appears too that the discussion of such novel doctrines was, at that
time at least, less freely tolerated in Italy than in other
countries. In 1597, Kepler writes to Galileo thus: "Confide Galilæe
et progredere. Si bene conjecto, pauci de præcipuis Europæ
Mathematicis a nobis secedere volent; tanta vis est veritatis. Si
tibi Italia minus est idonea ad publicationem et si aliqua habitures
es impedimenta, forsan Germania nobis hanc libertatem
concedet."--Venturi, _Mem. di Galileo_, vol. i. p. 19.

I would not however be understood to assert the condemnation of new
doctrines in science to be either a general or a characteristic
practice of the Romish Church. Certainly the intelligent and
cultivated minds of Italy, and many of the most eminent of her
ecclesiastics among them, have always been the foremost in promoting
and welcoming the progress of science: and, as I have stated, there
were found among the Italian ecclesiastics of Galileo's time many of
the earliest and most enlightened adherents of the Copernican
system. The condemnation of the doctrine of the earth's motion, is,
so far as I am aware, the only instance in which the Papal authority
has pronounced a decree upon a point of science. And the most candid
of the {281} adherents of the Romish Church condemn the assumption
of authority in such matters, which in this one instance, at least,
was made by the ecclesiastical tribunals. The author of the _Ages of
Faith_ (book viii. p. 248) says, "A congregation, it is to be
lamented, declared the new system to be opposed to Scripture, and
therefore heretical." In more recent times, as I have elsewhere
remarked,[27\5] the Church of Authority and the Church of Private
Judgment have each its peculiar temptations and dangers, when there
appears to be a discrepance between Scripture and Philosophy.

[Note 27\5: _Phil. Ind. Sci._ book x. chap. 4.]

But though we may acquit the popes and cardinals in Galileo's time
of stupidity and perverseness in rejecting manifest scientific
truths, I do not see how we can acquit them of dissimulation and
duplicity. Those persons appear to me to defend in a very strange
manner the conduct of the ecclesiastical authorities of that period,
who boast of the liberality with which Copernican professors were
placed by them in important offices, at the very time when the
motion of the earth had been declared by the same authorities
contrary to Scripture. Such merits cannot make us approve of their
conduct in demanding from Galileo a public recantation of the system
which they thus favored in other ways, and which they had repeatedly
told Galileo he might hold as much as he pleased. Nor can any one,
reading the plain language of the Sentence passed upon Galileo, and
of the Abjuration forced from him, find any value in the plea which
has been urged, that the opinion was denominated a _heresy_ only in
a wide, improper, and technical sense.

But if we are thus unable to excuse the conduct of Galileo's judges,
I do not see how we can give our unconditional admiration to the
philosopher himself. Perhaps the conventional decorum which, as we
have seen, was required in treating of the Copernican system, may
excuse or explain the furtive mode of insinuating his doctrines
which he often employs, and which some of his historians admire as
subtle irony, while others blame it as insincerity. But I do not see
with what propriety Galileo can be looked upon as a "Martyr of
Science." Undoubtedly he was very desirous of promoting what he
conceived to be the cause of philosophical truth; but it would seem
that, while he was restless and eager in urging his opinions, he was
always ready to make such submissions as the spiritual tribunals
required. He would really have acted as a martyr, if he had uttered
{282} his "E pur si muove," in the place of his abjuration, not
after it. But even in this case he would have been a martyr to a
cause of which the merit was of a mingled scientific character; for
his own special and favorite share in the reasonings by which the
Copernican system was supported, was the argument drawn from the
flux and reflux of the sea, which argument is altogether false. He
considered this as supplying a mechanical ground of belief, without
which the mere astronomical reasons were quite insufficient; but in
this case he was deserted by the mechanical sagacity which appeared
in his other speculations.]

The heliocentric doctrine had for a century been making its way into
the minds of thoughtful men, on the general ground of its simplicity
and symmetry. Galileo appears to have thought that now, when these
original recommendations of the system had been reinforced by his
own discoveries and reasonings, it ought to be universally
acknowledged as a truth and a reality. And when arguments against
the fixity of the sun and the motion of the earth were adduced from
the expressions of Scripture, he could not be satisfied without
maintaining his favorite opinion to be conformable to Scripture as
well as to Philosophy; and he was very eager in his attempts to
obtain from authority a declaration to this effect. The
ecclesiastical authorities were naturally averse to express
themselves in favor of a novel opinion, startling to the common
mind, and contrary to the most obvious meaning of the words of the
Bible; and when they were compelled to pronounce, they decided
against Galileo and his doctrines. He was accused before the
Inquisition in 1615; but at that period the result was that he was
merely recommended to confine himself to the mathematical reasonings
upon the system, and to abstain from meddling with the Scripture.
Galileo's zeal for his opinions soon led him again to bring the
question under the notice of the Pope, and the result was a
declaration of the Inquisition that the doctrine of the earth's
motion appeared to be contrary to the Sacred Scripture. Galileo was
prohibited from defending and teaching this doctrine in any manner,
and promised obedience to this injunction. But in 1632 he published
his **"_Dialogo delli due Massimi Sistemi del Mondo, Tolemaico e
Copernicano_:" and in this he defended the heliocentric system by
all the strongest arguments which its admirers used. Not only so,
but he introduced into this _Dialogue_ a character under the name of
Simplicius, in whose mouth was put the defence of all the ancient
dogmas, and who was represented as defeated at all points in the
discussion; {283} and he prefixed to the _Dialogue_ a Notice, _To
the Discreet Reader_, in which, in a vein of transparent irony, he
assigned his reasons for the publication. "Some years ago," he says,
"a wholesome edict was promulgated at Rome, which, in order to check
the perilous scandals of the present age, imposed silence upon the
Pythagorean opinion of the motion of the earth. There were not
wanting," he adds, "persons who rashly asserted that this decree was
the result, not of a judicious inquiry, but of a passion
ill-informed; and complaints were heard that counsellors, utterly
unacquainted with astronomical observations, ought not to be
allowed, with their undue prohibitions, to clip the wings of
speculative intellects. At the hearing of rash lamentations like
these, my zeal could not keep silence." And he then goes on to say
that he wishes, by the publication of his _Dialogue_ to show that
the subject had been fully examined at Rome. The result of this was
that Galileo was condemned for his infraction of the injunction laid
upon him in 1616; his _Dialogue_ was prohibited; he himself was
commanded to abjure on his knees the doctrine which he had taught;
and this abjuration he performed.

This celebrated event must be looked upon rather as a question of
decorum than a struggle in which the interests of truth and free
inquiry were deeply concerned. The general acceptance of the
Copernican System was no longer a matter of doubt. Several persons
in the highest positions, including the Pope himself, looked upon
the doctrine with favorable eyes; and had shown their interest in
Galileo and his discoveries. They had tried to prevent his involving
himself in trouble by discussing the question on scriptural grounds.
It is probable that his knowledge of those favorable dispositions
towards himself and his opinions led him to suppose that the
slightest color of professed submission to the Church in his belief,
would enable his arguments in favor of the system to pass unvisited:
the notice which I have quoted, in which the irony is quite
transparent and the sarcasm glaringly obvious, was deemed too flimsy
a veil for the purpose of decency, and indeed must have aggravated
the offence. But it is not to be supposed that the inquisitors
believed Galileo's abjuration to be sincere, or even that they
wished it to be so. It is stated that when Galileo had made his
renunciation of the earth's motion, he rose from his knees, and
stamping on the earth with his foot, said, _E pur si muove_--"And
yet it _does_ move." This is sometimes represented as the heroic
soliloquy of a mind cherishing its conviction of the truth in spite
of persecution; I think we may more naturally conceive it uttered as
a playful {284} epigram in the ear of a cardinal's secretary, with a
full knowledge that it would be immediately repeated to his master.

[2d Ed.] [Throughout the course of the proceedings against him,
Galileo was treated with great courtesy and indulgence. He was
condemned to a formal imprisonment and a very light discipline. "Te
damnamus ad formalem carcerem hujus S. Officii ad tempus arbitrio
nostro limitandum; et titulo pœnitentiæ salutaris præcipimus ut
tribus annis futuris recites **semel in hebdomadâ septem psalmos
penitentiales." But this confinement was reduced to his being placed
under some slight restrictions, first at the house of Nicolini, the
ambassador of his own sovereign, and afterwards at the country seat
of Archbishop Piccolomini, one of his own warmest friends.

It has sometimes been asserted or insinuated that Galileo was
subjected to bodily torture. An argument has been drawn from the
expressions used in his sentence: "Cum vero nobis videretur non esse
a te integram veritatem pronunciatam circa tuam intentionem;
judicavimus necesse esse venire ad rigorosum examen tui, in quo
respondisti catholicè." It has been argued by M. Libri (_Hist. des
Sciences Mathématiques en Italie_, vol. IV. p. 259), and M. Quinet
(_L'Ultramontanisme_, IV. Leçon, p. 104), that the _rigorosum
examen_ necessarily implies bodily torture, notwithstanding that no
such thing is mentioned by Galileo and his contemporaries, and
notwithstanding the consideration with which he was treated in all
other respects: but M. Biot more justly remarks (_Biogr. Univ._ Art.
_Galileo_), that such a procedure is incredible.

To the opinion of M. Biot, we may add that of Delambre, who rejects
the notion of Galileo's having been put to the torture, as
inconsistent with the general conduct of the authorities towards
him, and as irreconcilable with the accounts of the trial given by
Galileo himself, and by a servant of his, who never quitted him for
an instant. He adds also, that it is inconsistent with the words of
his sentence, "ne tuus iste gravis et perniciosus error ac
transgressio remaneat _omnino impunitus_;" for the error would have
been already very far from impunity, if Galileo had been previously
subjected to the rack. He adds, very reasonably, "il ne faut noircir
personne sans preuve, pas même l'Inquisition;"--we must not
calumniate even the Inquisition.]

The ecclesiastical authorities having once declared the doctrine of
the earth's motion to be contrary to Scripture and heretical, long
adhered in form to this declaration, and did not allow the Copernican
system to be taught in any other way than as an "hypothesis." The
{285} Padua edition of Galileo's works, published in 1744, contains
the _Dialogue_ which now, the editors say, "Esce finalmente a pubblico
libero uso colle debite licenze," is now at last freely published with
the requisite license; but they add, "quanto alla Quistione principale
del moto della terra, anche noi ci conformiamo alla ritrazione et
protesta dell' Autore, dichiarando nella piu solenne forma, che non
può, nè dee ammetersi se non come pura Ipotesi Mathematice, che serve
a spiegare piu agevolamento certi fenomeni;" "neither can nor ought to
be admitted except as a convenient hypothesis." And in the edition of
Newton's _Principia_, published in 1760, by Le Sueur and Jacquier, of
the Order of Minims, the editors prefix to the Third Book their
_Declaratio_, that though Newton assumes the hypothesis of the motion
of the earth, and therefore they had used similar language, they were,
in doing this, assuming a character which did not belong to them.
"Hinc alienam coacti sumus gerere personam." They add, "Cæterum latis
a summis Pontificibus contra telluris motum Decretis, nos obsequi
profitemur."

By thus making decrees against a doctrine which in the course of
time was established as an indisputable scientific truth, the See of
Rome was guilty of an unwise and unfortunate stretch of
ecclesiastical authority. But though we do not hesitate to pronounce
such a judgment on this case, we may add that there is a question of
no small real difficulty, which the progress of science often brings
into notice, as it did then. The Revelation on which our religion is
founded, seems to declare, or to take for granted, opinions on
points on which Science also gives her decision; and we then come to
this dilemma,--that doctrines, established by a scientific use of
reason, may seem to contradict the declarations of Revelation,
according to our view of its meaning;--and yet, that we cannot, in
consistency with our religious views, make reason a judge of the
truth of revealed doctrines. In the case of Astronomy, on which
Galileo was called in question, the general sense of cultivated and
sober-minded men has long ago drawn that distinction between
religious and physical tenets, which is necessary to resolve this
dilemma. On this point, it is reasonably held, that the phrases
which are employed in Scripture respecting astronomical facts, are
not to be made use of to guide our scientific opinions; they may be
supposed to answer their end if they fall in with common notions,
and are thus effectually subservient to the moral and religions
import of Revelation. But the establishment of this distinction was
not accomplished without long and distressing controversies. Nor, if
we wish to {286} include all cases in which the same dilemma may
again come into play is it easy to lay down an adequate canon for
the purpose. For we can hardly foresee, beforehand, what part of the
past history of the universe may eventually be found to come within
the domain of science; or what bearing the tenets, which science
establishes, may have upon our view of the providential and revealed
government of the world. But without attempting here to generalize
on this subject, there are two reflections which may be worth our
notice: they are supported by what took place in reference to
Astronomy on the occasion of which we are speaking; and may, at
other periods, be applicable to other sciences.

In the first place, the meaning which any generation puts upon the
phrases of Scripture, depends, more than is at first sight supposed
upon the received philosophy of the time. Hence, while men imagine
that they are contending for Revelation, they are, in fact,
contending for their own interpretation of Revelation, unconsciously
adapted to what they believe to be rationally probable. And the new
interpretation, which the new philosophy requires, and which appears
to the older school to be a fatal violence done to the authority of
religion, is accepted by their successors without the dangerous
results which were apprehended. When the language of Scripture,
invested with its new meaning, has become familiar to men, it is
found that the ideas which it calls up, are quite as reconcilable as
the former ones were with the soundest religious views. And the
world then looks back with surprise at the error of those who
thought that the essence of Revelation was involved in their own
arbitrary version of some collateral circumstance. At the present
day we can hardly conceive how reasonable men should have imagined
that religious reflections on the stability of the earth, and the
beauty and use of the luminaries which revolve round it, would be
interfered with by its being acknowledged that this rest and motion
are apparent only.

In the next place, we may observe that those who thus adhere
tenaciously to the traditionary or arbitrary mode of understanding
Scriptural expressions of physical events, are always strongly
condemned by succeeding generations. They are looked upon with
contempt by the world at large, who cannot enter into the obsolete
difficulties with which they encumbered themselves; and with pity by
the more considerate and serious, who know how much sagacity and
rightmindedness are requisite for the conduct of philosophers and
religious men on such occasions; but who know also how weak and vain
is the attempt {287} to get rid of the difficulty by merely
denouncing the new tenets as inconsistent with religious belief, and
by visiting the promulgators of them with severity such as the state
of opinions and institutions may allow. The prosecutors of Galileo
are still up to the scorn and aversion of mankind: although, as we
have seen, they did not act till it seemed that their position
compelled them to do so, and then proceeded with all the gentleness
and moderation which were compatible with judicial forms.


_Sect._ 5.--_The Heliocentric Theory confirmed on Physical
considerations.--_(_Prelude to Kepler's Astronomical Discoveries._)

BY physical views, I mean, as I have already said, those which
depend on the causes of the motions of matter, as, for instance, the
consideration of the nature and laws of the force by which bodies
fall downwards. Such considerations were necessarily and immediately
brought under notice by the examination of the Copernican theory;
but the loose and inaccurate notions which prevailed respecting the
nature and laws of force, prevented, for some time, all distinct
reasoning on this subject, and gave truth little advantage over
error. The formation of a new Science, the Science of Motion and its
Causes, was requisite, before the heliocentric system could have
justice done it with regard to this part of the subject.

This discussion was at first carried on, as was to be expected, in
terms of the received, that is, the Aristotelian doctrines. Thus,
Copernicus says that terrestrial things appear to be at rest when they
have a motion according to nature, that is, a circular motion; and
ascend or descend when they have, in addition to this, a rectilinear
motion by which they **endeavor to get into their own place. But his
disciples soon began to question the Aristotelian dogmas, and to seek
for sounder views by the use of their own reason. "The great argument
against this system," says Mæstlin, "is that heavy bodies are said to
move to the centre of the universe, and light bodies from the centre.
But I would ask, where do we get this experience of heavy and light
bodies? and how is our knowledge on these subjects extended so far
that we can reason with certainty concerning the centre of the whole
universe? Is not the only residence and home of all the things which
are heavy and light to us, the earth and the air which surrounds it?
and what is the earth and the ambient air, with respect to the
immensity of the universe? It is a point, a punctule, or something, if
there be any thing, still less. As our light and heavy bodies tend to
{288} the centre of our earth, it is credible that the sun, the moon,
and the other lights, have a similar affection, by which they remain
round as we see them; but none of these centres is necessarily the
centre of the universe."

The most obvious and important physical difficulty attendant upon
the supposition of the motion of the earth was thus stated: If the
earth move, how is it that a stone, dropped from the top of a high
tower, falls exactly at the foot of the tower? since the tower being
carried from west to east by the diurnal revolution of the earth,
the stone must be left behind to the west of the place from which it
was let fall. The proper answer to this was, that the motion which
the falling body received from its tendency downwards was
_compounded_ with the motion which, before it fell, it had in virtue
of the earth's rotation: but this answer could not be clearly made
or apprehended, till Galileo and his pupils had established the laws
of such Compositions of motion arising from different forces.
Rothman, Kepler, and other defenders of the Copernican system, gave
their reply somewhat at a venture, when they asserted that the
motion of the earth was communicated to bodies at its surface.
Still, the facts which indicate and establish this truth are
obvious, when the subject is steadily considered; and the
Copernicans soon found that they had the superiority of argument on
this point as well as others. The attacks upon the Copernican system
by Durret, Morin, Riccioli, and the defence of it by Galileo,
Lansberg, Gassendi,[28\5] left on all candid reasoners a clear
impression in favour of the system. Morin attempted to stop the
motion of the earth, which he called breaking its wings; his _Alæ
Terræ Fractæ_ was published in 1643, and answered by Gassendi. And
Riccioli, as late as 1653, in his _Almagestum Novum_, enumerated
fifty-seven Copernican arguments, and pretended to refute them all:
but such reasonings now made no converts; and by this time the
mechanical objections to the motion of the earth were generally seen
to be baseless, as we shall relate when we come to speak of the
progress of Mechanics as a distinct science. In the mean time, the
beauty and simplicity of the heliocentric theory were perpetually
winning the admiration even of those who, from one cause or other,
refused their assent to it. Thus Riccioli, the last of its
considerable opponents, allows its superiority in these respects;
and acknowledges (in 1653) that the Copernican belief appears rather
to increase than diminish under the condemnation of the decrees of
the Cardinals. He applies to it the lines of Horace:[29\5] {289}
  Per damna per cædes, ab ipso
  Sumit opes animumque ferro.
  Untamed its pride, unchecked its course,
  From foes and wounds it gathers force.

[Note 28\5: Del. _A. M._ vol. i. p. 594.]

[Note 29\5: _Almag. Nov._ p. 102.]

We have spoken of the influence of the motion of the earth on the
motions of bodies at its surface; but the notion of a physical
connection among the parts of the universe was taken up by Kepler in
another point of view, which would probably have been considered as
highly fantastical, if the result had not been, that it led to by
far the most magnificent and most certain train of truths which the
whole expanse of human knowledge can show. I speak of the persuasion
of the existence of numerical and geometrical laws connecting the
distances, times, and forces of the bodies which revolve about the
central sun. That steady and intense conviction of this governing
principle, which made its development and verification the leading
employment of Kepler's most active and busy life, cannot be
considered otherwise than as an example of profound sagacity. That
it was connected, though dimly and obscurely, with the notion of a
central agency or influence of some sort, emanating from the sun,
cannot be doubted. Kepler, in his first essay of this kind, the
_Mysterium Cosmographicum_, says, "The motion of the earth, which
Copernicus had proved by _mathematical_ reasons, I wanted to prove
by _physical_, or, if you prefer it, metaphysical." In the twentieth
chapter of that work, he endeavors to make out some relation between
the distances of the Planets from the Sun and their velocities. The
inveterate yet vague notions of forces which preside in this
attempt, may be judged of by such passages as the following:--"We
must suppose one of two things; either that the moving spirits, in
proportion as they are more removed from the sun, are more feeble;
or that there is one moving spirit in the centre of all the orbits,
namely, in the sun, which urges each body the more vehemently in
proportion as it is nearer; but in more distant spaces languishes in
consequence of the remoteness and attenuation of its virtue."

We must not forget, in reading such passages, that they were written
under a belief that force was requisite to keep up, as well as to
change the motion of each planet; and that a body, moving in a
circle, would _stop_ when the force of the central point ceased,
instead of moving off in a tangent to the circle, as we now know it
would do. The force which Kepler supposes is a tangential force, in
the direction of the body's motion, and nearly perpendicular to the
radius; the {290} force which modern philosophy has established, is
in the direction of the radius, and nearly perpendicular to the
body's path. Kepler was right no further than in his suspicion of a
connection between the cause of motion and the distance from the
centre; not only was his knowledge imperfect in all particulars, but
his most general conception of the mode of action of a cause of
motion was erroneous.

With these general convictions and these physical notions in his
mind, Kepler endeavored to detect numerical and geometrical
relations among the parts of the solar system. After extraordinary
labor, perseverance, and ingenuity, he was eminently successful in
discovering such relations; but the glory and merit of interpreting
them according to their physical meaning, was reserved for his
greater successor, Newton.




CHAPTER IV.

INDUCTIVE EPOCH OF KEPLER.


_Sect._ 1.--_Intellectual Character of Kepler._

SEVERAL persons,[30\5] especially in recent times, who have taken a
view of the discoveries of Kepler, appear to have been surprised and
somewhat discontented that conjectures, apparently so fanciful and
arbitrary as his, should have led to important discoveries. They
seem to have been alarmed at the _Moral_ that their readers might
draw, from the tale of a Quest of Knowledge, in which the Hero,
though fantastical and self-willed, and violating in his conduct, as
they conceived, all right rule and sound philosophy, is rewarded
with the most signal triumphs. Perhaps one or two reflections may in
some measure reconcile us to this result. {291}

[Note 30\5: Laplace, _Précis de l'Hist. d'Ast._ p. 94. "Il est
affligeant pour l'esprit humain de voir ce grand homme, même dans ses
derniers ouvrages, se complaire avec délices dans ses chimériques
spéculations, et les regarder comme l'âme et la vie de l'astronomie."

_Hist. of Ast._, L. U. K., p. 53. "This success [of Kepler] may well
inspire with dismay those who are accustomed to consider experiment
and rigorous induction as the only means to interrogate nature with
success."

_Life of Kepler_, L. U. K., p. 14, "Bad philosophy." P. 15,
"Kepler's miraculous good fortune in seizing truths across the
wildest and most absurd theories." P. 54, "The danger of attempting
to follow his method in the pursuit of truth."]

In the first place, we may observe that the leading thought which
suggested and animated all Kepler's attempts was true, and we may
add, sagacious and philosophical; namely, that there must be _some_
numerical or geometrical relations among the times, distances, and
velocities of the revolving bodies of the solar system. This settled
and constant conviction of an important truth regulated all the
conjectures, apparently so capricious and fanciful, which he made
and examined, respecting particular relations in the system.

In the next place, we may venture to say, that advances in knowledge
are not commonly made without the previous exercise of some boldness
and license in guessing. The discovery of new truths requires,
undoubtedly, minds careful and scrupulous in examining what is
suggested; but it requires, no less, such as are quick and fertile
in suggesting. What is Invention, except the talent of rapidly
calling before us many possibilities, and selecting the appropriate
one? It is true, that when we have rejected all the inadmissible
suppositions, they are quickly forgotten by most persons; and few
think it necessary to dwell on these discarded hypotheses, and on
the process by which they were condemned, as Kepler has done. But
all who discover truths must have reasoned upon many errors, to
obtain each truth; every accepted doctrine must have been one
selected out of many candidates. In making many conjectures, which
on trial proved erroneous, Kepler was no more fanciful or
unphilosophical than other discoverers have been. Discovery is not a
"cautious" or "rigorous" process, in the sense of abstaining from
such suppositions. But there are great differences in different
cases, in the facility with which guesses are proved to be errors,
and in the degree of attention with which the error and the proof
are afterwards dwelt on. Kepler certainly was remarkable for the
labor which he gave to such self-refutations, and for the candor and
copiousness with which he narrated them; his works are in this way
extremely curious and amusing; and are a very instructive exhibition
of the mental process of discovery. But in this respect, I venture
to believe, they exhibit to us the usual process (somewhat
caricatured) of inventive minds: they rather exemplify the _rule_ of
genius than (as has generally been hitherto taught) the _exception_.
We may add, that if many of Kepler's guesses now appear fanciful and
absurd, because time and observation have refuted them, others,
which were at the time equally gratuitous, have been confirmed by
succeeding discoveries in a manner which makes them appear
marvellously sagacious; as, for instance, his assertion of the
rotation of {292} the sun on his axis, before the invention of the
telescope, and his opinion that the obliquity of the ecliptic was
decreasing, but would, after a long-continued diminution, stop, and
then increase again.[31\5] Nothing can be more just, as well as more
poetically happy, than Kepler's picture of the philosopher's pursuit
of scientific truth, conveyed by means of an allusion to Virgil's
shepherd and shepherdess:
  Malo me Galatea petit, lasciva puella
  Et fugit ad salices et se cupit ante videri.
  Coy yet inviting, Galatea loves
  To sport in sight, then plunge into the groves;
  The challenge given, she darts along the green,
  Will not be caught, yet would not run unseen.

[Note 31\5: Bailly, _A. M._ iii. 175.]

We may notice as another peculiarity of Kepler's reasonings, the
length and laboriousness of the processes by which he discovered the
errors of his first guesses. One of the most important talents
requisite for a discoverer, is the ingenuity and skill which devises
means for rapidly testing false suppositions as they offer themselves.
This talent Kepler did not possess: he was not even a good
arithmetical calculator, often making mistakes, some of which he
detected and laments, while others escaped him to the last. But his
defects in this respect were compensated by his courage and
perseverance in undertaking and executing such tasks; and, what was
still more admirable, he never allowed the labor he had spent upon any
conjecture to produce any reluctance in abandoning the hypothesis, as
soon as he had evidence of its inaccuracy. The only way in which he
rewarded himself for his trouble, was by describing to the world, in
his lively manner, his schemes, exertions, and feelings.

The _mystical_ parts of Kepler's opinions, as his belief in
astrology, his persuasion that the earth was an animal, and many of
the loose moral and spiritual as well as sensible analyses by which
he represented to himself the powers which he supposed to prevail in
the universe, do not appear to have interfered with his discovery,
but rather to have stimulated his invention, and animated his
exertions. Indeed, where there are clear scientific ideas on one
subject in the mind, it does not appear that mysticism on others is
at all unfavorable to the successful prosecution of research.

I conceive, then, that we may consider Kepler's character as
containing the general features of the character of a scientific
discoverer, {293} though some of the features are exaggerated, and
some too feebly marked. His spirit of invention was undoubtedly very
fertile and ready, and this and his perseverance served to remedy
his deficiency in mathematical artifice and method. But the peculiar
physiognomy is given to his intellectual aspect by his dwelling in a
most prominent manner on those erroneous trains of thought which
other persons conceal from the world, and often themselves forget,
because they find means of stopping them at the outset. In the
beginning of his book (_Argumenta Capitum_) he says, "if Christopher
Columbus, if Magellan, if the Portuguese, when they narrate their
wanderings, are not only excused, but if we do not wish these
passages omitted, and should lose much pleasure if they were, let no
one blame me for doing the same." Kepler's talents were a kindly and
fertile soil, which he cultivated with abundant toil and vigor; but
with great scantiness of agricultural skill and implements. Weeds
and the grain throve and flourished side by side almost
undistinguished; and he gave a peculiar appearance to his harvest,
by gathering and preserving the one class of plants with as much
care and diligence as the other.


_Sect._ 2.--_Kepler's Discovery of his Third Law._

I SHALL now give some account of Kepler's speculations and
discoveries. The first discovery which he attempted, the relation
among the successive distances of the planets from the sun, was a
failure; his doctrine being without any solid foundation, although
propounded by him with great triumph, in a work which he called
_Mysterium Cosmographicum_, and which was published in 1596. The
account which he gives of the train of his thoughts on this subject,
namely, the various suppositions assumed, examined, and rejected, is
curious and instructive, for the reasons just stated; but we shall
not dwell upon these essays, since they led only to an opinion now
entirely abandoned. The doctrine which professed to give the true
relation of the orbits of the different planets, was thus
delivered:[32\5] "The orbit of the earth is a circle: round the
sphere to which this circle belongs, describe a dodecahedron; the
sphere including this will give the orbit of Mars. Round Mars
describe a tetrahedron; the circle including this will be the orbit
of Jupiter. Describe a cube round Jupiter's orbit; the circle
including this will be the orbit of Saturn. Now inscribe in the
Earth's orbit an icosahedron; the circle inscribed in it will be the
orbit of Venus. {294} Inscribe an octahedron in the orbit of Venus;
the circle inscribed in it will be Mercury's orbit. This is the
reason of the number of the planets." The five kinds of polyhedral
bodies here mentioned are the only "Regular Solids."

[Note 32\5: L. U. K. Kepler, 6.]

But though this part of the _Mysterium Cosmographicum_ was a
failure, the same researches continued to occupy Kepler's mind; and
twenty-two years later led him to one of the important rules known
to us as "Kepler's Laws;" namely, to the rule connecting the mean
distances of the planets from the sun with the times of their
revolutions. This rule is expressed in mathematical terms, by saying
that the squares of the periodic times are in the same proportion as
the cubes of the distances; and was of great importance to Newton in
leading him to the law of the sun's attractive force. We may
properly consider this discovery as the sequel of the train of
thought already noticed. In the beginning of the _Mysterium_, Kepler
had said, "In the year 1595, I brooded with the whole energy of my
mind on the subject of the Copernican system. There were three
things in particular of which I pertinaciously sought the causes why
they are not other than they are; the number, the size, and the
motion of the orbits." We have seen the nature of his attempt to
account for the two first of these points. He had also made some
essays to connect the motions of the planets with their distances,
but with his success in this respect he was not himself completely
satisfied. But in the fifth book of the _Harmonice Mundi_, published
in 1619, he says, "What I prophesied two-and-twenty years ago as
soon as I had discovered the Five Solids among the Heavenly Bodies;
what I firmly believed before I had seen the _Harmonics_ of Ptolemy;
what I promised my friends in the title of this book (_On the most
perfect Harmony of the Celestial Motions_) which I named before I
was sure of my discovery; what sixteen years ago I regarded as a
thing to be sought; that for which I joined Tycho Brahe, for which I
settled in Prague, for which I have devoted the best part of my life
to astronomical contemplations; at length I have brought to light,
and have recognized its truth beyond my most sanguine expectations."

The rule thus referred to is stated in the third Chapter of this fifth
Book. "It is," he says, "a most certain and exact thing that the
proportion which exists between the periodic times of any two planets
is precisely the sesquiplicate of the proportion of their mean
distances; that is, of the radii of the orbits. Thus, the period of
the earth is one year, that of Saturn thirty years; if any one trisect
the proportion, that {295} is, take the cube root of it, and double
the proportion so found, that is, square it, he will find the exact
proportion of the distances of the Earth and of Saturn from the sun.
For the cube root of 1 is 1, and the square of this is 1; and the cube
root of 30 is greater than 3, and therefore the square of it is
greater than 9. And Saturn at his mean distance from the sun is at a
little more than 9 times the mean distance of the Earth."

When we now look back at the time and exertions which the
establishment of this law cost Kepler, we are tempted to imagine that
he was strangely blind in not seeing it sooner. His object, we might
reason, was to discover a law connecting the distances and the
periodic times. What law of connection could be more simple and
obvious, we might say, than that one of these quantities should vary
as some _power_ of the other, or as some _root_; or as some
combination of the two, which in a more general view, may still be
called a _power_? And if the problem had been viewed in this way, the
question must have occurred, to _what_ power of the periodic times are
the distances proportional? And the answer must have been, the trial
being made, that they are proportional to the square of the cube root.
This _ex-post-facto_ obviousness of discoveries is a delusion to which
we are liable with regard to many of the most important principles. In
the case of Kepler, we may observe, that the process of connecting two
classes of quantities by comparing their _powers_, is obvious only to
those who are familiar with general algebraical views; and that in
Kepler's time, algebra had not taken the place of geometry, as the
most usual vehicle of mathematical reasoning. It may be added, also,
that Kepler always sought his _formal_ laws by means of _physical_
reasonings; and these, though vague or erroneous, determined the
nature of the mathematical connection which he assumed. Thus in the
_Mysterium_ he had been led by his notions of moving virtue of the sun
to this conjecture, among others--that, in the planets, the increase
of the periods will be double of the difference of the distances;
which supposition he found to give him an approach to the actual
proportion of the distances, but one not sufficiently close to satisfy
him.

The greater part of the fifth Book of the _Harmonics of the
Universe_ consists in attempts to explain various relations among
the distances, times, and eccentricities of the planets, by means of
the ratios which belong to certain concords and discords. This
portion of the work is so complex and laborious, that probably few
modern readers have had courage to go through it. Delambre
acknowledged that his patience {296} often failed him during the
task;[33\5] and subscribes to the judgment of Bailly: "After this
sublime effort, Kepler replunges himself in the relations of music
to the motions, the distance, and the eccentricities of the planets.
In all these harmonic ratios there is not one true relation; in a
crowd of ideas there is not one truth: he becomes a man after being
a spirit of light." Certainly these speculations are of no value,
but we may look on them with toleration, when we recollect that
Newton has sought for analogies between the spaces occupied by the
prismatic colors and the notes of the gamut.[34\5] The numerical
relations of Concords are so peculiar that we can easily suppose
them to have other bearings than those which first offer themselves.

[Note 33\5: _A. M._ a. 358.]

[Note 34\5: _Optics_, b. ii. p. iv. Obs. 5.]

It does not belong to my present purpose to speak at length of the
speculations concerning the forces producing the celestial motions
by which Kepler was led to this celebrated law, or of those which he
deduced from it, and which are found in the _Epitome Astronomiæ
Copernicanæ_, published in 1622. In that work also (p. 554), he
extended this law, though in a loose manner, to the satellites of
Jupiter. These _physical_ speculations were only a vague and distant
prelude to Newton's discoveries; and the law, as a _formal_ rule,
was complete in itself. We must now attend to the history of the
other two laws with which Kepler's name is associated.


_Sect._ 3.--_Kepler's Discovery of his First and Second
Laws.--Elliptical Theory of the Planets._

THE propositions designated as Kepler's First and Second Laws are
these: That the orbits of the planets are elliptical; and, That the
areas described, or _swept_, by lines drawn from the sun to the
planet, are proportional to the times employed in the motion.

The occasion of the discovery of these laws was the attempt to
reconcile the theory of Mars to the theory of eccentrics and
epicycles; the event of it was the complete overthrow of that
theory, and the establishment, in its stead, of the Elliptical
Theory of the planets. Astronomy was now ripe for such a change. As
soon as Copernicus had taught men that the orbits of the planets
were to be referred to the sun, it obviously became a question, what
was the true form of these orbits, and the rule of motion of each
planet in its own orbit. Copernicus represented the motions in
longitude by means of {297} eccentrics and epicycles, as we have
already said; and the motions in latitude by certain _librations_,
or alternate elevations and depressions of epicycles. If a
mathematician had obtained a collection of true positions of a
planet, the form of the orbit and the motion of the star would have
been determined with reference to the sun as well as to the earth;
but this was not possible, for though the _geocentric_ position, or
the direction in which the planet was seen, could be observed, its
distance from the earth was not known. Hence, when Kepler attempted
to determine the orbit of a planet, he combined the observed
geocentric places with successive modifications of the theory of
epicycles, till at last he was led, by one step after another, to
change the epicyclical into the elliptical theory. We may observe,
moreover, that at every step he endeavored to support his new
suppositions by what he called, in his fanciful phraseology,
"sending into the field a reserve of new physical reasonings on the
rout and dispersion of the veterans;"[35\5] that is, by connecting
his astronomical hypotheses with new imaginations, when the old ones
became untenable. We find, indeed, that this is the spirit in which
the pursuit of knowledge is generally carried on with success; those
men arrive at truth who eagerly endeavor to connect remote points of
their knowledge, not those who stop cautiously at each point till
something compels them to go beyond it.

[Note 35\5: I will insert this passage, as a specimen of Kepler's
fanciful mode of narrating the defeats which he received in the war
which he carried on with Mars. "Dum in hunc modum de Martis motibus
triumpho, eique ut planè devicto tabularum carceres et equationum
compedes necto, diversis nuntiatur locis, futilem victoriam ut
bellam totâ mole recrudescere. Nam domi quidam hostis ut captivus
contemptus, rupit omnia equationum vincula, carceresque tabularum
effregit. Foris speculatores profligerunt meas causarum physicarum
arcessitas copias earumque jugum excusserunt resumtà libertate.
Jamque parum abfuit quia hostis fugitivus sese cum rebellibus suis
conjungeret meque in desperationem adigeret: nisi raptim, nova
rationum physicarum subsidia, fusis et palantibus veteribus,
submisissem, et qua se captivus proripuisset, omni diligentia,
edoctus vestigiis ipsius nullâ morâ interpositâ inhæsisserem."]

Kepler joined Tycho Brahe at Prague in 1600, and found him and
Longomontanus busily employed in correcting the theory of Mars; and
he also then entered upon that train of researches which he
published in 1609 in his extraordinary work _On the Motions of
Mars_. In this work, as in others, he gives an account, not only of
his success, but of his failures, explaining, at length, the various
suppositions which he had made, the notions by which he had been led
to invent or to entertain them, the processes by which he had proved
their {298} falsehood, and the alternations of hope and sorrow, of
vexation and triumph, through which he had gone. It will not be
necessary for us to cite many passages of these kinds, curious and
amusing as they are.

One of the most important truths contained in the motions of Man is
the discovery that the plane of the orbit of the planet should be
considered with reference to the sun itself, instead of referring it
to any of the other centres of motion which the eccentric hypothesis
introduced: and that, when so considered, it had none of the
librations which Ptolemy and Copernicus had attributed to it. The
fourteenth chapter of the second part asserts, "Plana eccentricorum
esse ἀτάλαντα;" that the planes are _unlibrating_; retaining always
the same inclination to the ecliptic, and the same _line of nodes_.
With this step Kepler appears to have been justly delighted.
"Copernicus," he says, "not knowing the value of what he possessed
(his system), undertook to represent Ptolemy, rather than nature, to
which, however, he had approached more nearly than any other person.
For being rejoiced that the quantity of the latitude of each planet
was increased by the approach of the earth to the planet, according to
his theory, he did not venture to reject the rest of Ptolemy's
increase of latitude, but in order to express it, devised librations
of the planes of the eccentric, depending not upon its own eccentric,
but (most improbably) upon the orbit of the earth, which has nothing
to do with it. I always fought against this impertinent tying together
of two orbits, even before I saw the observations of Tycho; and I
therefore rejoice much that in this, as in others of my preconceived
opinions, the observations were found to be on my side." Kepler
established his point by a fair and laborious calculation of the
results of observations of Mars made by himself and Tycho Brahe; and
had a right to exult when the result of these calculations confirmed
his views of the symmetry and simplicity of nature.

We may judge of the difficulty of casting off the theory of eccentrics
and epicycles, by recollecting that Copernicus did not do it at all,
and that Kepler only did it after repeated struggles; the history of
which occupies thirty-nine Chapters of his book. At the end of them he
says, "This prolix disputation was necessary, in order to prepare the
way to the natural form of the equations, of which I am now to
treat.[36\5] My first error was, that the path of a planet is a
perfect circle;--an opinion which was a more mischievous thief of my
time, {299} in proportion as it was supported by the authority of all
philosophers, and apparently agreeable to metaphysics." But before he
attempts to correct this erroneous part of his hypothesis, he sets
about discovering the law according to which the different parts of
the orbit are described in the case of the earth, in which case the
eccentricity is so small that the effect of the oval form is
insensible. The result of this inquiry was[37\5] the Rule, that the
time of describing any arc of the orbit is proportional to the area
intercepted between the curve and two lines drawn from the sun to the
extremities of the arc. It is to be observed that this rule, at first,
though it had the recommendation of being selected after the
unavoidable abandonment of many, which were suggested by the notions
of those times, was far from being adopted upon any very rigid or
cautious grounds. A rule had been proved at the apsides of the orbit,
by calculation from observations, and had then been extended by
conjecture to other parts of the orbit; and the rule of the areas was
only an approximate and inaccurate mode of representing this rule,
employed for the purpose of brevity and convenience, in consequence of
the difficulty of applying, geometrically, that which Kepler now
conceived to be the true rule, and which required him to find the sum
of the lines drawn from the sun to _every_ point of the orbit. When he
proceeded to apply this rule to Mars, in whose orbit the oval form is
much more marked, additional difficulties came in his way; and here
again the true supposition, that the _oval_ is of that special kind
called _ellipse_, was adopted at first only in order to simplify
calculation,[38\5] and the deviation from exactness in the result was
attributed to the inaccuracy of those approximate processes. The
supposition of the oval had already been forced upon Purbach in the
case of Mercury, and upon Reinhold in the case of the Moon. The centre
of the epicycle was made to describe an egg-shaped figure in the
former case, and a lenticular figure in the latter.[39\5]

[Note 36\5: _De Stellâ Martis_, iii. 40.]

[Note 37\5: _De Stellâ Martis_, p. 194.]

[Note 38\5: Ib. iv. c. 47.]

[Note 39\5: L. U. K. Kepler, p. 30.]

It may serve to show the kind of labor by which Kepler was led to
his result, if we here enumerate, as he does in his forty-seventh
Chapter,[40\5] six hypotheses, on which he calculated the longitude
of Mars, in order to see which best agreed with observation.

[Note 40\5: _De Stellâ Martis_, p. 228.]

1. The simple eccentricity.

2. The bisection of the eccentricity, and the duplication of the
superior part of the equation. {300}

3. The bisection of the eccentricity, and a stationary point of
equations, after the manner of Ptolemy.

4. The vicarious hypothesis by a free section of the eccentricity
made to agree as nearly as possible with the truth.

5. The physical hypothesis on the supposition of a perfect circle.

6. The physical hypothesis on the supposition of a perfect ellipse.

By the physical hypothesis, he meant the doctrine that the time of a
planet's describing any part of its orbit is proportional to the
distance of the planet from the sun, for which supposition, as we
have said, he conceived that he had assigned physical reasons.

The two last hypotheses came the nearest to the truth, and differed
from it only by about eight minutes, the one in excess and the other
in defect. And, after being much perplexed by this remaining error,
it at last occurred to him[41\5] that he might take another
ellipsis, exactly intermediate between the former one and the
circle, and that this must give the path and the motion of the
planet. Making this assumption, and taking the areas to represent
the times, he now saw[42\5] that both the longitude and the
distances of Mars would agree with observation to the requisite
degree of accuracy. The rectification of the former hypothesis, when
thus stated, may, perhaps, appear obvious. And Kepler informs us
that he had nearly been anticipated in this step (c. 55). "David
Fabricius, to whom I had communicated my hypothesis of cap. 45, was
able, by his observations, to show that it erred in making the
distances too short at mean longitudes; of which he informed me by
letter while I was laboring, by repeated efforts, to discover the
true hypothesis. So nearly did he get the start of me in detecting
the truth." But this was less easy than it might seem. When Kepler's
first hypothesis was enveloped in the complex construction requisite
in order to apply it to each point of the orbit, it was far more
difficult to see where the error lay, and Kepler hit upon it only by
noticing the coincidences of certain numbers, which, as he says,
raised him as if from sleep, and gave him a new light. We may
observe, also, that he was perplexed to reconcile this new view,
according to which the planet described an exact ellipse, with his
former opinion, which represented the motion by means of libration
in an epicycle. "This," he says, "was my greatest trouble, that,
though I considered and reflected till I was almost mad, I could not
find why the planet to which, with so much probability, and with
such an exact {301} accordance of the distances, libration in the
diameter of the epicycle was attributed, should, according to the
indication of the equations, go in an elliptical path. What an
absurdity on my part! as if libration in the diameter might not be a
way to the ellipse!"

[Note 41\5: _De Stellâ Martis_, c. 58.]

[Note 42\5: Ibid. p. 235.]

Another scruple respecting this theory arose from the impossibility of
solving, by any geometrical construction, the problem to which Kepler
was thus led, namely, "To divide the area of a semicircle in a given
ratio, by a line drawn from any point of the diameter." This is still
termed "Kepler's Problem," and is, in fact, incapable of exact
geometrical solution. As, however, the calculation can be performed,
and, indeed, was performed by Kepler himself, with a sufficient degree
of accuracy to show that the elliptical hypothesis is true, the
insolubility of this problem is a mere mathematical difficulty in the
deductive process, to which Kepler's induction gave rise.

Of Kepler's physical reasonings we shall speak more at length on
another occasion. His numerous and fanciful hypotheses had
discharged their office, when they had suggested to him his many
lines of laborious calculation, and encouraged him under the
exertions and disappointments to which these led. The result of this
work was the formal laws of the motion of Mars, established by a
clear induction, since they represented, with sufficient accuracy,
the best observations. And we may allow that Kepler was entitled to
the praise which he claims in the motto on his first leaf. Ramus had
said that if any one would construct an astronomy without
hypothesis, he would be ready to resign to him his professorship in
the University of Paris. Kepler quotes this passage, and adds, "it
is well, Ramus, that you have run from this pledge, by quitting life
and your professorship;[43\5] if you held it still, I should, with
justice, claim it." This was not saying too much, since he had
entirely overturned the hypothesis of eccentrics and epicycles, and
had obtained a theory which was a mere representation of the motions
and distances as they were observed. {302}

[Note 43\5: Ramus perished in the Massacre of St. Bartholomew.]




CHAPTER V.

SEQUEL TO THE EPOCH OF KEPLER. RECEPTION, VERIFICATION, AND
EXTENSION OF THE ELLIPTICAL THEORY.


_Sect._ 1.--_Application of the Elliptical Theory to the Planets._

THE extension of Kepler's discoveries concerning the orbit of Mars
to the other planets, obviously offered itself as a strong
probability, and was confirmed by trial. This was made in the first
place upon the orbit of Mercury; which planet, in consequence of the
largeness of its eccentricity, exhibits more clearly than the others
the circumstances of the elliptical motion. These and various other
supplementary portions of the views to which Kepler's discoveries
had led, appeared in the latter part of his _Epitome Astronomiæ
Copernicanæ_, published in 1622.

The real verification of the new doctrine concerning the orbits and
motions of the heavenly bodies was, of course, to be found in the
construction of tables of those motions, and in the continued
comparison of such tables with observation. Kepler's discoveries had
been founded, as we have seen, principally on Tycho's observations.
Longomontanus (so called as being a native of Langberg in Denmark),
published in 1621, in his _Astronomia Danica_, tables founded upon
the theories as well as the observations of his countryman.
Kepler[44\5] in 1627 published his tables of the planets, which he
called _Rudolphine Tables_, the result and application of his own
theory. In 1633, Lansberg, a Belgian, published also _Tabulæ
Perpetuæ_, a work which was ushered into the world with considerable
pomp and pretension, and in which the author cavils very keenly at
Kepler and Brahe. We may judge of the impression made upon the
astronomical world in general by these rival works, from the account
which our countryman Jeremy Horrox has given of their effect on him.
He had been seduced by the magnificent promises of Lansberg, and the
praises of his admirers, which are prefixed to the work, and was
persuaded that the common opinion which preferred Tycho and Kepler
to him was a prejudice. In 1636, however, he became acquainted with
Crabtree, another young {303} astronomer, who lived in the same part
of Lancashire. By him Horrox was warned that Lansberg was not to be
depended on; that his hypotheses were vicious, and his observations
falsified or forced into agreement with his theories. He then read
the works and adopted the opinions of Kepler; and after some
hesitation which he felt at the thought of attacking the object of
his former idolatry, he wrote a dissertation on the points of
difference between them. It appears that, at one time, he intended
to offer himself as the umpire who was to adjudge the prize of
excellence among the three rival theories of Longomontanus, Kepler,
and Lansberg; and, in allusion to the story of ancient mythology,
his work was to have been called _Paris Astronomicus_; we easily see
that he would have given the golden apple to the Keplerian goddess.
Succeeding observations confirmed his judgment: and the _Rudolphine
Tables_, thus published seventy-six years after the Prutenic, which
were founded on the doctrines of Copernicus, were for a long time
those universally used.

[Note 44\5: Rheticus, _Narratio_, p. 98.]


_Sect._ 2.--_Application of the Elliptical Theory to the Moon._

THE reduction of the Moon's motions to rule was a harder task than
the formation of planetary tables, if accuracy was required; for the
Moon's motion is affected by an incredible number of different and
complex inequalities, which, till their law is detected, appear to
defy all theory. Still, however, progress was made in this work. The
most important advances were due to Tycho Brahe. In addition to the
first and second inequalities of the moon (the _Equation of the
Centre_, known very early, and the _Evection_, which Ptolemy had
discovered), Tycho proved that there was another inequality, which
he termed the _Variation_,[45\5] which depended on the moon's
position with respect to the sun, and which at its maximum was forty
minutes and a half, about a quarter of the evection. He also
perceived, though not very distinctly, the necessity of another
correction of the moon's place depending on the sun's longitude,
which has since been termed the _Annual Equation_.

[Note 45\5:  We have seen (chap. iii.), that Aboul-Wefa, in the
tenth century, had already noticed this inequality; but his
discovery had been entirely forgotten long before the time of Tycho,
and has only recently been brought again into notice.]

These steps concerned the Longitude of the Moon; Tycho also made
important advances in the knowledge of the Latitude. The Inclination
of the Orbit had hitherto been assumed to be the same at all {304}
times; and the motion of the Node had been supposed uniform. He
found that the inclination increased and diminished by twenty
minutes, according to the position of the line of nodes; and that
the nodes, though they regress upon the whole, sometimes go forwards
and sometimes go backwards.

Tycho's discoveries concerning the moon are given in his
_Progymnasmata_, which was published in 1603, two years after the
author's death. He represents the Moon's motion in longitude by
means of certain combinations of epicycles and eccentrics. But after
Kepler had shown that such devices are to be banished from the
planetary system, it was impossible not to think of extending the
elliptical theory to the moon. Horrox succeeded in doing this; and
in 1638 sent this essay to his friend Crabtree. It was published in
1673, with the numerical elements requisite for its application
added by Flamsteed. Flamsteed had also (in 1671-2) compared this
theory with observation, and found that it agreed far more nearly
than the _Philolaic Tables_ of Bullialdus, or the _Carolinian
Tables_ of Street (_Epilogus ad Tabulas_). Moreover Horrox, by
making the centre of the ellipse revolve in an epicycle, gave an
explanation of the evection, as well as of the equation of the
centre.[46\5]

[Note 46\5: Horrox (_Horrockes_ as he himself spelt his name) gave a
first sketch of his theory in letters to his friend Crabtree in
1638: in which the variation of the eccentricity is not alluded to.
But in Crabtree's letter to Gascoigne in 1642, he gives Horrox's
rule concerning it; and Flamsteed in his _Epilogue_ to the Tables,
published by Wallis along with Horrox's works in 1673, gave an
explanation of the theory which made it amount very nearly to a
revolution of the centre of the ellipse in an epicycle. Halley
afterwards made a slight alteration; but hardly, I think, enough to
justify Newton's assertion (_Princip._ Lib. iii. Prop. 35, Schol.),
"Halleius centrum ellipseos in epicyclo locavit." See Baily's
_Flamsteed_, p. 683.]

Modern astronomers, by calculating the effects of the perturbing
forces of the solar system, and comparing their calculations with
observation, have added many new corrections or equations to those
known at the time of Horrox; and since the Motions of the heavenly
bodies were even then affected by these variations as yet
undetected, it is clear that the Tables of that time must have shown
some errors when compared with observation. These errors much
perplexed astronomers, and naturally gave rise to the question
whether the motions of the heavenly bodies really were exactly
regular, or whether they were not affected by accidents as little
reducible to rule as wind and weather. Kepler had held the opinion
of the _casualty_ of such errors; but Horrox, far more
philosophically, argues against this opinion, though he {305} allows
that he is much embarrassed by the deviations. His arguments show a
singularly clear and strong apprehension of the features of the
case, and their real import. He says,[47\5] "these errors of the
tables are alternately in excess and defect; how could this constant
compensation happen if they were casual? Moreover, the alternation
from excess to defect is most rapid in the Moon, most slow in
Jupiter and Saturn, in which planets the error continues sometimes
for years. If the errors were casual, why should they not last as
long in the Moon as in Saturn? But if we suppose the tables to be
right in the mean motions, but wrong in the equations, these facts
are just what must happen; since Saturn's inequalities are of long
period, while those of the Moon are numerous, and rapidly changing."
It would be impossible, at the present moment, to reason better on
this subject; and the doctrine, that all the apparent irregularities
of the celestial motions are really regular, was one of great
consequence to establish at this period of the science.

[Note 47\5: _Astron. Kepler._ Proleg. p. 17.]


_Sect._ 3.--_Causes of the further Progress of Astronomy._

WE are now arrived at the time when theory and observation sprang
forwards with emulous energy. The physical theories of Kepler, and
the reasonings of other defenders of the Copernican theory, led
inevitably, after some vagueness and perplexity, to a sound science
of Mechanics; and this science in time gave a new face to Astronomy.
But in the mean time, while mechanical mathematicians were
generalizing from the astronomy already established, astronomers
were accumulating new facts, which pointed the way to new theories
and new generalizations. Copernicus, while he had established the
permanent length of the year, had confirmed the motion of the sun's
apogee, and had shown that the eccentricity of the earth's orbit,
and the obliquity of the ecliptic, were gradually, though slowly,
diminishing. Tycho had accumulated a store of excellent
observations. These, as well as the laws of the motions of the moon
and planets already explained, were materials on which the Mechanics
of the Universe was afterwards to employ its most matured powers. In
the mean time, the telescope had opened other new subjects of notice
and speculation; not only confirming the Copernican doctrine by the
phases of Venus, and the analogical examples of Jupiter and Saturn,
which with their Satellites {306} appeared like models of the Solar
System; but disclosing unexpected objects, as the Ring of Saturn,
and the Spots of the Sun. The art of observing made rapid advances,
both by the use of the telescope, and by the sounder notions of the
construction of instruments which Tycho introduced. Copernicus had
laughed at Rheticus, when he was disturbed about single minutes; and
declared that if he could be sure to ten minutes of space, he should
be as much delighted as Pythagoras was when he discovered the
property of the right-angled triangle. But Kepler founded the
revolution which he introduced on a quantity less than this.
"Since," he says,[48\5] "the Divine Goodness has given us in Tycho
an observer so exact that this error of eight minutes is impossible,
we must be thankful to God for this, and turn it to account. And
these eight minutes, which we must not neglect, will, of themselves,
enable us to reconstruct the whole of astronomy." In addition to
other improvements, the art of numerical calculation made an
inestimable advance by means of Napier's invention of Logarithms;
and the progress of other parts of pure mathematics was proportional
to the calls which astronomy and physics made upon them.

[Note 48\5: _De Stellâ Martis_, c. 19.]

The exactness which observation had attained enabled astronomers
both to verify and improve the existing theories, and to study the
yet unsystematized facts. The science was, therefore, forced along
by a strong impulse on all sides, and its career assumed a new
character. Up to this point, the history of European Astronomy was
only the sequel of the history of Greek Astronomy; for the
heliocentric system, as we have seen, had had a place among the
guesses, at least, of the inventive and acute intellects of the
Greek philosophers. But the discovery of Kepler's Laws, accompanied,
as from the first they were, with a conviction that the relations
thus brought to light were the effects and exponents of physical
causes, led rapidly and irresistibly to the Mechanical Science of
the skies, and collaterally, to the Mechanical Science of the other
parts of Nature: Sound, and Light, and Heat; and Magnetism, and
Electricity, and Chemistry. The history of these Sciences, thus
treated, forms the sequel of the present work, and will be the
subject of the succeeding volumes. And since, as I have said, our
main object in this work is to deduce, from the history of science,
the philosophy of scientific discovery, it may be regarded as
fortunate for our purpose that the history, after this point, so far
changes its aspect as to offer new materials for such speculations.
The details of {307} a history of astronomy, such as the history of
astronomy since Newton has been, though interesting to the special
lovers of that science, would be too technical, and the features of
the narrative too monotonous and unimpressive, to interest the
general reader, or to suggest a comprehensive philosophy of science.
But when we pass from the Ideas of Space and Time to the Ideas of
Force and Matter, of Mediums by which action and sensation are
produced, and of the Intimate Constitution of material bodies, we
have new fields of inquiry opened to us. And when we find that in
these fields, as well as in astronomy, there are large and striking
trains of unquestioned discovery to be narrated, we may gird
ourselves afresh to the task of writing, and I hope, of reading, the
remaining part of the History of the Inductive Sciences, in the
trust that it will in some measure help us to answer the important
questions, What is Truth? and, How is it to be discovered?



{{309}}
BOOK VI.

_THE MECHANICAL SCIENCES._


HISTORY OF MECHANICS,
INCLUDING
FLUID MECHANICS.



  ΚΡΑΤΟΣ ΒIΑ ΤΕ, σφῷν μὲν ἐντολὴ Διὸς
  Ἔχει Τέλος δὴ, κ' οὐδὲν ἐμποδῶν ἔτι
          ÆSCHYLUS. _Prom. Vinct._ 13.

  You, FORCE and POWER, have done your destined task:
  And naught impedes the work of other hands.



{{311}}
INTRODUCTION.


WE enter now upon a new region of the human mind. In passing from
Astronomy to Mechanics we make a transition from the _formal_ to the
_physical_ sciences;--from time and space to force and matter;--from
_phenomena_ to _causes_. Hitherto we have been concerned only with
the paths and orbits, the periods and cycles, the angles and
distances, of the objects to which our sciences applied, namely, the
heavenly bodies. How these motions are produced;--by what agencies,
impulses, powers, they are determined to be what they are;--of what
nature are the objects themselves;--are speculations which we have
hitherto not dwelt upon. The history of such speculations now comes
before us; but, in the first place, we must consider the history of
speculations concerning motion in general, terrestrial as well as
celestial. We must first attend to Mechanics, and afterwards return
to Physical Astronomy.

In the same way in which the development of Pure Mathematics, which
began with the Greeks, was a necessary condition of the progress of
Formal Astronomy, the creation of the science of Mechanics now
became necessary to the formation and progress of Physical
Astronomy. Geometry and Mechanics were studied for their own sakes;
but they also supplied ideas, language, and reasoning to other
sciences. If the Greeks had not cultivated Conic Sections, Kepler
could not have superseded Ptolemy; if the Greeks had cultivated
Dynamics,[1\6] Kepler might have anticipated Newton. {312}

[Note 1\6: _Dynamics_ is the science which treats of the Motions of
Bodies; _Statics_ is the science which treats of the Pressure of
Bodies which are in equilibrium, and therefore at rest.]




CHAPTER I.

PRELUDE TO THE EPOCH OF GALILEO.


_Sect._ 1.--_Prelude to the Science of Statics._

SOME steps in the science of Motion, or rather in the science of
Equilibrium, had been made by the ancients, as we have seen.
Archimedes established satisfactorily the doctrine of the Lever,
some important properties of the Centre of Gravity, and the
fundamental proposition of Hydrostatics. But this beginning led to
no permanent progress. Whether the distinction between the
principles of the doctrine of Equilibrium and of Motion was clearly
seen by Archimedes, we do not know; but it never was caught hold of
by any of the other writers of antiquity, or by those of the
Stationary Period. What was still worse, the point which Archimedes
had won was not steadily maintained.

We have given some examples of the general ignorance of the Greek
philosophers on such subjects, in noticing the strange manner in
which Aristotle refers to mathematical properties, in order to
account for the equilibrium of a lever, and the attitude of a man
rising from a chair. And we have seen, in speaking of the indistinct
ideas of the Stationary Period, that the attempts which were made to
extend the statical doctrine of Archimedes, failed, in such a manner
as to show that his followers had not clearly apprehended the idea
on which his reasoning altogether depended. The clouds which he had,
for a moment, cloven in his advance, closed after him, and the
former dimness and confusion settled again on the land.

This dimness and confusion, with respect to all subjects of
mechanical reasoning, prevailed still, at the period we now have to
consider; namely, the period of the first promulgation of the
Copernican opinions. This is so important a point that I must
illustrate it further.

Certain general notions of the connection of cause and effect in
motion, exist in the human mind at all periods of its development, and
are implied in the formation of language and in the most familiar
employments of men's thoughts. But these do not constitute a _science_
of {313} Mechanics, any more than the notions of _square_ and _round_
make a Geometry, or the notions of _months_ and _years_ make an
Astronomy. The unfolding these Notions into distinct Ideas, on which
can be founded principles and reasonings, is further requisite, in
order to produce a science; and, with respect to the doctrines of
Motion, this was long in coming to pass; men's thoughts remained long
entangled in their primitive and unscientific confusion.

We may mention one or two features of this confusion, such as we
find in authors belonging to the period now under review.

We have already, in speaking of the Greek School Philosophy, noticed
the attempt to explain some of the differences among Motions, by
classifying them into Natural Motions and Violent Motions; and we have
spoken of the assertion that heavy bodies fall quicker in proportion
to their greater weight. These doctrines were still retained: yet the
views which they implied were essentially erroneous and unsound; for
they did not refer distinctly to a measurable Force as the cause of
all motion or change of motion; and they confounded the causes which
_produce_ and those which _preserve_, motion. Hence such principles
did not lead immediately to any advance of knowledge, though efforts
were made to apply them, in the cases both of terrestrial Mechanics
and of the motions of the heavenly bodies.

The effect of the Inclined Plane was one of the first, as it was one
of the most important, propositions, on which modern writers employed
themselves. It was found that a body, when supported on a sloping
surface, might be sustained or raised by a force or exertion which
would not have been able to sustain or raise it without such support.
And hence, _The Inclined Plane_ was placed in the list of Mechanical
Powers, or simple machines by which the efficacy of forces is
increased: the question was, in what proportion this increase of
efficiency takes place. It is easily seen that the force requisite to
sustain a body is smaller, as the slope on which it rests is smaller;
Cardan (whose work, _De Proportionibus Numerorum, Motuum, Ponderum,_
&c., was published in 1545) asserts that the force is double when the
angle of inclination is double, and so on for other proportions; this
is probably a guess, and is an erroneous one. Guido Ubaldi, of
Marchmont, published at Pesaro, in 1577, a work which he called
_Mechanicorum Liber_, in which he endeavors to prove that an acute
wedge will produce a greater mechanical effect than an obtuse one,
without determining in what proportion. There is, he observes, "a
certain repugnance" between the direction in which the side of the
wedge tends to {314} move the obstacle, and the direction in which it
really does move. Thus the Wedge and the Inclined Plane are connected
in principle. He also refers the Screw to the Inclined Plane and the
Wedge, in a manner which shows a just apprehension of the question.
Benedetti (1585) treats the Wedge in a different manner; not exact,
but still showing some powers of thought on mechanical subjects.
Michael Varro, whose _Tractatus de Motu_ was published at Geneva in
1584, deduces the wedge from the composition of hypothetical motions,
in a way which may appear to some persons an anticipation of the
doctrine of the Composition of Forces.

There is another work on subjects of this kind, of which several
editions were published in the sixteenth century, and which treats
this matter in nearly the same way as Varro, and in favour of which a
claim has been made[2\6] (I think an unfounded one), as if it
contained the true principle of this problem. The work is "Jordanus
Nemorarius _De Ponderositate_." The date and history of this author
were probably even then unknown; for in 1599, Benedetti, correcting
some of the errors of Tartalea, says they are taken "a Jordano quodam
antiquo." The book was probably a kind of school-book, and much used;
for an edition printed at Frankfort, in 1533, is stated to be _Cum
gratia et privilegio Imperiali, Petro Apiano mathematico Ingolstadiano
ad xxx annos concesso_. But this edition does not contain the Inclined
Plane. Though those who compiled the work assert in words something
like the inverse proportion of Weights and their Velocities, they had
not learnt at that time how to apply this maxim to the Inclined Plane;
nor were they ever able to render a sound reason for it. In the
edition of Venice, 1565, however, such an application is attempted.
The reasonings are founded on the Aristotelian assumption, "that
bodies descend more quickly in proportion as they are heavier." To
this principle are added some others; as, that "a body is heavier in
proportion as it descends more directly to the centre," and that, in
proportion as a body descends more obliquely, the intercepted part of
the direct descent is smaller. By means of these principles, the
"descending force" of bodies, on inclined planes, was compared, by a
process, which, so far as it forms a line of proof at all, is a
somewhat curious example of confused and vicious reasoning. When two
bodies are supported on two inclined planes, and are connected by a
string passing over the junction of the planes, so that when one
descends the other ascends, {315} they must move through equal spaces
on the planes; but on the plane which is more oblique (that is, more
nearly horizontal), the vertical descent will be smaller in the same
proportion in which the plane is longer. Hence, by the Aristotelian
principle, the weight of the body on the longer plane is less; and, to
produce an equality of effect, the body must be greater in the same
proportion. We may observe that the Aristotelian principle is not only
false, but is here misapplied; for its genuine meaning is, that when
bodies _fall freely_ by gravity, they move quicker in proportion as
they are heavier; but the rule is here applied to the motions which
bodies _would_ have, if they were moved by a force extraneous to their
gravity. The proposition was supposed by the Aristotelians to be true
of _actual_ velocities; it is applied by Jordanus to _virtual_
velocities, without his being aware what he was doing. This confusion
being made, the result is got at by taking for granted that bodies
_thus_ proved to be equally _heavy_, have equal powers of descent on
the inclined planes; whereas, in the previous part of the reasoning,
the weight was supposed to be proportional to the descent in the
vertical direction. It is obvious, in all this, that though the author
had adopted the false Aristotelian principle, he had not settled in
his own mind whether the motions of which it spoke were actual or
virtual motions;--motions in the direction of the inclined plane, or
of the intercepted parts of the vertical, corresponding to these; nor
whether the "descending force" of a body was something different from
its weight. We cannot doubt that, if he had been required to point
out, with any exactness, the cases to which his reasoning applied, he
would have been unable to do so; not possessing any of those clear
fundamental Ideas of Pressure and Force, on which alone any real
knowledge on such subjects must depend. The whole of Jordanus's
reasoning is an example of the confusion of thought of his period, and
of nothing more. It no more supplied the want of some man of genius,
who should give the subject a real scientific foundation, than
Aristotle's knowledge of the proportion of the weights on the lever
superseded the necessity of Archimedes's proof of it.

[Note 2\6: Mr. Drinkwater's _Life of Galileo_, in the Lib. Usef. Kn.
p. 83.]

We are not, therefore, to wonder that, though this pretended theorem
was copied by other writers, as by Tartalea, in his _Quesiti et
Inventioni Diversi_, published in 1554, no progress was made in the
real solution of any one mechanical problem by means of it. Guido
Ubaldi, who, in 1577, writes in such a manner as to show that he had
taken a good hold of his subject for his time, refers to Pappus's
solution of the problem of the Inclined Plane,  but makes no mention
of that of {316} Jordanus and Tartalea.[3\6] No progress was likely
to occur, till the mathematicians had distinctly recovered the
genuine Idea of Pressure, as a Force producing equilibrium, which
Archimedes had possessed, and which was soon to reappear in Stevinus.

[Note 3\6: Ubaldi mentions and blames Jordanus's way of treating the
Lever. (See his Preface.)]

The properties of the Lever had always continued known to
mathematicians, although, in the dark period, the superiority of the
proof given by Archimedes had not been recognized. We are not to be
surprised, if reasonings like those of Jordanus were applied to
demonstrate the theories of the Lever with apparent success. Writers
on Mechanics were, as we have seen, so vacillating in their mode of
dealing with words and propositions, that their maxims could be made
to prove any thing which was already known to be true.

We proceed to speak of the beginning of the real progress of
Mechanics in modern times.


_Sect._ 2.--_Revival of the Scientific Idea of
Pressure.--Stevinus.--Equilibrium of Oblique Forces._

THE doctrine of the Centre of Gravity was the part of the mechanical
speculations of Archimedes which was most diligently prosecuted
after his time. Pappus and others, among the ancients, had solved
some new problems on this subject, and Commandinus, in 1565,
published _De Centro Gravitatis Solidorum_. Such treatises
contained, for the most part, only mathematical consequences of the
doctrines of Archimedes; but the mathematicians also retained a
steady conviction of the mechanical property of the Centre of
Gravity, namely, that all the weight of the body might be collected
there, without any change in the mechanical results; a conviction
which is closely connected with our fundamental conceptions of
mechanical action. Such a principle, also, will enable us to
determine the result of many simple mechanical arrangements; for
instance, if a mathematician of those days had been asked whether a
solid ball could be made of such a form, that, when placed on a
horizontal plane, it should go on rolling forwards without limit
merely by the effect of its own weight, he would probably have
answered, that it could not; for that the centre of gravity of the
ball would seek the lowest position it could find, and that, when it
had found this, the ball could have no tendency to roll any further.
And, in making this assertion, the supposed reasoner would not be
{317} anticipating any wider proof of the impossibility of a
_perpetual motion_ drawn from principles subsequently discovered,
but would be referring the question to certain fundamental
convictions, which, whether put into Axioms or not, inevitably
accompany our mechanical conceptions.

In the same way, Stevinus of Bruges, in 1586, when he published his
_Beghinselen der Waaghconst_ (Principles of Equilibrium), had been
asked why a loop of chain, hung over a triangular beam, could not,
as he asserted it could not, go on moving round and round
perpetually, by the action of its own weight, he would probably have
answered, that the weight of the chain, if it produced motion at
all, must have a tendency to bring it into some certain position,
and that when the chain had reached this position, it would have no
tendency to go any further; and thus he would have reduced the
impossibility of such a perpetual motion, to the conception of
gravity, as a force tending to produce equilibrium; a principle
perfectly sound and correct.

Upon this principle thus applied, Stevinus did establish the
fundamental property of the Inclined Plane. He supposed a loop of
string, loaded with fourteen equal balls at equal distances, to hang
over a triangular support which was composed of two inclined planes
with a horizontal base, and whose sides, being unequal in the
proportion of two to one, supported four and two balls respectively.
He showed that this loop must hang at rest, because any motion would
only bring it into the same condition in which it was at first; and
that the festoon of eight balls which hung down below the triangle
might be removed without disturbing the equilibrium; so that four
balls on the longer plane would balance two balls on the shorter
plane; or in other words, the weights would be as the lengths of the
planes intercepted by the horizontal line.

Stevinus showed his firm possession of the truth contained in this
principle, by deducing from it the properties of forces acting in
oblique directions under all kinds of conditions; in short, he
showed his entire ability to found upon it a complete doctrine of
equilibrium; and upon his foundations, and without any additional
support, the mathematical doctrines of Statics might have been
carried to the highest pitch of perfection they have yet reached.
The formation of the science was finished; the mathematical
development and exposition of it were alone open to extension and
change.

[2d Ed.] ["Simon Stevin of Bruges," as he usually designates himself
in the title-page of his work, has lately become an object of
general interest in his own country, and it has been resolved to
erect a {318} statue in honor of him in one of the public places of
his native city. He was born in 1548, as I learn from M. Quetelet's
notice of him, and died in 1620. Montucla says that he died in 1633;
misled apparently by the preface to Albert Girard's edition of
Stevin's works, which was published in 1634, and which speaks of a
death which took place in the preceding year; but on examination it
will be seen that this refers to Girard, not to Stevin.

I ought to have mentioned, in consideration of the importance of the
proposition, that Stevin distinctly states the _triangle of forces_;
namely, that three forces which act upon a point are in equilibrium
when they are parallel and proportional to the three sides of any
plane triangle. This includes the principle of the _Composition of
Statical Forces_. Stevin also applies his principle of equilibrium
to cordage, pulleys, funicular polygons, and especially to the bits
of bridles; a branch of mechanics which he calls _Chalinothlipsis_.

He has also the merit of having seen very clearly, the distinction
of statical and dynamical problems. He remarks that the question,
"What force will _support_ a loaded wagon on an inclined plane? is a
statical question, depending on simple conditions; but that the
question, What force will _move_ the wagon? requires additional
considerations to be introduced.

In Chapter iv. of this Book, I have noticed Stevin's share in the
rediscovery of the _Laws of the Equilibrium of Fluids_. He
distinctly explains the _hydrostatic paradox_, of which the
discovery is generally ascribed to Pascal.

Earlier than Stevinus, Leonardo da Vinci must have a place among the
discoverers of the Conditions of Equilibrium of Oblique Forces. He
published no work on this subject; but extracts from his manuscripts
have been published by Venturi, in his _Essai sur les Ouvrages
Physico-Mathematiques de Leonard da Vinci, avec des Fragmens tirés
de ses Manuscrits apportés d'Italie_, Paris, 1797: and by Libri, in
his _Hist. des Sc. Math. en Italie_, 1839. I have also myself
examined these manuscripts in the Royal Library at Paris.

It appears that, as early as 1499, Leonardo gave a perfectly correct
statement of the proportion of the forces exerted by a cord which
acts obliquely and supports a weight on a lever. He distinguishes
between the real lever, and the _potential levers_, that is, the
perpendiculars drawn from the centre upon the directions of the
forces. This is quite sound and satisfactory. These views must in
all probability have been sufficiently promulgated in Italy to
influence the speculations of Galileo; {319} whose reasonings
respecting the lever much resemble those of Leonardo.--Da Vinci also
anticipated Galileo in _asserting_ that the time of descent of a
body down an inclined plane is to the time of descent down its
vertical length in the proportion of the length of the plane to the
height. But this cannot, I think, have been more than a guess: there
is no vestige of a proof given.]

The contemporaneous progress of the other branch of mechanics, the
Doctrine of Motion, interfered with this independent advance of
Statics; and to that we must now turn. We may observe, however, that
true propositions respecting the composition of forces appear to
have rapidly diffused themselves. The _Tractatus de Motu_ of Michael
Varro of Geneva, already noticed, printed in 1584, had asserted,
that the forces which balance each other, acting on the sides of a
right-angled triangular wedge, are in the proportion of the sides of
the triangle; and although this assertion does not appear to have
been derived from a distinct idea of pressure, the author had hence
rightly deduced the properties of the wedge and the screw. And
shortly after this time, Galileo also established the same results
on different principles. In his Treatise _Delle Scienze Mecaniche_
(1592), he refers the Inclined Plane to the Lever, in a sound and
nearly satisfactory manner; imagining a lever so placed, that the
motion of a body at the extremity of one of its arms should be in
the same direction as it is upon the plane. A slight modification
makes this an unexceptionable proof.


_Sect._ 3.--_Prelude to the Science of Dynamics.--Attempts at the
First Law of Motion._

WE have already seen, that Aristotle divided Motions into Natural
and Violent. Cardan endeavored to improve this division by making
three classes: _Voluntary_ Motion, which is circular and uniform,
and which is intended to include the celestial motions; _Natural_
Motion, which is stronger towards the end, as the motion of a
falling body,--this is in a straight line, because it is motion to
an end, and nature seeks her ends by the shortest road; and thirdly,
_Violent_ Motion, including in this term all kinds different from
the former two. Cardan was aware that such Violent Motion might be
produced by a very small force; thus he asserts, that a spherical
body resting on a horizontal plane may be put in motion by any force
which is sufficient to cleave the air; for which, however, he
erroneously assigns as a reason, {320} the smallness of the point of
contact.[4\6] But the most common mistake of this period was, that
of supposing that as force is requisite to move a body, so a
perpetual supply of force is requisite to keep it in motion. The
whole of what Kepler called his "physical" reasoning, depended upon
this assumption. He endeavored to discover the forces by which the
motions of the planets about the sun might be produced; but, in all
cases, he considered the velocity of the planet as produced by, and
exhibiting the effect of, a force which acted in the direction of
the motion. Kepler's essays, which are in this respect so feeble and
unmeaning, have sometimes been considered as disclosing some distant
anticipation of Newton's discovery of the existence and law of
central forces. There is, however, in reality, no other connection
between these speculations than that which arises from the use of
the term _force_ by the two writers in two utterly different
meanings. Kepler's Forces were certain imaginary qualities which
appeared in the actual motion which the bodies had; Newton's Forces
were causes which appeared by the change of motion: Kepler's Forces
urged the bodies forwards; Newton's deflected the bodies from such a
progress. If Kepler's Forces were destroyed, the body would
instantly stop; if Newton's were annihilated, the body would go on
uniformly in a straight line. Kepler compares the action of his
Forces to the way in which a body might be driven round, by being
placed among the sails of a windmill; Newton's Forces would be
represented by a rope pulling the body to the centre. Newton's Force
is merely mutual attraction; Kepler's is something quite different
from this; for though he perpetually illustrates his views by the
example of a magnet, he warns us that the sun differs from the
magnet in this respect, that its force is not attractive, but
directive.[5\6] Kepler's essays may with considerable reason be
asserted to be an anticipation of the Vortices of Descartes; but
they can with no propriety whatever be said to anticipate Newton's
Dynamical Theory.

[Note 4\6: In speaking of the force which would draw a body up an
inclined plane he observes, that "per communem animi sententiam,"
when the plane becomes horizontal, the requisite force is nothing.]

[Note 5\6: _Epitome Astron. Copern._ p. 176.]

The confusion of thought which prevented mathematicians from seeing
the difference between producing and preserving motion, was, indeed,
fatal to all attempts at progress on this subject. We have already
noticed the perplexity in which Aristotle involved himself, by his
endeavors to find a reason for the continued motion of a stone {321}
after the moving power had ceased to act; and that he had ascribed
it to the effect of the air or other medium in which the stone
moves. Tartalea, whose _Nuova Scienza_ is dated 1550, though a good
_pure_ mathematician, is still quite in the dark on mechanical
matters. One of his propositions, in the work just mentioned, is (B.
i. Prop. 3), "The more a heavy body recedes from the beginning, or
approaches the end of violent motion, the slower and more inertly it
goes;" which he applies to the horizontal motion of projectiles. In
like manner most other writers about this period conceived that a
cannon-ball goes forwards till it loses all its projectile motion,
and then falls downwards. Benedetti, who has already been mentioned,
must be considered as one of the first enlightened opponents of this
and other Aristotelian errors or puzzles. In his _Speculationum
Liber_ (Venice, 1585), he opposes Aristotle's mechanical opinions,
with great expressions of respect, but in a very sweeping manner.
His chapter xxiv. is headed, "Whether this eminent man was right in
his opinion concerning violent and natural motion." And after
stating the Aristotelian opinion just mentioned, that the body is
impelled by the air, he says that the air must impede rather than
impel the body, and that[6\6] "the motion of the body, separated
from the mover, arises by a certain natural impression from the
impetuosity (_ex impetuositate_) received from the mover." He adds,
that in natural motions this _impetuosity_ continually increases by
the continued action of the cause,--namely, the propension of going
to the place assigned it by nature; and that thus the velocity
increases as the body moves from the beginning of its path. This
statement shows a clearness of conception with regard to the cause
of accelerated motion, which Galileo himself was long in acquiring.

[Note 6\6: P. 184.]

Though Benedetti was thus on the way to the First Law of
Motion,--that all motion is uniform and rectilinear, except so far
as it is affected by extraneous forces;--this Law was not likely to
be either generally conceived, or satisfactorily proved, till the
other Laws of Motion, by which the action of Forces is regulated,
had come into view. Hence, though a partial apprehension of this
principle had preceded the discovery of the Laws of Motion, we must
place the establishment of the principle in the period when those
Laws were detected and established, the period of Galileo and his
followers. {322}




CHAPTER II.

INDUCTIVE EPOCH OF GALILEO.--DISCOVERY OF THE LAWS OF MOTION IN
SIMPLE CASES.


_Sect._ 1.--_Establishment of the First Law of Motion._

AFTER mathematicians had begun to doubt or reject the authority of
Aristotle, they were still some time in coming to the conclusion,
that the distinction of Natural and Violent Motions was altogether
untenable;--that the velocity of a body in motion increased or
diminished in consequence of the action of extrinsic causes, not of
any property of the motion itself;--and that the apparently
universal fact, of bodies growing slower and slower, as if by their
own disposition, till they finally stopped, from which Motions had
been called Violent, arose from the action of external obstacles not
immediately obvious, as the friction and the resistance of the air
when a ball runs on the ground, and the action of gravity, when it
is thrown upwards. But the truth to which they were at last led,
was, that such causes would account for _all_ the diminution of
velocity which bodies experience when apparently left to themselves
and that without such causes, the motion of all bodies would go on
forever, in a straight line and with a uniform velocity.

Who first announced this Law in a general form, it may be difficult
to point out; its exact or approximate truth was necessarily taken
for granted in all complete investigations on the subject of the
laws of motion of falling bodies, and of bodies projected so as to
describe curves. In Galileo's first attempt to solve the problem of
falling bodies, he did not carry his analysis back to the notion of
force, and therefore this law does not appear. In 1604 he had an
erroneous opinion on this subject  and we do not know when he was
led to the true doctrine which he published in his _Discorso_, in
1638. In his third Dialogue he gives the instance of water in a
vessel, for the purpose of showing that circular motion has a
tendency to continue. And in his first Dialogue on the Copernican
System[7\6] (published in 1630), he asserts {323} Circular Motion
alone to be naturally uniform, and retains the distinction between
Natural and Violent Motion. In the _Dialogues on Mechanics_,
however, published in 1638, but written apparently at an earlier
period, in treating of Projectiles,[8\6] he asserts the true Law.
"Mobile super planum horizontale projectum mente concipio omni
secluso impedimento; jam constat ex his quæ fusius alibi dicta sunt,
illius motum equabilem et perpetuum super ipso plano futurum esse,
si planum in infinitum extendatur." "Conceive a movable body upon a
horizontal plane, and suppose all obstacles to motion to be removed;
it is then manifest, from what has been said more at large in
another place, that the body's motion will be uniform and perpetual
upon the plane, if the plane be indefinitely extended." His pupil
Borelli, in 1667 (in the treatise _De Vi Percussionis_), states the
proposition generally, that "Velocity is, by its nature, uniform,
and perpetual;" and this opinion appears to have been, at that time,
generally diffused, as we find evidence in Wallis and others. It is
commonly said that Descartes was the first to state this generally.
His _Principia_ were published in 1644; but his proofs of this First
Law of Motion are rather of a theological than of a mechanical kind.
His reason for this Law is,[9\6] "the immutability and simplicity of
the operation by which God preserves motion in matter. For he only
preserves it precisely as it is in that moment in which he preserves
it, taking no account of that which may have been previously."
Reasoning of this abstract and _à priori_ kind, though it may be
urged in favor of true opinions after they have been inductively
established, is almost equally capable of being called in on the
side of error, as we have seen in the case of Aristotle's
philosophy. We ought not, however, to forget that the reference to
these abstract and _à priori_ principles is an indication of the
absolute universality and necessity which we look for in complete
Sciences, and a result of those faculties by which such Science is
rendered possible, and suitable to man's intellectual nature.

[Note 7\6: Dial. **i. p. 40.]

[Note 8\6: **p. 141.]

[Note 9\6: _Princip._ p. 34.]

The induction by which the First Law of Motion is established,
consists, as induction consists in all cases, in conceiving clearly
the Law, and in perceiving the subordination of Facts to it. But the
Law speaks of bodies not acted upon by any external force,--a case
which never occurs in fact; and the difficulty of the step consisted
in bringing all the common cases in which motion is gradually
extinguished, under the notion of the action of a retarding force.
In order to do this, {324} Hooke and others showed that, by
diminishing the obvious resistances, the retardation also became
less; and men were gradually led to a distinct appreciation of the
Resistance, Friction, &c., which, in all terrestrial motions,
prevent the Law from being evident; and thus they at last
established by experiment a Law which cannot be experimentally
exemplified. The natural uniformity of motion was proved by
examining all kinds of cases in which motion was not uniform. Men
culled the abstract Rule out of the concrete Experiment; although
the Rule was, in every case, mixed with other Rules, and each Rule
could be collected from the Experiment only by supposing the others
known. The perfect simplicity which we necessarily seek for in a law
of nature, enables us to disentangle the complexity which this
combination appears at first sight to occasion.

The First Law of Motion asserts that the motion of a body, when left
to itself will not only be uniform, but rectilinear also. This
latter part of the law is indeed obvious of itself as soon as we
conceive a body detached from all special reference to external
points and objects. Yet, as we have seen, Galileo asserted that the
naturally uniform motion of bodies was that which takes place in a
circle. Benedetti, however, in 1585, had entertained sound notions
on this subject. In commenting on Aristotle's question, why we
obtain an advantage in throwing by using a sling, he says,[10\6] that
the body, when whirled round, tends to go on in a straight line. In
Galileo's second Dialogue, he makes one of his interlocutors
(Simplicio), when appealed to on this subject, after thinking
intently for a little while, give the same opinion; and the
principle is, from this time, taken for granted by the authors who
treat of the motion of projectiles. Descartes, as might be supposed,
gives the same reason for this as for the other part of the law,
namely, the immutability of the Deity.

[Note 10\6: "Corpus vellet recta iter peragere."
_**Speculationum Liber_, p. 160.]


_Sect._ 2.--_Formation and Application of the Notion of Accelerating
Force.--Laws of Falling Bodies._

WE have seen how rude and vague were the attempts of Aristotle and
his followers to obtain a philosophy of bodies falling downwards or
thrown in any direction. If the First Law of Motion had been clearly
known, it would then, perhaps, have been seen that the way to
understand and analyze the motion of any body, is to consider the
{325} Causes of _change_ of motion which at each instant operate
upon it; and thus men would have been led to the notion of
Accelerating Forces, that is, Forces which act upon bodies already
in motion, and accelerate, retard, or deflect their motions. It was,
however, only after many attempts that they reached this point. They
began by considering the _whole motion_ with reference to certain
ill-defined abstract Notions, instead of considering, with a clear
apprehension of the conditions of Causation, the _successive parts_
of which the motion consists. Thus, they spoke of the tendency of
bodies to the Centre, or to their Own Place;--of Projecting Force,
of Impetus, of Retraction;--with little or no profit to knowledge.
The indistinctness of their notions may, perhaps, be judged of from
their speculations concerning projectiles. Santbach,[11\6] in 1561,
imagined that a body thrown with great velocity, as, for instance, a
ball from a cannon, went in a straight line till all its velocity
was exhausted, and then fell directly downwards. He has written a
treatise on gunnery, founded on this absurd assumption. To this
succeeded another doctrine, which, though not much more
philosophical than the former, agreed much better with the
phenomena. Nicolo Tartalea (_Nuova Scienza_, Venice, 1550; _Quesiti
et Inventioni Diversi_, 1554) and **Gualter Rivius (_Architectura_,
&c., Basil, 1582) represented the path of a cannon-ball as
consisting, first of a straight line in the direction of the
original projection, then of an arc of a circle in which it went on
till its motion became vertical downwards, and then of a vertical
line in which it continued to fall. The latter of these writers,
however, was aware that the path must, from the first, be a curve;
and treated it as a straight line, only because the curvature is
very slight. Even Santbach's figure represents the path of the ball
as partially descending before its final fall, but then it descends
by _steps_, not in a curve. Santbach, therefore, did not conceive
the _Composition_ of the effect of gravity with the existing motion,
but supposed them to act alternately; Rivius, however, understood
this Composition, and saw that gravity must act as a deflecting
force at every point of the path. Galileo, in his second
Dialogue,[12\6] makes Simplicius come to the same conclusion.
"Since," he says, "there is nothing to support the body, when it
quits that which projects it, it cannot be but that its proper
gravity must operate," and it must immediately begin to decline
downwards. {326}

[Note 11\6: _Problematum Astronomicorum et Geometricorum Sectiones_
vii. &c. &c. Auctore Daniele Santbach, Noviomago. Basileæ, 1561.]

[Note 12\6: P. 147.]

The Force of Gravity which thus produces deflection and curvature in
the path of a body thrown _obliquely_, constantly increases the
velocity of a body when it falls _vertically_ downwards. The
universality of this increase was obvious, both from reasoning and in
fact; the law of it could only be discovered by closer consideration;
and the full analysis of the problem required a distinct measure of
the quantity of Accelerating Force. Galileo, who first solved this
problem, began by viewing it as a question of fact, but conjectured
the solution by taking for granted that the rule must be the simplest
possible. "Bodies," he says,[13\6] "will fall in the most simple way,
because Natural Motions are always the most simple. When a stone
falls, if we consider the matter attentively, we shall find that there
is no addition, no increase, of the velocity more simple than that
which is always added in the same manner," that is, when equal
additions take place in equal times; "which we shall easily understand
if we attend to the close connection of motion and time." From this
Law, thus assumed, he deduced that the spaces described from the
beginning of the motion must be as the squares of the times; and,
again, assuming that the laws of descent for balls rolling down
inclined planes, must be the same as for bodies falling freely, he
verified this conclusion by experiment.

[Note 13\6: _Dial. Sc._ iv. p. 91.]

It will, perhaps, occur to the reader that this argument, from the
simplicity of the assumed law, is somewhat insecure. It is not
always easy for us to discern what that greatest simplicity is,
which nature adopts in her laws. Accordingly, Galileo was led wrong
by this way of viewing the subject before he was led right. He at
first supposed, that the Velocity which the body had acquired at any
point must be proportional to the _Space_ described from the point
where the motion began. This false law is as simple in its
enunciation as the true law, that the Velocity is proportional to
the _Time_: it had been asserted as the true law by M. Varro (_De
Motu Tractatus_, Genevæ, 1584), and by Baliani, a gentleman of
Genoa, who published it in 1638. It was, however, soon rejected by
Galileo, though it was afterwards taken up and defended by Casræus,
one of Galileo's opponents. It so happens, indeed, that the false
law is not only at variance with fact, but with itself: it involves
a mathematical self-contradiction. This circumstance, however, was
accidental: it would be easy to state laws of the increase of
velocity which should be simple, and yet false in fact, though quite
possible in their own nature. {327}

The Law of Velocity was hitherto, as we have seen, treated as a law
of phenomena, without reference to the Causes of the law. "The cause
of the acceleration of the motions of falling bodies is not,"
Galileo observes, "a necessary part of the investigation. Opinions
are different. Some refer it to the approach to the centre; others
say that there is a certain extension of the centrical medium,
which, closing behind the body, pushes it forwards. For the present,
it is enough for us to demonstrate certain properties of Accelerated
Motion, the acceleration being according to the very simple Law,
that the Velocity is proportional to the Time. And if we find that
the properties of such motion are verified by the motions of bodies
descending freely, we may suppose that the assumption agrees with
the laws of bodies falling freely by the action of gravity."[14\6]

[Note 14\6: Gal. _Op._ iii. 91, 92.]

It was, however, an easy step to conceive this acceleration as
caused by the continual action of Gravity. This account had already
been given by Benedetti, as we have seen. When it was once adopted,
Gravity was considered as a _constant_ or _uniform_ force; on this
point, indeed, the adherents of the law of Galileo and of that of
Casræus were agreed; but the question was, what _is_ a Uniform
Force? The answer which Galileo was led to give was obviously
this;--_that_ is a Uniform Force which generates equal velocities in
equal successive times; and this principle leads at once to the
doctrine, that Forces are to be compared by comparing the Velocities
generated by them in equal times.

Though, however, this was a consequence of the rule by which Gravity
is represented as a Uniform Force, the subject presents some
difficulty at first sight. It is not immediately obvious that we may
thus measure forces by the Velocity _added_ in a given time, without
taking into account the velocity they have already. If we
communicate velocity to a body by the hand or by a spring, the
effect we produce in a second of time is lessened, when the body has
already a velocity which withdraws it from the pressure of the
agent. But it appears that this is not so in the case of gravity;
the velocity added in one second is the same, whatever downward
motion the body already possesses. A body falling from rest acquires
a velocity, in one second, of thirty-two feet; and if a cannon-ball
were shot downwards with a velocity of 1000 feet a second, it would
equally, at the end of one second, have received an accession of 32
feet to its velocity.

This conception of Gravity as a Uniform Force,--as constantly and
{328} equally _increasing_ the velocity of a descending body,--will
become clear by a little attention; but it undoubtedly presents
difficulty at first. Accordingly, we find that Descartes did not
accept it. "It is certain," he says, "that a stone is not equally
disposed to receive a new motion or increase of velocity when it is
already moving very quickly, and when it is moving slowly."

Descartes showed, by other expressions, that he had not caught hold
of the true notion of accelerating force. Thus, he says in a letter
to Mersenne, "I am astonished at what you tell me, of having found,
by experiment, that bodies thrown up in the air take neither more
nor less time to rise than to fall again; and you will excuse me if
I say that I look upon the experiment as a very difficult one to
make accurately." Yet it is clear from the Notion of a Constant
Force that (omitting the resistance of the air) this equality must
take place; for the Force which will gradually destroy the whole
velocity in a certain time in ascending, will, in the same time,
generate again the same velocity by the same gradations inverted;
and therefore the same space will be passed over in the same time in
the descent and in the ascent.

Another difficulty arose from a necessary consequence of the Laws of
Falling Bodies thus established;--the proposition, namely, that in
acquiring its motion, a body passes through every intermediate degree
of velocity, from the smallest conceivable, up to that which it at
last acquires. When a body falls from rest, it begins to fall with
_no_ velocity; the velocity increases with the time; and in
one-thousandth part of a second, the body has only acquired
one-thousandth part of the velocity which it has at the end of one
second.

This is certain, and manifest on consideration; yet there was at first
much difficulty raised on the subject of this assertion; and disputes
took place concerning the velocity with which a body _begins_ to fall.
On this subject also Descartes did not form clear notions. He writes
to a correspondent, "I have been revising my notes on Galileo, in
which I have not said expressly that falling bodies do not pass
through every degree of slowness, but I said that this cannot be known
without knowing what Weight is, which comes to the same thing; as to
your example, I grant that it proves that every degree of velocity is
infinitely divisible, but not that a falling body actually passes
through all these divisions."

The Principles of the Motion of Falling Bodies being thus established
by Galileo, the Deduction of the principal mathematical consequences
was, as is usual, effected with great rapidity, and is to be found
{329} in his works, and in those of his scholars and successors. The
motion of bodies falling freely was, however, in such treatises,
generally combined with the motion of bodies Falling along Inclined
Planes; a part of the theory of which we have still to speak.

The Notion of Accelerating Force and of its operation, once formed,
was naturally applied in other cases than that of bodies falling
freely. The different velocities with which heavy and light bodies
fall were explained by the different resistance of the air, which
diminishes the accelerating force;[15\6] and it was boldly asserted,
that in a vacuum a lock of wool and a piece of lead would fall equally
quickly. It was also maintained[16\6] that any falling body, however
large and heavy, would always have its velocity in some degree
diminished by the air in which it falls, and would at last be reduced
to a state of uniform motion, as soon as the resistance upwards became
equal to the accelerating force downwards. Though the law of progress
of a body to this limiting velocity was not made out till the
_Principia_ of Newton appeared, the views on which Galileo made this
assertion are perfectly sound, and show that he had clearly conceived
the nature and operation of accelerating and retarding force.

[Note 15\6: Galileo, iii. 43.]

[Note 16\6: iii. 54.]

When Uniform Accelerating Forces had once been mastered, there
remained only mathematical difficulties in the treatment of Variable
Forces. A Variable Force was measured by the _Limit_ of the
increment of the Velocity, compared with the increment of the Time;
just as a Variable Velocity was measured by the Limit of the
increment of the Space compared with that of the Time.

With this introduction of the Notion of Limits, we are, of course, led
to the Higher Geometry, either in its geometrical or its analytical
form. The general laws of bodies falling by the action of any Variable
Forces were given by Newton in the Seventh Section of the _Principia_.
The subject is there, according to Newton's preference of geometrical
methods, treated by means of the Quadrature of Curves; the Doctrine of
Limits being exhibited in a peculiar manner in the First Section of
the work, in order to prepare the way for such applications of it.
Leibnitz, the Bernouillis, Euler, and since their time, many other
mathematicians, have treated such questions by means of the analytical
method of limits, the Differential Calculus. The Rectilinear Motion of
bodies acted upon by variable forces is, of course, a simpler problem
than their Curvilinear Motion, to which we have now to proceed. But it
{330} may be remarked that Newton, having established the laws of
Curvilinear Motion independently, has, in a great part of his Seventh
Section, deduced the simpler case of the Rectilinear Motion from the
move complex problem, by reasonings of great ingenuity and beauty.


_Sect._ 3.--_Establishment of the Second Law of Motion.--Curvilinear
Motions._

A SLIGHT degree of distinctness in men's mechanical notions enabled
them to perceive, as we have already explained, that a body which
traces a curved line must be urged by some force, by which it is
constantly made to deviate from that rectilinear path, which it
would pursue if acted upon by no force. Thus, when a body is made to
describe a circle, as when a stone is whirled round in a sling, we
find that the string does exert such a force on the stone; for the
string is stretched by the effort, and if it be too slender, it may
thus be broken. This _centrifugal force_ of bodies moving in circles
was noticed even by the ancients. The effect of force to produce
curvilinear motion also appears in the paths described by
projectiles. We have already seen that though Tartalea did not
perceive this correctly, Rivius, about the same time, did.

To see that a transverse force would produce a curve, was one step;
to determine what the curve is, was another step, which involved the
discovery of the Second Law of Motion. This step was made by
Galileo. In his _Dialogues on Motion_, he asserts that a body
projected horizontally will retain a uniform motion in the
horizontal direction, and will have, compounded with this, a
uniformly accelerated motion downwards, that is, the motion of a
body falling vertically from rest; and will thus describe the curve
called a parabola.

The Second Law of Motion consists of this assertion in a general
form;--namely, that in all cases the motion which the force will
produce is compounded with the motion which the body previously has.
This was not obvious; for Cardan had maintained,[17\6] that "if a
body is moved by two motions at once, it will come to the place
resulting from their composition slower than by either of them." The
proof of the truth of the law to Galileo's mind was, so far as we
collect from the Dialogue itself, the simplicity of the supposition,
and his clear perception of the causes which, in some cases,
produced an obvious deviation in practice {331} from this
theoretical result. For it may be observed, that the curvilinear
paths ascribed to military projectiles by Rivius and Tartalea, and
by other writers who followed them, as Digges and Norton in our own
country, though utterly different from the theoretical form, the
parabola, do, in fact, approach nearer the true paths of a cannon or
musket ball than a parabola would do; and this approximation more
especially exists in that which at first sight appears most absurd
in the old theory; namely, the assertion that the ball, which
ascends in a sloping direction, finally descends vertically. In
consequence of the resistance of the air, this is really the path of
a projectile; and when the velocity is very great, as in military
projectiles, the deviation from the parabolic form is very manifest.
This cause of discrepancy between the theory, which does not take
resistance into the account, and the fact, Galileo perceived; and
accordingly he says,[18\6] that the velocities of the projectiles,
in such cases, may be considered as excessive and supernatural. With
the due allowance to such causes, he maintained that his theory was
verified, and might be applied in practice. Such practical
applications of the doctrine of projectiles no doubt had a share in
establishing the truth of Galileo's views. We must not forget,
however, that the full establishment of this second law of motion
was the result of the theoretical and experimental discussions
concerning the motion of the earth: its fortunes were involved in
those of the Copernican system; and it shared the triumph of that
doctrine. This triumph was already decisive, indeed, in the time of
Galileo, but not complete till the time of Newton.

[Note 17\6: _Op._ vol. iv. p. 490.]

[Note 18\6: _Op._ vol. iii. p. 147.]


_Sect._ 4.--_Generalization of the Laws of Equilibrium.--Principle
of Virtual Velocities._

IT was known, even as early as Aristotle, that the two weights which
balance each other on the lever, if they move at all, move with
velocities which are in the inverse proportions of the weights. The
peculiar resources of the Greek language, which could state this
relation of inverse proportionality in a single word (ἀντιπέπονθεν),
fixed it in men's minds, and prompted them to generalize from this
property. Such attempts were at first made with indistinct ideas,
and on conjecture only, and had, therefore, no scientific value.
This is the judgment which we must pass on the book of Jordanus
Nemorarius, which {332} we have already mentioned. Its reasonings
are professedly on Aristotelian principles, and exhibit the common
Aristotelian absence of all distinct mechanical ideas. But in Varro,
whose _Tractatus de Motu_ appeared in 1584, we find the principle,
in a general form, not satisfactorily proved, indeed, but much more
distinctly conceived. This is his first theorem: "Duarum virium
connexarum quarum (si moveantur) motus erunt ipsis ἀντιπεπονθῶς
proportionales, neutra alteram movebit, sed equilibrium facient."
The proof offered of this is, that the resistance to a force is as
the motion produced; and, as we have seen, the theorem is rightly
applied in the example of the wedge. From this time it appears to
have been usual to prove the properties of machines by means of this
principle. This is done, for instance, in _Les Raisons des Forces
Mouvantes_, the production of Solomon de Caus, engineer to the
Elector Palatine, published at Antwerp in 1616; in which the effect
of Toothed-Wheels and of the Screw is determined in this manner, but
the Inclined Plane is not treated of. The same is the case in Bishop
Wilkins's _Mathematical Magic_, in 1648.

When the true doctrine of the Inclined Plane had been established,
the laws of equilibrium for all the simple machines or Mechanical
Powers, as they had usually been enumerated in books on Mechanics,
were brought into view; for it was easy to see that the _Wedge_ and
the _Screw_ involved the same principle as the _Inclined Plane_, and
the _Pulley_ could obviously be reduced to the _Lever_. It was,
also, not difficult for a person with clear mechanical ideas to
perceive how any other combination of bodies, on which pressure and
traction are exerted, may be reduced to these simple machines, so as
to disclose the relation of the forces. Hence by the discovery of
Stevinus, all problems of equilibrium were essentially solved.

The conjectural generalization of the property of the lever, which
we have just mentioned, enabled mathematicians to express the
solution of all these problems by means of one proposition. This was
done by saying, that in raising a weight by any machine, we _lose_
in Time what we _gain_ in Force; the weight raised moves as much
_slower_ than the power, as it is _larger_ than the power. This was
explained with great clearness by Galileo, in the preface to his
_Treatise on Mechanical Science_, published in 1592.

The motions, however, which we here suppose the parts of the machine
to have, are not motions which the forces produce; for at present we
are dealing with the case in which the forces balance each other,
and therefore produce no motion. But we ascribe to the {333} Weights
and Powers hypothetical motions, arising from some other cause; and
then, by the construction of the machine, the velocities of the
Weights and Powers must have certain definite ratios. These
velocities, being thus hypothetically supposed and not actually
produced, are called _Virtual_ Velocities. And the general law of
equilibrium is, that in any machine, the Weights which balance each
other, are reciprocally to each other as their Virtual Velocities.
This is called the _Principle of Virtual Velocities_.

This Principle (which was afterwards still further generalized) is,
by some of the admirers of Galileo, dwelt upon as one of his great
services to Mechanics. But if we examine it more nearly, we shall
see that it has not much importance in our history. It is a
generalization, but a generalization established rather by
enumeration of cases, than by any induction proceeding upon one
distinct Idea, like those generalizations of Facts by which Laws are
primarily established. It rather serves verbally to conjoin Laws
previously known, than to exhibit a connection in them: it is rather
a help for the memory than a proof for the reason.

The Principle of Virtual Velocities is so far from implying any
clear possession of mechanical ideas, that any one who knows the
property of the Lever, whether he is capable of seeing the reason
for it or not, can see that the greater weight moves slower in the
exact proportion of its greater magnitude. Accordingly, Aristotle,
whose entire want of sound mechanical views we have shown, has yet
noticed this truth. When Galileo treats of it, instead of offering
any reasons which could independently establish this principle, he
gives his readers a number of analogies and illustrations, many of
them very loose ones. Thus the raising a great weight by a small
force, he illustrates by supposing the weight broken into many small
parts, and conceiving those parts raised one by one. By other
persons, the analogy, already intimated, of gain and loss is
referred to as an argument for the principle in question. Such
images may please the fancy, but they cannot be accepted as
mechanical reasons.

Since Galileo neither first enunciated this rule, nor ever proved it
as an independent principle of Mechanics, we cannot consider the
discovery of it as one of his mechanical achievements. Still less
can we compare his reference to this principle with Stevinus's proof
of the Inclined Plane; which, as we have seen, was rigorously
inferred from the sound axiom, that a body cannot put itself in
motion. If we were to assent to the really self-evident axioms of
Stevinus, only in virtue {334} of the unproved verbal generalization
of Galileo, we should be in great danger of allowing ourselves to be
referred successively from one truth to another, without any
reasonable hope of ever arriving at any thing ultimate and
fundamental.

But though this Principle of Virtual Velocity cannot be looked upon
as a great discovery of Galileo, it is a highly useful rule; and the
various forms under which he and his successors urged it, tended
much to dissipate the vague wonder with which the effects of
machines had been looked upon; and thus to diffuse sounder and
clearer notions on such subjects.

The Principle of Virtual Velocities also affected the progress of
mechanical science in another way: it suggested some of the
analogies by the aid of which the Third Law of Motion was made out;
leading to the adoption of the notion of _Momentum_ as the
arithmetical product of weight and velocity. Since on a machine on
which a weight of two pounds at one part balances three pounds at
another part, the former weight would move through three inches
while the latter would move through two inches; we see (since three
multiplied into two is equal to two multiplied into three) that the
_Product_ of the weight and the velocity is the same for the two
balancing weights; and if we call this Product _Momentum_, the Law
of Equilibrium is, that when two weights balance on a machine, the
Momentum of the two would be the same, if they were put in motion.

The Notion of Momentum was here employed in connection with Virtual
Velocities; but it also came under consideration in treating of
Actual Velocities, as we shall soon see.


_Sect._ 5.--_Attempts at the Third Law of Motion.--Notion of
Momentum._

IN the questions we have hitherto had to consider respecting Motion,
no regard is had to the Size of the body moved, but only to the
Velocity and Direction of the motion. We must now trace the progress
of knowledge respecting the mode in which the Mass of the body
influences the effect of Force. This is a more difficult and complex
branch of the subject; but it is one which requires to be noticed,
as obviously as the former. Questions belonging to this department
of Mechanics, as well as to the others, occur in Aristotle's
Mechanical Problems. "Why," says he, "is it, that neither very small
nor very large bodies go far when we throw them; but, in order that
this may {335} happen, the thing thrown must have a certain
proportion to the agent which throws it? Is it that what is thrown
or pushed must react[19\6] against that which pushes it; and that a
body so large as not to yield at all, or so small as to yield
entirely, and not to react, produces no throw or push?" The same
confusion of ideas prevailed after his time; and mechanical
questions were in vain discussed by means of general and abstract
terms, employed with no distinct and steady meaning; such as
_impetus_, _power_, _momentum_, _virtue_, _energy_, and the like.
From some of these speculations we may judge how thorough the
confusion in men's heads had become. Cardan perplexes himself with
the difficulty, already mentioned, of the comparison of the forces
of bodies at rest and in motion. If the Force of a body depends on
its velocity, as it appears to do, how is it that a body at rest has
any Force at all, and how can it resist the slightest effort, or
exert any pressure? He flatters himself that he solves the question,
by asserting that bodies at rest have an occult motion. "Corpus
movetur occulto motu quiescendo."--Another puzzle, with which he
appears to distress himself rather more wantonly, is this: "If one
man can draw half of a certain weight, and another man also one
half; when the two act together, these proportions should be
compounded; so that they ought to be able to draw one half of one
half, or one quarter only." The talent which ingenious men had for
getting into such perplexities, was certainly at one time very
great. Arriaga,[20\6] who wrote in 1639, is troubled to discover how
several flat weights, lying one upon another on a board, should
produce a greater pressure than the lowest one alone produces, since
that alone touches the board. Among other solutions, he suggests
that the board affects the upper weight, which it does not touch, by
determining its _ubication_, or _whereness_.

[Note 19\6: ἀντερείδειν.]

[Note 20\6: Rod. de Arriaga, _Cursus Philosophicus_. Paris, 1639.]

Aristotle's doctrine, that a body ten times as heavy as another,
will fall ten times as fast, is another instance of the confusion of
Statical and Dynamical Forces: the Force of the greater body, while
_at rest_, is ten times as great as that of the other; but the Force
as measured by the _velocity_ produced, is equal in the two cases.
The two bodies would fall downwards with the same rapidity, except
so far as they are affected by accidental causes. The merit of
proving this by experiment, and thus refuting the Aristotelian
dogma, is usually ascribed to Galileo, who made his experiment from
the famous leaning tower of Pisa, about 1590. But others about the
same time had not {336} overlooked so obvious a fact--F.
Piccolomini, in his _Liber Scientiæ de Natura_, published at Padua,
in 1597, says, "On the subject of the motion of heavy and light
bodies, Aristotle has put forth various opinions, which are contrary
to sense and experience, and has delivered rules concerning the
proportion of quickness and slowness, which are palpably false. For
a stone twice as great does _not_ move twice as fast." And Stevinus,
in the Appendix to his Statics, describes his having made the
experiment, and speaks with great correctness of the apparent
deviations from the rule, arising from the resistance of the air.
Indeed, the result followed by very obvious reasoning; for ten
bricks, in contact with each other, side by side, would obviously
fall in the same time as one; and these might be conceived to form a
body ten times as large as one of them. Accordingly, Benedetti, in
1585, reasons in this manner with regard to bodies of different
size, though he retains Aristotle's error as to the different
velocity of bodies of different density.

The next step in this subject is more clearly due to Galileo; he
discovered the true proportion which the Accelerating Force of a
body falling down an inclined plane bears to the Accelerating Force
of the same body falling freely. This was at first a happy
conjecture; it was then confirmed by experiments, and, finally,
after some hesitation, it was referred to its true principle, the
Third Law of Motion, with proper elementary simplicity. The
Principle here spoken of is this:--that for the same body, the
Dynamical effect of force is as the Statical effect; that is, the
Velocity which any force generates in a given time when it puts the
body in motion, is proportional to the Pressure which the same force
produces in a body at rest. The Principle, so stated, appears very
simple and obvious; yet this was not the form in which it suggested
itself either to Galileo or to other persons who sought to prove it.
Galileo, in his _Dialogues on Motion_, assumes, as his fundamental
proposition on this subject, one much less evident than that we have
quoted, but one in which that is involved. His Postulate is,[21\6]
that when the same body falls down different planes of the same
height, the velocities acquired are equal. He confirms and
illustrates this by a very ingenious experiment on a pendulum,
showing that the weight swings to the same height whatever path it
be compelled to follow. Torricelli, in his treatise published 1644,
says that he had heard that Galileo had, towards the end of his
life, proved his {337} assumption, but that, not having seen the
proof, he will give his own. In this he refers us to the right
principle, but appears not distinctly to conceive the proof, since
he estimates _momentum_ indiscriminately by the statical Pressure of
a body, and by its Velocity when in motion; as if these two
quantities were self-evidently equal. Huyghens, in 1673, expresses
himself dissatisfied with the proof by which Galileo's assumption
was supported in the later editions of his works. His own proof
rests on this principle;--that if a body fall down one inclined
plane, and proceed up another with the velocity thus acquired, it
cannot, under any circumstances, ascend to a higher position than
that from which it fell. This principle coincides very nearly with
Galileo's experimental illustration. In truth, however, Galileo's
principle, which Huyghens thus slights, may be looked upon as a
satisfactory statement of the true law  namely, that, in the same
body, the velocity produced is as the pressure which produces it.
"We are agreed," he says,[22\6] "that, in a movable body, the
_impetus_, _energy_, _momentum_, or _propension to motion_, is as
great as is the _force_ or _least resistance_ which suffices to
_support_ it." The various terms here used, both for dynamical and
statical Force, show that Galileo's ideas were not confused by the
ambiguity of any one term, as appears to have happened to some
mathematicians. The principle thus announced, is, as we shall see,
one of great extent and value; and we read with interest the
circumstances of its discovery, which are thus narrated.[23\6] When
Viviani was studying with Galileo, he expressed his dissatisfaction
at the want of any clear reason for Galileo's postulate respecting
the equality of velocities acquired down inclined planes of the same
heights; the consequence of which was, that Galileo, as he lay, the
same night, sleepless through indisposition, discovered the proof
which he had long sought in vain, and introduced it in the
subsequent editions. It is easy to see, by looking at the proof,
that the discoverer had had to struggle, not for intermediate steps
of reasoning between remote notions, as in a problem of geometry,
but for a clear possession of ideas which were near each other, and
which he had not yet been able to bring into contact, because he had
not yet a sufficiently firm grasp of them. Such terms as Momentum
and Force had been sources of confusion from the time of Aristotle;
and it required considerable steadiness of thought to compare the
forces of bodies at rest and in motion under the obscurity and
vacillation thus produced. {338}

[Note 21\6: _Opere_, iii. 96.]

[Note 22\6: Galileo, _Op._ iii. 104.]

[Note 23\6: Drinkwater, _Life of Galileo_, p. 59.]

The term _Momentum_ had been introduced to express the force of
bodies in motion, before it was known what that effect was. Galileo,
in his _Discorso intorno alle Cose che stanno in su l' Acqua_, says,
that "Momentum is the force, efficacy, or virtue, with which the
motion moves and the body moved resists, depending not upon weight
only, but upon the velocity, inclination, and any other cause of
such virtue." When he arrived at more precision in his views, he
determined, as we have seen, that, in the same body, the Momentum is
_proportional_ to the Velocity; and, hence it was easily seen that
in different bodies it was proportional to the Velocity and Mass
jointly. The principle thus enunciated is capable of very extensive
application, and, among other consequences, leads to a determination
of the results of the mutual Percussion of Bodies. But though
Galileo, like others of his predecessors and contemporaries, had
speculated concerning the problem of Percussion, he did not arrive
at any satisfactory conclusion; and the problem remained for the
mathematicians of the next generation to solve.

We may here notice Descartes and his Laws of Motion, the publication
of which is sometimes spoken of as an important event in the history
of Mechanics. This is saying far too much. The _Principia_ of
Descartes did little for physical science. His assertion of the Laws
of Motion, in their most general shape, was perhaps an improvement
in form; but his Third Law is false in substance. Descartes claimed
several of the discoveries of Galileo and others of his
contemporaries; but we cannot assent to such claims, when we find
that, as we shall see, he did not understand, or would not apply,
the Laws of Motion when he had them before him. If we were to
compare Descartes with Galileo, we might say, that of the mechanical
truths which were easily attainable in the beginning of the
seventeenth century, Galileo took hold of as many, and Descartes of
as few, as was well possible for a man of genius.

[2d Ed.] [The following remarks of M. Libri appear to be just. After
giving an account of the doctrines put forth on the subject of
Astronomy, Mechanics, and other branches of science, by Leonardo da
Vinci, Fracastoro, Maurolycus, Commandinus, Benedetti, he adds
(_Hist. des Sciences Mathématiques en Italie_, t. iii. p. 131):
"This short analysis is sufficient to show that, at the period at
which we are arrived, Aristotle no longer reigned unquestioned in
the Italian Schools. If we had to write the history of philosophy,
we should prove by a multitude of facts that it was the Italians who
overthrew the ancient idol of philosophers. Men go on incessantly
repeating that the {339} struggle was begun by Descartes, and they
proclaim him the legislator of modern philosophers. But when we
examine the philosophical writings of Fracastoro, of Benedetti, of
Cardan, and above all, those of Galileo; when we see on all sides
energetic protests raised against the peripatetic doctrines; we ask,
what there remained for the inventor of vortices to do, in
overturning the natural philosophy of Aristotle? In addition to
this, the memorable labors of the School of Cosenza, of Telesius, of
Giordano Bruno, of Campanella; the writings of Patricius, who was,
besides, a good geometer; of Nizolius, whom Leibnitz esteemed so
highly, and of the other metaphysicians of the same epoch,--prove
that the ancient philosophy had already lost its empire on that side
the Alps, when Descartes threw himself upon the enemy now put to the
rout. The yoke was cast off in Italy, and all Europe had only to
follow the example, without its being necessary to give a new
impulse to real science."

In England, we are accustomed to hear Francis Bacon, rather than
Descartes, spoken of as the first great antagonist of the
Aristotelian schools, and the legislator of modern philosophy. But
it is true, both of one and the other, that the overthrow of the
ancient system had been effectively begun before their time by the
practical discoverers here mentioned, and others who, by experiment
and reasoning, established truths inconsistent with the received
Aristotelian doctrines. Gilbert in England, Kepler in Germany, as
well as Benedetti and Galileo in Italy, gave a powerful impulse to
the cause of real knowledge, before the influence of Bacon and
Descartes had produced any general effect. What Bacon really did was
this;--that by the august image which he presented of a future
Philosophy, the rival of the Aristotelian, and far more powerful and
extensive, he drew to it the affections and hopes of all men of
comprehensive and vigorous minds, as well as of those who attended
to special trains of discovery. He announced a New Method, not
merely a correction of special current errors; he thus converted the
Insurrection into a Revolution, and established a new philosophical
Dynasty. Descartes had, in some degree, the same purpose; and, in
addition to this, he not only proclaimed himself the author of a New
Method, but professed to give a complete system of the results of
the Method. His physical philosophy was put forth as complete and
demonstrative, and thus involved the vices of the ancient dogmatism.
Telesius and Campanella had also grand notions of an entire reform
in the method of philosophizing, as I have noticed in the
_Philosophy of the Inductive Sciences_, Book xii.] {340}




CHAPTER  III.

SEQUEL TO THE EPOCH OF GALILEO.--PERIOD OF VERIFICATION AND
DEDUCTION.


THE evidence on which Galileo rested the truth of the Laws of Motion
which he asserted, was, as we have seen, the simplicity of the laws
themselves, and the agreement of their consequences with facts;
proper allowances being made for disturbing causes. His successors
took up and continued the task of making repeated comparisons of the
theory with practice, till no doubt remained of the exactness of the
fundamental doctrines: they also employed themselves in simplifying,
as much as possible, the mode of stating these doctrines, and in
tracing their consequences in various problems by the aid of
mathematical reasoning. These employments led to the publication of
various Treatises on Falling Bodies, Inclined Planes, Pendulums,
Projectiles, Spouting Fluids, which occupied a great part of the
seventeenth century.

The authors of these treatises may be considered as the School of
Galileo. Several of them were, indeed, his pupils or personal
friends. Castelli was his disciple and astronomical assistant at
Florence, and afterwards his correspondent. Torricelli was at first
a pupil of Castelli, but became the inmate and amanuensis of Galileo
in 1641, and succeeded him in his situation at the court of Florence
on his death, which took place a few months afterwards. Viviani
formed one of his family during the three last years of his life;
and surviving him and his contemporaries (for Viviani lived even
into the eighteenth century), has a manifest pleasure and pride in
calling himself the last of the disciples of Galileo. Gassendi, an
eminent French mathematician and professor, visited him in 1628; and
it shows us the extent of his reputation when we find Milton
referring thus to his travels in Italy:[24\6] "There it was that I
found and visited the famous Galileo, grown old, a prisoner in the
Inquisition, for thinking in astronomy otherwise than the Franciscan
and Dominican licensers thought."

[Note 24\6: _Speech for the Liberty of Unlicensed Printing._]

Besides the above writers, we may mention, as persons who pursued and
illustrated Galileo's doctrines, Borelli, who was professor at
Florence and Pisa; Mersenne, the correspondent of Descartes, who was
{341} professor at Paris; Wallis, who was appointed Savilian professor
at Oxford in 1649, his predecessor being ejected by the parliamentary
commissioners. It is not necessary for us to trace the progress of
purely mathematical inventions, which constitute a great part of the
works of these authors; but a few circumstances may be mentioned.

The question of the proof of the Second Law of Motion was, from the
first, identified with the controversy respecting the truth of the
Copernican System; for this law supplied the true answer to the most
formidable of the objections against the motion of the earth;
namely, that if the earth were moving, bodies which were dropt from
an elevated object would be left behind by the place from which they
fell. This argument was reproduced in various forms by the opponents
of the new doctrine; and the answers to the argument, though they
belong to the history of Astronomy, and form part of the Sequel to
the Epoch of Copernicus, belong more peculiarly to the history of
Mechanics, and are events in the sequel to the Discoveries of
Galileo. So far, indeed, as the mechanical controversy was
concerned, the advocates of the Second Law of Motion appealed, very
triumphantly, to experiment. Gassendi made many experiments on this
subject publicly, of which an account is given in his _Epistolæ tres
de Motu Impresso a Motore Translato_[25\6] It appeared in these
experiments, that bodies let fall downwards, or cast upwards,
forwards, or backwards, from a ship, or chariot, or man, whether at
rest, or in any degree of motion, had always the same motion
relatively to the _motor_. In the application of this principle to
the system of the world, indeed, Gassendi and other philosophers of
his time were greatly hampered; for the deference which religious
scruples required, did not allow them to say that the earth really
moved, but only that the physical reasons against its motion were
invalid. This restriction enabled Riccioli and other writers on the
geocentric side to involve the subject in metaphysical difficulties;
but the conviction of men was not permanently shaken by these, and
the Second Law of Motion was soon assumed as unquestioned.

[Note 25\6: Mont. ii. 199.]

The Laws of the Motion of Falling Bodies, as assigned by Galileo,
were confirmed by the reasonings of Gassendi and Fermat, and the
experiments of Riccioli and Grimaldi; and the effect of resistance
was pointed out by **Mersenne and Dechales. The parabolic motion of
Projectiles was more especially illustrated by experiments on the
jet which spouts from an orifice in a vessel full of fluid. This
mode of experimenting {342} is well adapted to attract notice, since
the curve described, which is transient and invisible in the case of
a single projectile, becomes permanent and visible when we have a
continuous stream. The doctrine of the motions of fluids has always
been zealously cultivated by the Italians. Castelli's treatise,
_Della Misura dell' Acque Corrente_ (1638), is the first work on
this subject, and Montucla with justice calls him "the creator of a
new branch of hydraulics;"[26\6] although he mistakenly supposed the
velocity of efflux to be as the depth of the orifice from the
surface. **Mersenne and Torricelli also pursued this subject, and
after them, many others.

[Note 26\6: Mont. ii. 201.]

Galileo's belief in the near approximation of the curve described by
a cannon-ball or musket-ball to the theoretical parabola, was
somewhat too obsequiously adopted by succeeding practical writers on
artillery. They underrated, as he had done, the effect of the
resistance of the air, which is in effect so great as entirely to
change the form and properties of the curve. Notwithstanding this,
the parabolic theory was employed, as in Anderson's _Art of Gunnery_
(1674); and Blondel, in his _Art de jeter les Bombes_ (1688), not
only calculated Tables on this supposition, but attempted to answer
the objections which had been made respecting the form of the curve
described. It was not till a later period (1740), when Robins made a
series of careful and sagacious experiments on artillery, and when
some of the most eminent mathematicians calculated the curve, taking
into account the resistance, that the Theory of Projectiles could be
said to be verified in fact.

The Third Law of Motion was still in some confusion when Galileo died,
as we have seen. The next great step made in the school of Galileo was
the determination of the Laws of the motions of bodies in their Direct
Impact, so far as this impact affects the motion of translation. The
difficulties of the problem of Percussion arose, in part, from the
heterogeneous nature of Pressure (of a body at rest), and Momentum (of
a body in motion); and, in part, from mixing together the effects of
percussion on the parts of a body, as, for instance, cutting,
bruising, and breaking, with its effect in moving the whole.

The former difficulty had been seen with some clearness by Galileo
himself. In a posthumous addition to his _Mechanical Dialogues_, he
says, "There are two kinds of resistance in a movable body, one
internal, as when we say it is more difficult to lift a weight of a
thousand pounds than a weight of a hundred; another respecting
space, as {343} when we say that it requires more force to throw a
stone one hundred paces than fifty."[27\6] Reasoning upon this
difference, he comes to the conclusion that "the Momentum of
percussion is infinite, since there is no resistance, however great,
which is not overcome by a force of percussion, however
small."[28\6] He further explains this by observing that the
resistance to percussion must occupy some portion of time, although
this portion may be insensible. This correct mode of removing the
apparent incongruity of continuous and instantaneous force, was a
material step in the solution of the problem.

[Note 27\6: _Op._ iii. 210.]

[Note 28\6: iii. 211.]

The Laws of the mutual Impact of bodies were erroneously given by
Descartes in his _Principia_; and appear to have been first
correctly stated by Wren, Wallis, and Huyghens, who about the same
time (1669) sent papers to the Royal Society of London on the
subject. In these solutions, we perceive that men were gradually
coming to apprehend the Third Law of Motion in its most general
sense; namely, that the Momentum (which is proportional to the Mass
of the body and its Velocity jointly) may be taken for the measure
of the effect; so that this Momentum is as much diminished in the
striking body by the resistance it experiences, as it is increased
in the body struck by the Impact. This was sometimes expressed by
saying that "the Quantity of Motion remains unaltered," _Quantity of
Motion_ being used as synonymous with _Momentum_. Newton expressed
it by saying that "Action and Reaction are equal and opposite,"
which is still one of the most familiar modes of expressing the
Third Law of Motion.

In this mode of stating the Law, we see an example of a propensity
which has prevailed very generally among mathematicians; namely, a
disposition to present the fundamental laws of rest and of motion as
if they were equally manifest, and, indeed, identical. The close
analogy and connection which exists between the principles of
equilibrium and of motion, often led men to confound the evidence of
the two; and this confusion introduced an ambiguity in the use of
words, as we have seen in the case of Momentum, Force, and others.
The same may be said of _Action_ and _Reaction_, which have both a
statical and a dynamical signification. And by this means, the most
general statements of the laws of motion are made to coincide with
the most general statical propositions. For instance, Newton deduced
from his principles the conclusion, that by the mutual action of
bodies, the motion of their centre of gravity cannot be affected.
Marriotte, in his _Traité de la_ {344} _Percussion_ (1684), had
asserted this proposition for the case of direct impact. But by the
reasoners of Newton's time, the dynamical proposition, that the
motion of the centre of gravity is not altered by the actual free
motion and impact of bodies, was associated with the statical
proposition, that when bodies are in equilibrium, the centre of
gravity cannot be made to ascend or descend by the _virtual_ motions
of the bodies. This latter is a proposition which was assumed as
self-evident by Torricelli; but which may more philosophically be
proved from elementary statical principles.

This disposition to identify the elementary laws of equilibrium and
of motion, led men to think too slightingly of the ancient solid and
sufficient foundation of Statics, the doctrine of the lever. When
the progress of thought had opened men's minds to a more general
view of the subject, it was considered as a blemish in the science
to found it on the properties of one particular machine. Descartes
says in his Letters, that "it is ridiculous to prove the pulley by
means of the lever." And Varignon was led by similar reflections to
the project of his _Nouvelle Mécanique_, in which the whole of
statics should be founded on the composition of forces. This project
was published in 1687; but the work did not appear till 1725, after
the death of the author. Though the attempt to reduce the
equilibrium of all machines to the composition of forces, is
philosophical and meritorious, the attempt to reduce the composition
of Pressures to the composition of _Motions_, with which Varignon's
work is occupied, was a retrograde step in the subject, so far as
the progress of distinct mechanical ideas was concerned.

Thus, at the period at which we have now arrived, the Principles of
Elementary Mechanics were generally known and accepted; and there
was in the minds of mathematicians a prevalent tendency to reduce
them to the most simple and comprehensive form of which they
admitted. The execution of this simplification and extension, which
we term the generalization of the laws, is so important an event,
that though it forms part of the natural sequel of Galileo, we shall
treat of it in a separate chapter. But we must first bring up the
history of the mechanics of fluids to the corresponding point. {345}




CHAPTER IV.

DISCOVERY OF THE MECHANICAL PRINCIPLES OF FLUIDS.


_Sect._ 1.--_Rediscovery of the Laws of Equilibrium of Fluids._

WE have already said, that the true laws of the equilibrium of
fluids were discovered by Archimedes, and rediscovered by Galileo
and Stevinus; the intermediate time having been occupied by a
vagueness and confusion of thought on physical subjects, which made
it impossible for men to retain such clear views as Archimedes had
disclosed. Stevinus must be considered as the earliest of the
authors of this rediscovery; for his work (_Principles of Statik and
Hydrostatik_) was published in Dutch about 1585; and in this, his
views are perfectly distinct and correct. He restates the doctrines
of Archimedes, and shows that, as a consequence of them, it follows
that the pressure of a fluid on the bottom of a vessel may be much
greater than the weight of the fluid itself: this he proves, by
imagining some of the upper portions of the vessel to be filled with
fixed solid bodies, which take the place of the fluid, and yet do
not alter the pressure on the base. He also shows what will be the
pressure on any portion of a base in an oblique position; and hence,
by certain mathematical artifices which make an approach to the
Infinitesimal Calculus, he finds the whole pressure on the base in
such cases. This mode of treating the subject would take in a large
portion of our elementary Hydrostatics as the science now stands.
Galileo saw the properties of fluids no less clearly, and explained
them very distinctly, in 1612, in his _Discourse on Floating
Bodies_. It had been maintained by the Aristotelians, that _form_
was the cause of bodies floating; and collaterally, that ice was
_condensed_ water; apparently from a confusion of thought between
_rigidity_ and _density_. Galileo asserted, on the contrary, that
ice is _rarefied_ water, as appears by its floating: and in support
of this, he proved, by various experiments, that the floating of
bodies does not depend on their form. The happy genius of Galileo is
the more remarkable in this case, as the controversy was a good deal
perplexed by the mixture of phenomena of another kind, due to what
is usually called _capillary_ or _molecular attraction_. Thus it is
a fact, that a _ball_ {346} of ebony sinks in water, while a _flat
slip_ of the same material lies on the surface; and it required
considerable sagacity to separate such cases from the general rule.
Galileo's opinions were attacked by various writers, as Nozzolini,
Vincenzio di Grazia, Ludovico delle Colombe; and defended by his
pupil Castelli, who published a reply in 1615. These opinions were
generally adopted and diffused; but somewhat later, Pascal pursued
the subject more systematically, and wrote his _Treatise of the
Equilibrium of Fluids_ in 1653; in which he shows that a fluid,
inclosed in a vessel, necessarily presses equally in all directions,
by imagining two _pistons_ or sliding plugs, applied at different
parts, the surface of one being centuple that of the other: it is
clear, as he observes, that the force of one man acting at the first
piston, will balance the force of one hundred men acting at the
other. "And thus," says he, "it appears that a vessel full of water
is a new Principle of Mechanics, and a new Machine which will
multiply force to any degree we choose." Pascal also referred the
equilibrium of fluids to the "principle of virtual velocities,"
which regulates the equilibrium of other machines. This, indeed,
Galileo had done before him. It followed from this doctrine, that
the pressure which is exercised by the lower parts of a fluid arises
from the weight of the upper parts.

In all this there was nothing which was not easily assented to; but
the extension of these doctrines to the air required an additional
effort of mechanical conception. The pressure of the air on all
sides of us, and its weight above us, were two truths which had
never yet been apprehended with any kind of clearness. Seneca,
indeed,[29\6] talks of the "gravity of the air," and of its power of
diffusing itself when condensed, as the causes of wind; but we can
hardly consider such propriety of phraseology in him as more than a
chance; for we see the value of his philosophy by what he
immediately adds: "Do you think that we have forces by which we move
ourselves, and that the air is left without any power of moving?
when even water has a motion of its own, as we see in the growth of
plants." We can hardly attach much value to such a recognition of
the gravity and elasticity of the air.

[Note 29\6: _Quæst. Nat._ v. 5.]

Yet the effects of these causes were so numerous and obvious, that
the Aristotelians had been obliged to invent a principle to account
for them; namely, "Nature's Horror of a Vacuum." To this principle
were referred many familiar phenomena, as suction, breathing, the
{347} action of a pair of bellows, its drawing water if immersed in
water, its refusing to open when the rent is stopped up. The action
of a cupping instrument, in which the air is rarefied by fire; the
fact that water is supported when a full inverted bottle is placed
in a basin; or when a full tube, open below and closed above, is
similarly placed; the running out of the water, in this instance,
when the top is opened; the action of a siphon, of a syringe, of a
pump; the adhesion of two polished plates, and other facts, were all
explained by the _fuga vacui_. Indeed, we must contend that the
principle was a very good one, inasmuch as it brought together all
these facts which are really of the same kind, and referred them to
a common cause. But when urged as an ultimate principle, it was not
only _unphilosophical_, but _imperfect_ and _wrong_. It was
_unphilosophical_, because it introduced the notion of an emotion,
Horror, as an account of physical facts; it was _imperfect_, because
it was at best only a law of phenomena, not pointing out any
physical cause; and it was _wrong_, because it gave an unlimited
extent to the effect. Accordingly, it led to mistakes. Thus
Mersenne, in 1644, speaks of a siphon which shall go over a
mountain, being ignorant then that the effect of such an instrument
was limited to a height of thirty-four feet. A few years later,
however, he had detected this mistake; and in his third volume,
published in 1647, he puts his siphon in his _emendanda_, and speaks
correctly of the weight of air as supporting the mercury in the tube
of Torricelli. It was, indeed, by finding this horror of a vacuum to
have a limit at the height of thirty-four feet, that the true
principle was suggested. It was discovered that when attempts were
made to raise water higher than this. Nature tolerated a vacuum
above the water which rose. In 1643, Torricelli tried to produce
this vacuum at a smaller height, by using, instead of water, the
heavier fluid, quicksilver; an attempt which shows that the true
explanation, the balance of the weight of the water by another
pressure, had already suggested itself. Indeed, this appears from
other evidence. Galileo had already taught that the air has weight;
and Baliani, writing to him in 1630, says,[30\6] "If we were in a
vacuum, the weight of the air above our heads would be felt."
Descartes also appears to have some share in this discovery; for, in
a letter of the date of 1631, he explains the suspension of mercury
in a tube, closed at top, by the pressure of the column of air
reaching to the clouds. {348}

[Note 30\6: Drinkwater's _Galileo_, p. 90.]

Still men's minds wanted confirmation in this view; and they found
such confirmation, when, in 1647, Pascal showed practically, that if
we alter the length of the superincumbent column of air by going to
a high place, we alter the weight which it will support. This
celebrated experiment was made by Pascal himself on a church-steeple
in Paris, the column of mercury in the Torricellian tube being used
to compare the weights of the air; but he wrote to his
brother-in-law, who lived near the high mountain of Puy de Dôme in
Auvergne, to request him to make the experiment there, where the
result would be more decisive. "You see," he says, "that if it
happens that the height of the mercury at the top of the hill be
less than at the bottom (which I have many reasons to believe,
though all those who have thought about it are of a different
opinion), it will follow that the weight and pressure of the air are
the sole cause of this suspension, and not the horror of a vacuum:
since it is very certain that there is more air to weigh on it at
the bottom than at the top; while we cannot say that nature abhors a
vacuum at the foot of a mountain more than on its summit."--M.
Perrier, Pascal's correspondent, made the observation as he had
desired, and found a difference of three inches of mercury, "which,"
he says, "ravished us with admiration and astonishment."

When the least obvious case of the operation of the pressure and
weight of fluids had thus been made out, there were no further
difficulties in the progress of the theory of Hydrostatics. When
mathematicians began to consider more general cases than those of
the action of gravity, there arose differences in the way of stating
the appropriate principles: but none of these differences imply any
different conception of the fundamental nature of fluid equilibrium.


_Sect._ 2.--_Discovery of the Laws of Motion of Fluids._

THE art of conducting water in pipes, and of directing its motion
for various purposes, is very old. When treated systematically, it
has been termed _Hydraulics_: but _Hydrodynamics_ is the general
name of the science of the laws of the motions of fluids, under
those or other circumstances. The Art is as old as the commencement
of civilization: the Science does not ascend higher than the time of
Newton, though attempts on such subjects were made by Galileo and
his scholars.

When a fluid spouts from an orifice in a vessel, Castelli saw that
the velocity of efflux depends on the depth of the orifice below the
{349} surface: but he erroneously judged the velocity to be exactly
proportional to the depth. Torricelli found that the fluid, under
the inevitable causes of defect which occur in the experiment, would
spout nearly to the height of the surface: he therefore inferred,
that the full velocity is that which a body would acquire in falling
through the depth; and that it is consequently proportional to the
square root of the depth.--This, however, he stated only as a result
of experience, or law of phenomena, at the end of his treatise, _De
Motu Naturaliter Accelerato_, printed in 1643.

Newton treated the subject theoretically in the _Principia_ (1687);
but we must allow, as Lagrange says, that this is the least
satisfactory passage of that great work. Newton, having made his
experiments in another manner than Torricelli, namely, by measuring
the quantity of the efflux instead of its velocity, found a result
inconsistent with that of Torricelli. The velocity inferred from the
quantity discharged, was only that due to _half_ the depth of the
fluid.

In the first edition of the _Principia_,[31\6] Newton gave a train
of reasoning by which he theoretically demonstrated his own result,
going upon the principle, that the momentum of the issuing fluid is
equal to the momentum which the column vertically over the orifice
would generate by its gravity. But Torricelli's experiments, which
had given the velocity due to the whole depth, were confirmed on
repetition: how was this discrepancy to be explained?

[Note 31\6: B. ii. Prop. xxxvii.]

Newton explained the discrepancy by observing the contraction which
the jet, or vein of water, undergoes, just after it leaves the
orifice, and which he called the _vena contracta_. At the orifice,
the velocity is that due to half the height; at the _vena contracta_
it is that due to the whole height. The former velocity regulates
the quantity of the discharge; the latter, the path of the jet.

This explanation was an important step in the subject; but it made
Newton's original proof appear very defective, to say the least. In
the second edition of the _Principia_ (1714), Newton attacked the
problem in a manner altogether different from his former
investigation. He there assumed, that when a round vessel, containing
fluid, has a hole in its bottom, the descending fluid may be
conceived to be a conoidal mass, which has its base at the surface of
the fluid, and its narrow end at the orifice. This portion of the
fluid he calls the _cataract_; and supposes that while this part
descends, the surrounding {350} parts remain immovable, as if they
were frozen; in this way he finds a result agreeing with Torricelli's
experiments on the velocity of the efflux.

We must allow that the assumptions by which this result is obtained
are somewhat arbitrary; and those which Newton introduces in
attempting to connect the problem of issuing fluids with that of the
resistance to a body moving in a fluid, are no less so. But even up
to the present time, mathematicians have not been able to reduce
problems concerning the motions of fluids to mathematical principles
and calculations, without introducing some steps of this arbitrary
kind. And one of the uses of experiments on this subject is, to
suggest those hypotheses which may enable us, in the manner most
consonant with the true state of things, to reduce the motions of
fluids to those general laws of mechanics, to which we know they
must be subject.

Hence the science of the Motion of Fluids, unlike all the other
primary departments of Mechanics, is a subject on which we still
need experiments, to point out the fundamental principles. Many such
experiments have been made, with a view either to compare the
results of deduction and observation, or, when this comparison
failed, to obtain purely empirical rules. In this way the resistance
of fluids, and the motion of water in pipes, canals, and rivers, has
been treated. Italy has possessed, from early times, a large body of
such writers. The earlier works of this kind have been collected in
sixteen quarto volumes. Lecchi and Michelotti about 1765, Bidone
more recently, have pursued these inquiries. Bossut, Buat, Hachette,
in France, have labored at the same task, as have Coulomb and Prony,
Girard and Poncelet. Eytelwein's German treatise (_Hydraulik_)
contains an account of what others and himself have done. Many of
these trains of experiments, both in France and Italy, were made at
the expense of governments, and on a very magnificent scale. In
England less was done in this way during the last century, than in
most other countries. The _Philosophical Transactions_, for
instance, scarcely contain a single paper on this subject founded on
experimental investigations.[32\6] Dr. Thomas Young, who was at the
head of his countrymen in so many branches of science, was one of
the first to call back attention to this: and Mr. Rennie and others
have recently made valuable experiments. In many of the questions
now spoken of, the accordance which engineers are able to obtain,
between their calculated and observed results, {351} is very great:
but these calculations are performed by means of empirical formulæ,
which do not connect the facts with their causes, and still leave a
wide space to be traversed, in order to complete the science.

[Note 32\6: Rennie, _Report to Brit. Assoc._]

In the mean time, all the other portions of Mechanics were reduced
to general laws, and analytical processes; and means were found of
including Hydrodynamics, notwithstanding the difficulties which
attend its special problems, in this common improvement of form.
This progress we must relate.

[2d Ed.] [The hydrodynamical problems referred to above are, the
laws of a fluid issuing from a vessel, the laws of the motion of
water in pipes, canals, and rivers, and the laws of the resistance
of fluids. To these may be added, as an hydrodynamical problem
important in theory, in experiment, and in the comparison of the
two, the laws of waves. Newton gave, in the _Principia_, an
explanation of the waves of water (Lib. ii. Prop. 44), which appears
to proceed upon an erroneous view of the nature of the motion of the
fluid: but in his solution of the problem of sound, appeared, for
the first time, a correct view of the propagation of an undulation
in a fluid. The history of this subject, as bearing upon the theory
of sound, is given in Book viii.: but I may here remark, that the
laws of the motion of waves have been pursued experimentally by
various persons, as Bremontier (_Recherches sur le Mouvement des
Ondes_, 1809), Emy (_Du Mouvement des Ondes_, 1831), the Webers
(_Wellenlehre_, 1825); and by Mr. Scott Russell (_Reports of the
British Association_, 1844). The analytical theory has been carried
on by Poisson, Cauchy, and, among ourselves, by Prof. Kelland
(_Edin. Trans._) and Mr. Airy (in the article _Tides_, in the
_Encyclopædia Metropolitana_). And though theory and experiment have
not yet been brought into complete accordance, great progress has
been made in that work, and the remaining chasm between the two is
manifestly due only to the incompleteness of both.]

Perhaps the most remarkable case of fluid motion recently discussed,
is one which Mr. Scott Russell has presented experimentally; and
which, though novel, is easily seen to follow from known principles;
namely, the _Great Solitary Wave_. A wave may be produced, which
shall move along a canal unaccompanied by any other wave: and the
simplicity of this case makes the mathematical conditions and
consequences more simple than they are in most other problems of
Hydrodynamics. {352}




CHAPTER V.

GENERALIZATION OF THE PRINCIPLES OF MECHANICS.


_Sect._ 1.--_Generalization of the Second Law of Motion.--Central
Forces._

THE Second Law of Motion being proved for constant Forces which act
in parallel lines, and the Third Law for the Direct Action of
bodies, it still required great mathematical talent, and some
inductive power, to see clearly the laws which govern the motion of
any number of bodies, acted upon by each other, and by any forces,
anyhow varying in magnitude and direction. This was the task of the
generalization of the laws of motion.

Galileo had convinced himself that the velocity of projection, and
that which gravity alone would produce, are "both maintained,
without being altered, perturbed, or impeded in their mixture." It
is to be observed, however, that the truth of this result depends
upon a particular circumstance, namely, that gravity, at all points,
acts in lines, which, as to sense, are parallel. When we have to
consider cases in which this is not true, as when the force tends to
the centre of a circle, the law of composition cannot be applied in
the same way; and, in this case, mathematicians were met by some
peculiar difficulties.

One of these difficulties arises from the apparent inconsistency of
the statical and dynamical measures of force. When a body moves in a
circle, the force which urges the body to the centre is only a
_tendency_ to motion; for the body does not, in fact, approach to
the centre; and this mere tendency to motion is combined with an
actual motion, which takes place in the circumference. We appear to
have to compare two things which are heterogeneous. Descartes had
noticed this difficulty, but without giving any satisfactory
solution of it.[33\6] If we combine the actual motion to or from the
centre with the traverse motion about the centre, we obtain a result
which is false on mechanical principles. Galileo endeavored in this
way to find the curve described by a body which falls towards the
earth's centre, and is, at the same time, carried {353} round by the
motion of the earth; and obtained an erroneous result. Kepler and
Fermat attempted the same problem, and obtained solutions different
from that of Galileo, but not more correct.

[Note 33\6: _Princip._ P. iii. 59.]

Even Newton, at an early period of his speculations, had an
erroneous opinion respecting this curve, which he imagined to be a
kind of spiral. Hooke animadverted upon this opinion when it was
laid before the Royal Society of London in 1679, and stated, more
truly, that, supposing no resistance, it would be "an eccentric
ellipsoid," that is, a figure resembling an ellipse. But though he
had made out the approximate form of the curve, in some unexplained
way, we have no reason to believe that he possessed any means of
determining the mathematical properties of the curve described in
such a case. The perpetual composition of a central force with the
previous motion of the body, could not be successfully treated
without the consideration of the Doctrine of Limits, or something
equivalent to that doctrine. The first example which we have of the
right solution of such a problem occurs, so far as I know, in the
Theorems of Huyghens concerning Circular Motion, which were
published, without demonstration, at the end of his _Horologium
Oscillatorium_, in 1673. It was there asserted that when equal
bodies describe circles, if the times are equal, the centrifugal
forces will be as the diameters of the circles; if the velocities
are equal, the forces will be reciprocally as the diameters, and so
on. In order to arrive at these propositions, Huyghens must,
virtually at least, have applied the Second Law of Motion to the
limiting elements of the curve, according to the way in which
Newton, a few years later, gave the demonstration of the theorems of
Huyghens in the _Principia_.

The growing persuasion that the motions of the heavenly bodies about
the sun might be explained by the action of central forces, gave a
peculiar interest to these mechanical speculations, at the period
now under review. Indeed, it is not easy to state separately, as our
present object requires us to do, the progress of Mechanics, and the
progress of Astronomy. Yet the distinction which we have to make is,
in its nature, sufficiently marked. It is, in fact, no less marked
than the distinction between speaking logically and speaking truly.
The framers of the science of motion were employed in establishing
those notions, names, and rules, in conformity to which _all_
mechanical _truth must_ be expressed; but _what was the truth_ with
regard to the mechanism of the universe remained to be determined by
other means. Physical Astronomy, at the period of which we speak,
eclipsed and overlaid {354} theoretical Mechanics, as, a little
previously, Dynamics had eclipsed and superseded Statics.

The laws of variable force and of curvilinear motion were not much
pursued, till the invention of Fluxions and of the Differential
Calculus again turned men's minds to these subjects, as easy and
interesting exercises of the powers of these new methods. Newton's
_Principia_, of which the first two Books are purely dynamical, is
the great exception to this assertion; inasmuch as it contains
correct solutions of a great variety of the most general problems of
the science; and indeed is, even yet, one of the most complete
treatises which we possess upon the subject.

We have seen that Kepler, in his attempts to explain the curvilinear
motions of the planets by means of a central force, failed, in
consequence of his belief that a continued transverse action of the
central body was requisite to keep up a continual motion. Galileo
had founded his theory of projectiles on the principle that such an
action was not necessary; yet Borelli, a pupil of Galileo, when, in
1666, he published his theory of the Medicean Stars (the satellites
of Jupiter), did not keep quite clear of the same errors which had
vitiated Kepler's reasonings. In the same way, though Descartes is
sometimes spoken of as the first promulgator of the First Law of
Motion, yet his theory of Vortices must have been mainly suggested
by a want of an entire confidence in that law. When he represented
the planets and satellites as owing their motions to oceans of fluid
diffused through the celestial spaces, and constantly whirling round
the central bodies, he must have felt afraid of trusting the planets
to the operation of the laws of motion in free space. Sounder
physical philosophers, however, began to perceive the real nature of
the question. As early as 1666, we read, in the Journals of the
Royal Society, that "there was read a paper of Mr. Hooke's
explicating the inflexion of a direct motion into a curve by a
supervening attractive principle;" and before the publication of the
_Principia_ in 1687, Huyghens, as we have seen, in Holland, and, in
our own country, Wren, Halley, and Hooke, had made some progress in
the true mechanics of circular motion,[34\6] and had distinctly
contemplated the problem of the motion of a body in an ellipse by a
central force, though they could not solve it. Halley went to
Cambridge in 1684,[35\6] for the express purpose of consulting
Newton upon the subject of the production of the elliptical motion
of the planets by means of a central {355} force, and, on the 10th
of December,[36\6] announced to the Royal Society that he had seen
Mr. Newton's book, _De Motu Corporum_. The feeling that
mathematicians were on the brink of discoveries such as are
contained in this work was so strong, that Dr. Halley was requested
to remind Mr. Newton of his promise of entering them in the Register
of the Society, "for securing the invention to himself till such
time as he can be at leisure to publish it." The manuscript, with
the title _Philosophiæ Naturalis Principia Mathematica_, was
presented to the society (to which it was dedicated) on the 28th of
April, 1686. Dr. Vincent, who presented it, spoke of the novelty and
dignity of the subject; and the president (Sir J. Hoskins) added,
with great truth, "that the method was so much the more to be prized
as it was both invented and perfected at the same time."

[Note 34\6: Newt. _Princip._ Schol. to Prop. iv.]

[Note 35\6: Sir D. Brewster's _Life of Newton_, p. 154.]

[Note 36\6: Id. p. 184.]

The reader will recollect that we are here speaking of the
_Principia_ as a Mechanical Treatise only; we shall afterwards have
to consider it as containing the greatest discoveries of Physical
Astronomy. As a work on Dynamics, its merit is, that it exhibits a
wonderful store of refined and beautiful mathematical artifices,
applied to solve all the most general problems which the subject
offered. The _Principia_ can hardly be said to contain any new
inductive discovery respecting the principles of mechanics; for
though Newton's _Axioms or Laws of Motion_ which stand at the
beginning of the book, are a much clearer and more general statement
of the grounds of Mechanics than had yet appeared, they do not
involve any doctrines which had not been previously stated or taken
for granted by other mathematicians.

The work, however, besides its unrivalled mathematical skill,
employed in tracing out, deductively, the consequences of the laws
of motion, and its great cosmical discoveries, which we shall
hereafter treat of, had great philosophical value in the history of
Dynamics, as exhibiting a clear conception of the new character and
functions of that science. In his Preface, Newton says, "Rational
Mechanics must be the science of the Motions which result from any
Forces, and of the Forces which are required for any Motions,
accurately propounded and demonstrated. For many things induce me to
suspect, that all natural phenomena may depend upon some Forces by
which the particles of bodies are either drawn towards each other,
and cohere, or repel and recede from each other: and these Forces
being hitherto unknown, philosophers have pursued their researches
in vain. And I hope {356} that the principles expounded in this work
will afford some light, either to this mode of philosophizing, or to
some mode which is more true."

Before we pursue this subject further, we must trace the remainder
of the history of the Third Law.


_Sect._ 2.--_Generalization of the Third Law of Motion.--Centre of
Oscillation.--Huyghens._

THE Third Law of Motion, whether expressed according to Newton's
formula (by the equality of Action and Reaction), or in any other of
the ways employed about the same time, easily gave the solution of
mechanical problems in all cases of _direct_ action; that is, when
each body acted directly on others. But there still remained the
problems in which the action is _indirect_;--when bodies, in motion,
act on each other by the intervention of levers, or in any other
way. If a rigid rod, passing through two weights, be made to swing
about its upper point, so as to form a pendulum, each weight will
act and react on the other by means of the rod, considered as a
lever turning about the point of suspension. What, in this case,
will be the effect of this action and reaction? In what time will
the pendulum oscillate by the force of gravity? Where is the point
at which a single weight must be placed to oscillate in the same
time? in other words, where is the _Centre of Oscillation_?

Such was the problem--an example only of the general problem of
indirect action--which mathematicians had to solve. That it was by
no means easy to see in what manner the law of the communication of
motion was to be extended from simpler cases to those where rotatory
motion was produced, is shown by this;--that Newton, in attempting
to solve the mechanical problem of the Precession of the Equinoxes,
fell into a serious error on this very subject. He assumed that,
when a part has to communicate rotatory movement to the whole (as
the protuberant portion of the terrestrial spheroid, attracted by
the sun and moon, communicates a small movement to the whole mass of
the earth), the quantity of the _motion_, "motus," will not be
altered by being communicated. This principle is true, if, by
_motion_, we understand what is called _moment of inertia_, a
quantity in which both the velocity of each particle and its
distance from the axis of rotation are taken into account: but
Newton, in his calculations of its amount, considered the velocity
only; thus making _motion_, in this case, identical with the
_momentum_ which he introduces in treating of the simpler case {357}
of the third law of motion, when the action is direct. This error
was retained even in the later editions of the _Principia_.[37\6]

[Note 37\6: B. iii. Lemma iii. to Prop, xxxix.]

The question of the centre of oscillation had been proposed by
Mersenne somewhat earlier,[38\6] in 1646. And though the problem was
out of the reach of any principles at that time known and
understood, some of the mathematicians of the day had rightly solved
some cases of it, by proceeding as if the question had been to find
the _Centre of Percussion_. The Centre of Percussion is the point
about which the momenta of all the parts of a body balance each
other, when it is in motion about any axis, and is stopped by
striking against an obstacle placed at that centre. Roberval found
this point in some easy cases; Descartes also attempted the problem;
their rival labors led to an angry controversy: and Descartes was,
as in his physical speculations he often was, very presumptuous,
though not more than half right.

[Note 38\6: Mont. ii. 423.]

Huyghens was hardly advanced beyond boyhood when Mersenne first
proposed this problem; and, as he says,[39\6] could see no principle
which even offered an opening to the solution, and had thus been
repelled at the threshold. When, however, he published his
_Horologium Oscillatorium_ in 1673, the fourth part of that work was
on the Centre of Oscillation or Agitation; and the principle which
he then assumed, though not so simple and self-evident as those to
which such problems were afterwards referred, was perfectly correct
and general, and led to exact solutions in all cases. The reader has
already seen repeatedly in the course of this history, complex and
derivative principles presenting themselves to men's minds, before
simple and elementary ones. The "hypothesis" assumed by Huyghens was
this; "that if any weights are put in motion by the force of
gravity, they _cannot_ move so that the centre of gravity of them
all shall rise _higher_ than the place from which it descended."
This being assumed, it is easy to show that the centre of gravity
will, under all circumstances, rise _as high_ as its original
position; and this consideration leads to a determination of the
oscillation of a compound pendulum. We may observe, in the principle
thus selected, a conviction that, in all mechanical action, the
centre of gravity may be taken as the representative of the whole
system. This conviction, as we have seen, may be traced in the
axioms of Archimedes and Stevinus; and Huyghens, when he proceeds
upon it, undertakes to show,[40\6] that he assumes only this, that a
heavy body cannot, of itself, move upwards. {358}

[Note 39\6: _Hor. Osc._ Pref.]

[Note 40\6: _Hor. Osc._ p. 121.]

Clear as Huyghen's principle appeared to himself, it was, after some
time, attacked by the Abbé Catelan, a zealous Cartesian. Catelan
also put forth principles which he conceived were evident, and
deduced from them conclusions contradictory to those of Huyghens.
His principles, now that we know them to be false, appear to us very
gratuitous. They are these; "that in a compound pendulum, the sum of
the velocities of the component weights is equal to the sum of the
velocities which they would have acquired if they had been detached
pendulums;" and "that the time of the vibration of a compound
pendulum is an arithmetic mean between the times of the vibrations
of the weights, moving as detached pendulums." Huyghens easily
showed that these suppositions would make the centre of gravity
ascend to a greater height than that from which it fell; and after
some time, James Bernoulli stept into the arena, and ranged himself
on the side of Huyghens. As the discussion thus proceeded, it began
to be seen that the question really was, in what manner the Third
Law of Motion was to be extended to cases of indirect action;
whether by distributing the action and reaction according to
statical principles, or in some other way. "I propose it to the
consideration of mathematicians," says Bernoulli in 1686, "what law
of the communication of velocity is observed by bodies in motion,
which are sustained at one extremity by a fixed fulcrum, and at the
other by a body also moving, but more slowly. Is the excess of
velocity which must be communicated from the one body to the other
to be distributed in the same proportion in which a load supported
on the lever would be distributed?" He adds, that if this question
be answered in the affirmative, Huyghens will be found to be in
error; but this is a mistake. The principle, that the action and
reaction of bodies thus moving are to be distributed according to
the rules of the lever, is true; but Bernoulli mistook, in
estimating this action and reaction by the _velocity_ acquired at
any moment; instead of taking, as he should have done, the
_increment_ of velocity which gravity tended to impress in the next
instant. This was shown by the Marquis de l'Hôpital; who adds, with
justice, "I conceive that I have thus fully answered the call of
Bernoulli, when he says, I propose it to the consideration of
mathematicians, &c."

We may, from this time, consider as known, but not as fully
established, the principle that "When bodies in motion affect each
other, the action and reaction are distributed according to the laws
of Statics;" although there were still found occasional difficulties
in the {359} generalization and application of the role. James
Bernoulli, in 1703, gave "a General Demonstration of the Centre of
Oscillation, drawn from the nature of the Lever." In this
demonstration[41\6] he takes as a fundamental principle, that bodies
in motion, connected by levers, balance, when the products of their
momenta and the lengths of the levers are equal in opposite
directions. For the proof of this proposition, he refers to Marriotte,
who had asserted it of weights acting by percussion,[42\6] and in
order to prove it, had balanced the effect of a weight on a lever by
the effect of a jet of water, and had confirmed it by other
experiments.[43\6] Moreover, says Bernoulli, there is no one who
denies it. Still, this kind of proof was hardly satisfactory or
elementary enough. John Bernoulli took up the subject after the death
of his brother James, which happened in 1705. The former published in
1714 his _Meditatio de Naturâ Centri Oscillationis_. In this memoir,
he assumes, as his brother had done, that the effects of forces on a
lever in motion are distributed according to the common rules of the
lever.[44\6] The principal generalization which he introduced was,
that he considered gravity as a force soliciting to motion, which
might have different intensities in different bodies. At the same
time, Brook Taylor in England solved the problem, upon the same
principles as Bernoulli; and the question of priority on this subject
was one point in the angry intercourse which, about this time, became
common between the English mathematicians and those of the Continent.
Hermann also, in his _Phoronomia_, published in 1716, gave a proof
which, as he informs us, he had devised before he saw John
Bernoulli's. This proof is founded on the statical equivalence of the
"_solicitations of gravity_" and the "_vicarious solicitations_" which
correspond to the actual motion of each part; or, as it has been
expressed by more modern writers, the equilibrium of the _impressed_
and _effective forces_.

[Note 41\6: _Op._ ii. 930.]

[Note 42\6: _Choq. des Corps_, p. 296.]

[Note 43\6: Ib. Prop. xi.]

[Note 44\6: P. 172.]

It was shown by John Bernoulli and Hermann, and was indeed easily
proved, that the proposition assumed by Huyghens as the foundation
of his solution, was, in fact, a consequence of the elementary
principles which belong to this branch of mechanics. But this
assumption of Huyghens was an example of a more general proposition,
which by some mathematicians at this time had been put forward as an
original and elementary law; and as a principle which ought to
supersede the usual measure of the forces of bodies in motion; this
principle they called "_the Conservation of Vis Viva_." The attempt
to {360} make this change was the commencement of one of the most
obstinate and curious of the controversies which form part of the
history of mechanical science. The celebrated Leibnitz was the
author of the new opinion. In 1686, he published, in the Leipsic
Acts, "A short Demonstration of a memorable Error of Descartes and
others, concerning the natural law by which they think that God
always preserves the same quantity of motion; in which they pervert
mechanics." The principle that the same quantity of motion, and
therefore of moving force, is always preserved in the world, follows
from the equality of action and reaction; though Descartes had,
after his fashion, given a theological reason for it; Leibnitz
allowed that the quantity of moving force remains always the same,
but denied that this force is measured by the quantity of motion or
momentum. He maintained that the same force is requisite to raise a
weight of one pound through four feet, and a weight of four pounds
through one foot, though the momenta in this case are as one to two.
This was answered by the Abbé de Conti; who truly observed, that
allowing the effects in the two cases to be equal, this did not
prove the forces to be equal; since the effect, in the first case,
was produced in a double time, and therefore it was quite consistent
to suppose the force only half as great. Leibnitz, however,
persisted in his innovation; and in 1695 laid down the distinction
between _vires mortuæ_, or pressures, and _vires vivæ_, the name he
gave to his own measure of force. He kept up a correspondence with
John Bernoulli, whom he converted to his peculiar opinions on this
subject; or rather, as Bernoulli says,[45\6] made him think for
himself, which ended in his proving directly that which Leibnitz had
defended by indirect reasons. Among other arguments, he had
pretended to show (what is certainly not true), that if the common
measure of forces be adhered to, a perpetual motion would be
possible. It is easy to collect many cases which admit of being very
simply and conveniently reasoned upon by means of the _vis viva_,
that is, by taking the force to be proportional to the _square_ of
the velocity, and not to the velocity itself. Thus, in order to give
the arrow _twice_ the velocity, the bow must be _four_ times as
strong; and in all cases in which no account is taken of the time of
producing the effect, we may conveniently use similar methods.

[Note 45\6: _Op._ iii. 40.]

But it was not till a later period that the question excited any
general notice. The Academy of Sciences of Paris in 1724 proposed
{361} as a subject for their prize dissertation the laws of the
impact of bodies. Bernoulli, as a competitor, wrote a treatise, upon
Leibnitzian principles, which, though not honored with the prize,
was printed by the Academy with commendation.[46\6] The opinions
which he here defended and illustrated were adopted by several
mathematicians; the controversy extended from the mathematical to
the literary world, at that time more attentive than usual to
mathematical disputes, in consequence of the great struggle then
going on between the Cartesian and the Newtonian system. It was,
however, obvious that by this time the interest of the question, so
far as the progress of Dynamics was concerned, was at an end; for
the combatants all agreed as to the results in each particular case.
The Laws of Motion were now established; and the question was, by
means of what definitions and abstractions could they be best
expressed;--a metaphysical, not a physical discussion, and therefore
one in which "the paper philosophers," as Galileo called them, could
bear a part. In the first volume of the _Transactions of the Academy
of St. Petersburg_, published in 1728, there are three Leibnitzian
memoirs by Hermann, Bullfinger, and Wolff. In England, Clarke was an
angry assailant of the German opinion, which S'Gravesande
maintained. In France, Mairan attacked the _vis viva_ in 1728; "with
strong and victorious reasons," as the Marquise du Chatelet
declared, in the first edition of her _Treatise on Fire_.[47\6] But
shortly after this praise was published, the Chateau de Cirey, where
the Marquise usually lived, became a school of Leibnitzian opinions,
and the resort of the principal partisans of the _vis viva_. "Soon,"
observes Mairan, "their language was changed; the _vis viva_ was
enthroned by the side of the _monads_." The Marquise tried to
retract or explain away her praises; she urged arguments on the
other side. Still the question was not decided; even her friend
Voltaire was not converted. In 1741 he read a memoir _On the Measure
and Nature of Moving Forces_, in which he maintained the old
opinion. Finally, D'Alembert in 1743 declared it to be, as it truly
was, a mere question of words; and by the turn which Dynamics then
took, it ceased to be of any possible interest or importance to
mathematicians.

[Note 46\6: _Discours sur les Loix de la Communication du Mouvement_.]

[Note 47\6: Mont. iii. 640.]

The representation of the laws of motion and of the reasonings
depending on them, in the most general form, by means of analytical
language, cannot be said to have been fully achieved till the time of
D'Alembert; but as we have already seen, the discovery of these laws
{362} had taken place somewhat earlier; and that law which is more
particularly expressed in D'Alembert's Principle (_the equality of the
action gained and lost_) was, it has been seen, rather led to by the
general current of the reasoning of mathematicians about the end of
the seventeenth century than discovered by any one. Huyghens,
Marriotte, the two Bernoulli's, L'Hôpital, Taylor, and Hermann, have
each of them their name in the history of this advance; but we cannot
ascribe to any of them any great real inductive sagacity shown in what
they thus contributed, except to Huyghens, who first seized the
principle in such a form as to find the centre of oscillation by means
of it. Indeed, in the steps taken by the others, language itself had
almost made the generalization for them at the time when they wrote;
and it required no small degree of acuteness and care to distinguish
the old cases, in which the law had already been applied, from the new
cases, in which they had to apply it.




CHAPTER VI.

SEQUEL TO THE GENERALIZATION OF THE PRINCIPLES OF MECHANICS.--PERIOD
OF MATHEMATICAL DEDUCTION.--ANALYTICAL MECHANICS.


WE have now finished the history of the discovery of Mechanical
Principles, strictly so called. The three Laws of Motion,
generalized in the manner we have described, contain the materials
of the whole structure of Mechanics; and in the remaining progress
of the science, we are led to no new truth which was not implicitly
involved in those previously known. It may be thought, therefore,
that the narrative of this progress is of comparatively small
interest. Nor do we maintain that the application and development of
principles is a matter of so much importance to the philosophy of
science, as the advance towards and to them. Still, there are many
circumstances in the latter stages of the progress of the science of
Mechanics, which well deserve notice, and make a rapid survey of
that part of its history indispensable to our purpose.

The Laws of Motion are expressed in terms of Space and Number; the
development of the consequences of these laws must, therefore, be
performed by means of the reasonings of mathematics; and the science
{363} of Mechanics may assume the various aspects which belong to the
different modes of dealing with mathematical quantities. Mechanics,
like pure mathematics, may be geometrical or may be analytical; that
is, it may treat space either by a direct consideration of its
properties, or by a symbolical representation of them: Mechanics, like
pure mathematics, may proceed from special cases, to problems and
methods of extreme generality;--may summon to its aid the curious and
refined relations of symmetry, by which general and complex conditions
are simplified;--may become more powerful by the discovery of more
powerful analytical artifices;--may even have the generality of its
principles further expanded, inasmuch as symbols are a more general
language than words. We shall very briefly notice a series of
modifications of this kind.

1. _Geometrical Mechanics. Newton, &c._--The first great
systematical Treatise on Mechanics, in the most general sense, is
the two first Books of the _Principia_ of Newton. In this work, the
method employed is predominantly geometrical: not only space is not
represented symbolically, or by reference to number; but numbers,
as, for instance, those which measure time and force, are
represented by spaces; and the laws of their changes are indicated
by the properties of curve lines. It is well known that Newton
employed, by preference, methods of this kind in the exposition of
his theorems, even where he had made the discovery of them by
analytical calculations. The intuitions of space appeared to him, as
they have appeared to many of his followers, to be a more clear and
satisfactory road to knowledge, than the operations of symbolical
language. Hermann, whose _Phoronomia_ was the next great work on
this subject, pursued a like course; employing curves, which he
calls "the scale of velocities," "of forces," &c. Methods nearly
similar were employed by the two first Bernoullis, and other
mathematicians of that period; and were, indeed, so long familiar,
that the influence of them may still be traced in some of the terms
which are used on such subjects; as, for instance, when we talk of
"reducing a problem to quadratures," that is, to the finding the
area of the curves employed in these methods.

2. _Analytical Mechanics. Euler._--As analysis was more cultivated,
it gained a predominancy over geometry; being found to be a far more
powerful instrument for obtaining results; and possessing a beauty
and an evidence, which, though different from those of geometry, had
great attractions for minds to which they became familiar. The
person who did most to give to analysis the generality and  {364}
symmetry which are now its pride, was also the person who made
Mechanics analytical; I mean Euler. He began his execution of this
task in various memoirs which appeared in the _Transactions of the
Academy of Sciences at St. Petersburg_, commencing with its earliest
volumes; and in 1736, he published there his _Mechanics, or the
Science of Motion analytically expounded; in the way of a Supplement
to the Transactions of the Imperial Academy of Sciences_. In the
preface to this work, he says, that though the solutions of problems
by Newton and Hermann were quite satisfactory, yet he found that he
had a difficulty in applying them to new problems, differing little
from theirs; and that, therefore, he thought it would be useful to
extract an analysis out of their synthesis.

3. _Mechanical Problems._--In reality, however, Euler has done much
more than merely give analytical methods, which may be applied to
mechanical problems: he has himself applied such methods to an
immense number of cases. His transcendent mathematical powers, his
long and studious life, and the interest with which he pursued the
subject, led him to solve an almost inconceivable number and variety
of mechanical problems. Such problems suggested themselves to him on
all occasions. One of his memoirs begins, by stating that, happening
to think of the line of Virgil,
  Anchora de prorà jacitur stant litore puppes;
  The anchor drops, the rushing keel is staid;
he could not help inquiring what would be the nature of the ship's
motion under the circumstances here described. And in the last few
days of his life, after his mortal illness had begun, having seen in
the newspapers some statements respecting balloons, he proceeded to
calculate their motions; and performed a difficult integration, in
which this undertaking engaged him. His Memoirs occupy a very large
portion of the _Petropolitan Transactions_ during his life, from 1728
to 1783; and he declared that he should leave papers which might
enrich the publications of the Academy of Petersburg for twenty years
after his death;--a promise which has been more than fulfilled; for,
up to 1818, the volumes usually contain several Memoirs of his. He and
his contemporaries may be said to have exhausted the subject; for
there are few mechanical problems which have been since treated, which
they have not in some manner touched upon.

I do not dwell upon the details of such problems; for the next great
step in Analytical Mechanics, the publication of D'Alembert's {365}
Principle in 1743, in a great degree superseded their interest. The
Transactions of the Academies of Paris and Berlin, as well as St.
Petersburg, are filled, up to this time, with various questions of
this kind. They require, for the most part, the determination of the
motions of several bodies, with or without weight, which pull or
push each other by means of threads, or levers, to which they are
fastened, or along which they can slide; and which, having a certain
impulse given them at first, are then left to themselves, or are
compelled to move in given lines and surfaces. The postulate of
Huyghens, respecting the motion of the centre of gravity, was
generally one of the principles of the solution; but other
principles were always needed in addition to this; and it required
the exercise of ingenuity and skill to detect the most suitable in
each case. Such problems were, for some time, a sort of trial of
strength among mathematicians: the principle of D'Alembert put an
end to this kind of challenges, by supplying a direct and general
method of resolving, or at least of throwing into equations, any
imaginable problem. The mechanical difficulties were in this way
reduced to difficulties of pure mathematics.

4. _D'Alembert's Principle._--D'Alembert's Principle is only the
expression, in the most general form, of the principle upon which
John Bernoulli, Hermann, and others, had solved the problem of the
centre of oscillation. It was thus stated, "The motion _impressed_
on each particle of any system by the forces which act upon it, may
be resolved into two, the _effective_ motion, and the motion gained
or _lost_: the effective motions will be the real motions of the
parts, and the motions gained and lost will be such as would keep
the system at rest." The distinction of _statics_, the doctrine of
equilibrium, and _dynamics_, the doctrine of motion, was, as we have
seen, fundamental; and the difference of difficulty and complexity
in the two subjects was well understood, and generally recognized by
mathematicians. D'Alembert's principle reduces every dynamical
question to a statical one; and hence, by means of the conditions
which connect the possible motions of the system, we can determine
what the actual motions must be. The difficulty of determining the
laws of equilibrium, in the application of this principle in complex
cases is, however, often as great as if we apply more simple and
direct considerations.

5. _Motion in Resisting Media. Ballistics._--We shall notice more
particularly the history of some of the problems of mechanics.
Though John Bernoulli always spoke with admiration of Newton's
_Principia_, and of its author, he appears to have been well
disposed to point out {366} real or imagined blemishes in the work.
Against the validity of Newton's determination of the path described
by a body projected in any part of the solar system, Bernoulli urges
a cavil which it is difficult to conceive that a mathematician, such
as he was, could seriously believe to be well founded. On Newton's
determination of the path of a body in a resisting medium, his
criticism is more just. He pointed out a material error in this
solution: this correction came to Newton's knowledge in London, in
October, 1712, when the impression of the second edition of the
Principia was just drawing to a close, under the care of Cotes at
Cambridge; and Newton immediately cancelled the leaf and corrected
the error.[48\6]

[Note 48\6: MS. Correspondence in Trin. Coll. Library.]

This problem of the motion of a body in a resisting medium, led to
another collision between the English and the German mathematicians.
The proposition to which we have referred, gave only an indirect
view of the nature of the curve described by a projectile in the
air; and it is probable that Newton, when he wrote the _Principia_,
did not see his way to any direct and complete solution of this
problem. At a later period, in 1718, when the quarrel had waxed hot
between the admirers of Newton and Leibnitz, Keill, who had come
forward as a champion on the English side, proposed this problem to
the foreigners as a challenge. Keill probably imagined that what
Newton had not discovered, no one of his time would be able to
discover. But the sedulous cultivation of analysis by the Germans
had given them mathematical powers beyond the expectations of the
English; who, whatever might be their talents, had made little
advance in the effective use of general methods; and for a long
period seemed to be fascinated to the spot, in their admiration of
Newton's excellence. Bernoulli speedily solved the problem; and
reasonably enough, according to the law of honor of such challenges,
called upon the challenger to produce his solution. Keill was unable
to do this; and after some attempts at procrastination, was driven
to very paltry evasions. Bernoulli then published his solution, with
very just expressions of scorn towards his antagonist. And this may,
perhaps, be considered as the first material addition which was made
to the _Principia_ by subsequent writers.

6. _Constellation of Mathematicians._--We pass with admiration along
the great series of mathematicians, by whom the science of
theoretical mechanics has been cultivated, from the time of Newton
to our own. There is no group of men of science whose fame is {367}
higher or brighter. The great discoveries of Copernicus, Galileo,
Newton, had fixed all eyes on those portions of human knowledge on
which their successors employed their labors. The certainty
belonging to this line of speculation seemed to elevate
mathematicians above the students of other subjects; and the beauty
of mathematical relations, and the subtlety of intellect which may
be shown in dealing with them, were fitted to win unbounded
applause. The successors of Newton and the Bernoullis, as Euler,
Clairaut, D'Alembert, Lagrange, Laplace, not to introduce living
names, have been some of the most remarkable men of talent which the
world has seen. That their talent is, for the most part, of a
different kind from that by which the laws of nature were
discovered, I shall have occasion to explain elsewhere; for the
present, I must endeavor to arrange the principal achievements of
those whom I have mentioned.

The series of persons is connected by social relations. Euler was
the pupil of the first generation of Bernoullis, and the intimate
friend of the second generation; and all these extraordinary men, as
well as Hermann, were of the city of Basil, in that age a spot
fertile of great mathematicians to an unparalleled degree. In 1740,
Clairaut and Maupertuis visited John Bernoulli, at that time the
Nestor of mathematicians, who died, full of age and honors, in 1748.
Euler, several of the Bernoullis, Maupertuis, Lagrange, among other
mathematicians of smaller note, were called into the north by
Catharine of Russia and Frederic of Prussia, to inspire and instruct
academies which the brilliant fame then attached to science, had
induced those monarchs to establish. The prizes proposed by these
societies, and by the French Academy of Sciences, gave occasion to
many of the most valuable mathematical works of the century.

7. _The Problem of Three Bodies._--In 1747, Clairaut and D'Alembert
sent, on the same day, to this body, their solutions of the celebrated
"Problem of Three Bodies," which, from that time, became the great
object of attention of mathematicians;--the bow in which each tried
his strength, and endeavored to shoot further than his predecessors.

This problem was, in fact, the astronomical question of the effect
produced by the attraction of the sun, in disturbing the motions of
the moon about the earth; or by the attraction of one planet,
disturbing the motion of another planet about the sun; but being
expressed generally, as referring to one body which disturbs any two
others, it became a mechanical problem, and the history of it
belongs to the present subject. {368}

One consequence of the synthetical form adopted by Newton in the
_Principia_, was, that his successors had the problem of the solar
system to begin entirely anew. Those who would not do this, made no
progress, as was long the case with the English. Clairaut says, that
he tried for a long time to make some use of Newton's labors; but
that, at last, he resolved to take up the subject in an independent
manner. This, accordingly, he did, using analysis throughout, and
following methods not much different from those still employed. We
do not now speak of the comparison of this theory with observation,
except to remark, that both by the agreements and by the
discrepancies of this comparison, Clairaut and other writers were
perpetually driven on to carry forwards the calculation to a greater
and greater degree of accuracy.

One of the most important of the cases in which this happened, was
that of the movement of the Apogee of the Moon; and in this case, a
mode of approximating to the truth, which had been depended on as
nearly exact, was, after having caused great perplexity, found by
Clairaut and Euler to give only half the truth. This same Problem of
Three Bodies was the occasion of a memoir of Clairaut, which gained
the prize of the Academy of St. Petersburg in 1751; and, finally, of
his _Théorie de la Lune_, published in 1765. D'Alembert labored at
the same time on the same problem; and the value of their methods,
and the merit of the inventors, unhappily became a subject of
controversy between those two great mathematicians. Euler also, in
1753, published a _Theory of the Moon_, which was, perhaps, more
useful than either of the others, since it was afterwards the basis
of Mayer's method, and of his Tables. It is difficult to give the
general reader any distinct notion of these solutions. We may
observe, that the quantities which determine the moon's position,
are to be determined by means of certain algebraical equations,
which express the mechanical conditions of the motion. The
operation, by which the result is to be obtained, involves the
process of integration; which, in this instance, cannot be performed
in an immediate and definite manner; since the quantities thus to be
operated on depend upon the moon's position, and thus require us to
know the very thing which we have to determine by the operation. The
result must be got at, therefore, by successive approximations: we
must first find a quantity near the truth; and then, by the help of
this, one nearer still; and so on; and, in this manner, the moon's
place will be given by a converging series of terms. The form of
these terms depends upon the relations of position between the sun
{369} and moon, their apogees, the moon's nodes, and other
quantities; and by the variety of combinations of which these admit,
the terms become very numerous and complex. The magnitude of the
terms depends also upon various circumstances; as the relative force
of the sun and earth, the relative times of the solar and lunar
revolutions, the eccentricities and inclinations of the two orbits.
These are combined so as to give terms of different orders of
magnitudes; and it depends upon the skill and perseverance of the
mathematician how far he will continue this series of terms. For
there is no limit to their number: and though the methods of which
we have spoken do theoretically enable us to calculate as many terms
as we please, the labor and the complexity of the operations are so
serious that common calculators are stopped by them. None but very
great mathematicians have been able to walk safely any considerable
distance into this avenue,--so rapidly does it darken as we proceed.
And even the possibility of doing what has been done, depends upon
what we may call accidental circumstances; the smallness of the
inclinations and eccentricities of the system, and the like. "If
nature had not favored us in this way," Lagrange used to say, "there
would have been an end of the geometers in this problem." The
expected return of the comet of 1682 in 1759, gave a new interest to
the problem, and Clairaut proceeded to calculate the case which was
thus suggested. When this was treated by the methods which had
succeeded for the moon, it offered no prospect of success, in
consequence of the absence of the favorable circumstances just
referred to, and, accordingly, Clairaut, after obtaining the six
equations to which he reduces the solution,[49\6] adds, "Integrate
them who can" (Intègre maintenant qui pourra). New methods of
approximation were devised for this case.

[Note 49\6: _Journal des Sçavans_, Aug. 1759.]

The problem of three bodies was not prosecuted in consequence of its
analytical beauty, or its intrinsic attraction; but its great
difficulties were thus resolutely combated from necessity; because
in no other way could the theory of universal gravitation be known
to be true or made to be useful. The construction of _Tables of the
Moon_, an object which offered a large pecuniary reward, as well as
mathematical glory, to the successful adventurer, was the main
purpose of these labors.

The _Theory of the Planets_ presented the Problem of Three Bodies in
a new form, and involved in peculiar difficulties; for the {370}
approximations which succeed in the Lunar theory fail here.
Artifices somewhat modified are required to overcome the
difficulties of this case.

Euler had investigated, in particular, the motions of Jupiter and
Saturn, in which there was a secular acceleration and retardation,
known by observation, but not easily explicable by theory. Euler's
memoirs, which gained the prize of the French Academy, in 1748 and
1752, contained much beautiful analysis; and Lagrange published also
a theory of Jupiter and Saturn, in which he obtained results
different from those of Euler. Laplace, in 1787, showed that this
inequality arose from the circumstance that two of Saturn's years
are very nearly equal to five of Jupiter's.

The problems relating to Jupiter's _Satellites_, were found to be
even more complex than those which refer to the planets: for it was
necessary to consider each satellite as disturbed by the other three
at once; and thus there occurred the Problem of _Five_ Bodies. This
problem was resolved by Lagrange.[50\6]

[Note 50\6: Bailly, _Ast. Mod._ iii. 178.]

Again, the newly-discovered _small Planets_, Juno, Ceres, Vesta,
Pallas, whose orbits almost coincide with each other, and are more
inclined and more eccentric than those of the ancient planets, give
rise, by their perturbations, to new forms of the problem, and
require new artifices.

In the course of these researches respecting Jupiter, Lagrange and
Laplace were led to consider particularly the _secular Inequalities_
of the solar system; that is, those inequalities in which the duration
of the cycle of change embraces very many revolutions of the bodies
themselves. Euler in 1749 and 1755, and Lagrange[51\6] in 1766, had
introduced the method of the _Variation of the Elements_ of the orbit;
which consists in tracing the effect of the perturbing forces, not as
directly altering the place of the planet, but as producing a change
from one instant to another, in the dimensions and position of the
Elliptical orbit which the planet describes.[52\6] Taking this view,
he {371} determines the secular changes of each of the _elements_ or
determining quantities of the orbit. In 1773, Laplace also attacked
this subject of secular changes, and obtained expressions for them. On
this occasion, he proved the celebrated proposition that, "the mean
motions of the planets are invariable:" that is, that there is, in the
revolutions of the system, no progressive change which is not finally
stopped and reversed; no increase, which is not, after some period,
changed into decrease; no retardation which is not at last succeeded
by acceleration; although, in some cases, millions of years may elapse
before the system reaches the turning-point. Thomas Simpson noticed
the same consequence of the laws of universal attraction. In 1774 and
1776, Lagrange[53\6] still labored at the secular equations; extending
his researches to the nodes and inclinations; and showed that the
invariability of the mean motions of the planets, which Laplace had
proved, neglecting the fourth powers of the eccentricities and
inclinations of the orbits,[54\6] was true, however far the
approximation was carried, so long as the squares of the disturbing
masses were neglected. He afterwards improved his methods;[55\6] and,
in 1783, he endeavored to extend the calculation of the changes of the
elements to the periodical equations, as well as the secular.

[Note 51\6: Gautier, _Prob. de Trois Corps_, p. 155.]

[Note 52\6: In the first edition of this History, I had ascribed to
Lagrange the invention of the Method of Variation of Elements in the
theory of Perturbations. But justice to Euler requires that we should
assign this distinction to him; at least, next to Newton, whose mode
of representing the paths of bodies by means of a _Revolving Orbit_,
in the Ninth Section of the _Principia_, may be considered as an
anticipation of the method of variation of elements. In the fifth
volume of the _Mécanique Céleste_, livre xv. p. 305, is an abstract of
Euler's paper of 1749; where Laplace adds, "C'est le premier essai de
la méthode de la variation des constantes arbitraires." And in page
310 is an abstract of the paper of 1756: and speaking of the method,
Laplace says, "It consists in regarding the elements of the elliptical
motion as variable in virtue of the perturbing forces. Those elements
are, 1, the axis major; 2, the epoch of the body being at the apse; 3,
the eccentricity; 4, the movement of the apse; 5, the inclination; 6,
the longitude of the node;" and he then proceeds to show how Euler did
this. It is possible that Lagrange knew nothing of Euler's paper. See
_Méc. Cél._ vol. v. p. 312. But Euler's conception and treatment of
the method are complete, so that he must be looked upon as the author
of it.]

[Note 53\6: Gautier, p. 104.]

[Note 54\6: Ib. p. 184.]

[Note 55\6: Ib. p. 196.]

8. _Mécanique Céleste_, _&c._--Laplace also resumed the
consideration of the secular changes; and, finally, undertook his
vast work, the _Mécanique Céleste_, which he intended to contain a
complete view of the existing state of this splendid department of
science. We may see, in the exultation which the author obviously
feels at the thought of erecting this monument of his age, the
enthusiasm which had been excited by the splendid course of
mathematical successes of which I have given a sketch. The two first
volumes of this great work appeared in 1799. The third and fourth
volumes were published in 1802 and 1805 respectively. Since its
publication, little has been added to the solution of the great
problems of which it treats. In 1808, Laplace presented to the
French Bureau des Longitudes, a Supplement to the _Mécanique
Céleste_; the object of which was to improve still further {372} the
mode of obtaining the secular variations of the elements. Poisson
and Lagrange proved the invariability of the major axes of the
orbits, as far as the second order of the perturbing forces. Various
other authors have since labored at this subject. Burckhardt, in
1808, extended the perturbing function as far as the sixth order of
the eccentricities. Gauss, Hansen, and Bessel, Ivory, MM. Lubbock,
Plana, Pontécoulant, and Airy, have, at different periods up to the
present time, either extended or illustrated some particular part of
the theory, or applied it to special cases; as in the instance of
Professor Airy's calculation of an inequality of Venus and the
earth, of which the period is 240 years. The approximation of the
Moon's motions has been pushed to an almost incredible extent by M.
Damoiseau, and, finally, Plana has once more attempted to present,
in a single work (three thick quarto volumes), all that has hitherto
been executed with regard to the theory of the Moon.

I give only the leading points of the progress of analytical
dynamics. Hence I have not spoken in detail of the theory of the
Satellites of Jupiter, a subject on which Lagrange gained a prize
for a Memoir, in 1766, and in which Laplace discovered some most
curious properties in 1784. Still less have I referred to the purely
speculative question of _Tautochronous Curves_ in a resisting
medium, though it was a subject of the labors of Bernoulli, Euler,
Fontaine, D'Alembert, Lagrange, and Laplace. The reader will rightly
suppose that many other curious investigations are passed over in
utter silence.

[2d Ed.] [Although the analytical calculations of the great
mathematicians of the last century had determined, in a
demonstrative manner, a vast series of inequalities to which the
motions of the sun, moon, and planets were subject in virtue of
their mutual attraction, there were still unsatisfactory points in
the solutions thus given of the great mechanical problems suggested
by the System of the Universe. One of these points was the want of
any evident mechanical significance in the successive members of
these series. Lindenau relates that Lagrange, near the end of his
life, expressed his sorrow that the methods of approximation
employed in Physical Astronomy rested on arbitrary processes, and
not on any insight into the results of mechanical action. But
something was subsequently done to remove the ground of this
complaint. In 1818, Gauss pointed out that secular equations may be
conceived to result from the disturbing body being distributed along
its orbit so as to form a ring, and thus made the result conceivable
more distinctly than as a mere result of calculation. And it appears
{373} to me that Professor Airy's treatise entitled _Gravitation_,
published at Cambridge in 1834, is of great value in supplying
similar modes of conception with regard to the mechanical origin of
many of the principal inequalities of the solar system.

Bessel in 1824, and Hansen in 1828, published works which are
considered as belonging, along with those of Gauss, to a new era in
physical astronomy.[56\6] Gauss's _Theoria Motuum Corporum
Celestium_, which had Lalande's medal assigned to it by the French
Institute, had already (1810) resolved all problems concerning the
determination of the place of a planet or comet in its orbit in
function of the elements. The value of Hansen's labors respecting
the Perturbations of the Planets was recognized by the Astronomical
Society of London, which awarded to them its gold medal.

[Note 56\6: _Abhand. der Akad. d. Wissensch. zu Berlin_. 1824; and
_Disquisitiones circa Theoriam Perturbationum_. See Jahn. _Gesch.
der Astron._ p. 84.]

The investigations of M. Damoiseau, and of MM. Plana and Carlini, on
the Problem of the Lunar Theory, followed nearly the same course as
those of their predecessors. In these, as in the _Mécanique Céleste_
and in preceding works on the same subject, the Moon's co-ordinates
(time, radius vector, and latitude) were expressed in function of
her true longitude. The integrations were effected in series, and
then by reversion of the series, the longitude was expressed in
function of the time; and then in the same manner the other two
co-ordinates. But Sir John Lubbock and M. Pontécoulant have made the
_mean_ longitude of the moon, that is, the time, the independent
variable, and have expressed the moon's co-ordinates in terms of
sines and cosines of angles increasing proportionally to the time.
And this method has been adopted by M. Poisson (_Mem. Inst._ xiii.
1835, p. 212). M. Damoiseau, like Laplace and Clairaut, had deduced
the successive coefficients of the lunar inequalities by numerical
equations. But M. Plana expresses explicitly each coefficient in
general terms of the letters expressing the constants of the
problem, arranging them according to the order of the quantities,
and substituting numbers at the end of the operation only. By
attending to this arrangement, MM. Lubbock and Pontécoulant have
verified or corrected a large portion of the terms contained in the
investigations of MM. Damoiseau and Plana. Sir John Lubbock has
calculated the polar co-ordinates of the Moon directly; M. Poisson,
on the other hand, has obtained the variable elliptical elements; M.
Pontécoulant conceives that the method of variation or arbitrary
{374} constants may most conveniently be reserved for secular
inequalities and inequalities of long periods.

MM. Lubbock and Pontécoulant have made the mode of treating the
Lunar Theory and the Planetary Theory agree with each other, instead
of following two different paths in the calculation of the two
problems, which had previously been done.

Prof. Hansen, also, in his _Fundamenta Nova Investigationis Orbitæ
veræ quam Luna perlustrat_ (_Gothæ_, 1838), gives a general method,
including the Lunar Theory and the Planetary Theory as two special
cases. To this is annexed a solution of the _Problem of Four Bodies_.

I am here speaking of the Lunar and Planetary Theories as Mechanical
Problems only. Connected with this subject, I will not omit to
notice a very general and beautiful method of solving problems
respecting the motion of systems **of mutually attracting bodies,
given by Sir W. R. Hamilton, in the _Philosophical Transactions_ for
1834-5 ("On a General Method in Dynamics"). His method consists in
investigating the _Principal Function_ of the co-ordinates of the
bodies: this function being one, by the differentiation of which,
the co-ordinates of the bodies of the system may be found. Moreover,
an approximate value of this function being obtained, the same
formulæ supply a means of successive approximation without limit.]

9. _Precession. Motion of Rigid Bodies._--The series of
investigations of which I have spoken, extensive and complex as it
is, treats the moving bodies as points only, and takes no account of
any peculiarity of their form or motion of their parts. The
investigation of the motion of a body of any magnitude and form, is
another branch of analytical mechanics, which well deserves notice.
Like the former branch, it mainly owed its cultivation to the
problems suggested by the solar system. Newton, as we have seen,
endeavored to calculate the effect of the attraction of the sun and
moon in producing the _precession of the equinoxes_; but in doing
this he made some mistakes. In 1747, D'Alembert solved this problem
by the aid of his "Principle;" and it was not difficult for him to
show, as he did in his _Opuscules_, in 1761, that the same method
enabled him to determine the motion of a body of any figure acted
upon by any forces. But, as the reader will have observed in the
course of this narrative, the great mathematicians of this period
were always nearly abreast of each other in their
advances.--Euler,[57\6] in the mean time, had published, in 1751, a
solution of the {375} problem of the precession; and in 1752, a
memoir which he entitled _Discovery of a New Principle of
Mechanics_, and which contains a solution of the general problem of
the alteration of rotary motion by forces. D'Alembert noticed with
disapprobation the assumption of priority which this title implied,
though allowing the merit of the memoir. Various improvements were
made in these solutions; but the final form was given them by Euler;
and they were applied to a great variety of problems in his _Theory
of the Motion of Solid and Rigid Bodies_, which was written[58\6]
about 1760, and published in 1765. The formulæ in this work were
much simplified by the use of a discovery of Segner, that every body
has three axes which were called Principal Axes, about which alone
(in general) it would permanently revolve. The equations which Euler
and other writers had obtained, were attacked as erroneous by Landen
in the Philosophical Transactions for 1785; but I think it is
impossible to consider this criticism otherwise than as an example
of the inability of the English mathematicians of that period to
take a steady hold of the analytical generalizations to which the
great Continental authors had been led. Perhaps one of the most
remarkable calculations of the motion of a rigid body is that which
Lagrange performed with regard to the _Moon's Libration_; and by
which he showed that the Nodes of the Moon's Equator and those of
her Orbit must always coincide.

[Note 57\6: _Ac. Berl._ 1745, 1750.]

[Note 58\6: See the preface to the book.]

10. _Vibrating Strings._--Other mechanical questions, unconnected
with astronomy, were also pursued with great zeal and success. Among
these was the problem of a vibrating string, stretched between two
fixed points. There is not much complexity in the mechanical
conceptions which belong to this case, but considerable difficulty
in reducing them to analysis. Taylor, in his _Method of Increments_,
published in 1716, had annexed to his work a solution of this
problem; obtained on suppositions, limited indeed, but apparently
conformable to the most common circumstances of practice. John
Bernoulli, in 1728, had also treated the same problem. But it
assumed an interest altogether new, when, in 1747, D'Alembert
published his views on the subject; in which he maintained that,
instead of one kind of curve only, there were an infinite number of
different curves, which answered the conditions of the question. The
problem, thus put forward by one great mathematician, was, as usual,
taken up by the others, whose names the reader is now so familiar
with in such an association. In {376} 1748, Euler not only assented
to the generalization of D'Alembert, but held that it was not
necessary that the curves so introduced should be defined by any
algebraical condition whatever. From this extreme indeterminateness
D'Alembert dissented; while Daniel Bernoulli, trusting more to
physical and less to analytical reasonings, maintained that both
these generalizations were inapplicable in fact, and that the
solution was really restricted, as had at first been supposed, to
the form of the trochoid, and to other forms derivable from that. He
introduced, in such problems, the "Law of Coexistent Vibrations,"
which is of eminent use in enabling us to conceive the results of
complex mechanical conditions, and the real import of many
analytical expressions. In the mean time, the wonderful analytical
genius of Lagrange had applied itself to this problem. He had formed
the Academy of Turin, in conjunction with his friends Saluces and
Cigna; and the first memoir in their Transactions was one by him on
this subject: in this and in subsequent writings he has established,
to the satisfaction of the mathematical world, that the functions
introduced in such cases are not necessarily continuous, but are
arbitrary to the same degree that the motion is so practically;
though capable of expression by a series of circular functions. This
controversy, concerning the degree of lawlessness with which the
conditions of the solution may be assumed, is of consequence, not
only with respect to vibrating strings, but also with respect to
many problems, belonging to a branch of Mechanics which we now have
to mention, the Doctrine of Fluids.

11. _Equilibrium of Fluids. Figure of the Earth. Tides._--The
application of the general doctrines of Mechanics to fluids was a
natural and inevitable step, when the principles of the science had
been generalized. It was easily seen that a fluid is, for this
purpose, nothing more than a body of which the parts are movable
amongst each other with entire facility; and that the mathematician
must trace the consequences of this condition upon his equations.
This accordingly was done, by the founders of mechanics, both for
the cases of the equilibrium and of motion. Newton's attempt to
solve the problem of the _figure of the earth_, supposing it fluid,
is the first example of such an investigation: and this solution
rested upon principles which we have already explained, applied with
the skill and sagacity which distinguished all that Newton did.

We have already seen how the generality of the principle, that
fluids press equally in all directions, was established. In applying
it to calculation, Newton took for his fundamental principle, the
equal {377} weight of columns of the fluid reaching to the centre;
Huyghens took, as his basis, the **perpendicularity of the resulting
force at each point to the surface of the fluid; Bouguer conceived
that both principles were necessary; and Clairaut showed that the
equilibrium of _all_ canals is requisite. He also was the first
mathematician who deduced from this principle the Equations of
Partial Differentials by which these laws are expressed; a step
which, as Lagrange says,[59\6] changed the face of Hydrostatics, and
made it a new science. Euler simplified the mode of obtaining the
Equations of Equilibrium for any forces whatever; and put them in
the form which is now generally adopted in our treatises.

[Note 59\6: _Méc. Analyt._ ii. p. 180.]

The explanation of the _Tides_, in the way in which Newton attempted
it in the third book of the _Principia_, is another example of a
hydrostatical investigation: for he considered only the form that
the ocean would have if it were at rest. The memoirs of Maclaurin,
Daniel Bernoulli, and Euler, on the question of the Tides, which
shared among them the prize of the Academy of Sciences in 1740, went
upon the same views.

The _Treatise of the Figure of the Earth_, by Clairaut, in 1743,
extended Newton's solution of the same problem, by supposing a solid
nucleus covered with a fluid of different density. No peculiar
novelty has been introduced into this subject, except a method
employed by Laplace for determining the attractions of spheroids of
small eccentricity, which is, as Professor Airy has said,[60\6] "a
calculus the most singular in its nature, and the most powerful in
its effects, of any which has yet appeared."

[Note 60\6: _Enc. Met._ Fig. of Earth, p. 192.]

12. _Capillary Action._--There is only one other problem of the
statics of fluids on which it is necessary to say a word,--the
doctrine of Capillary Attraction. Daniel Bernoulli,[61\6] in 1738,
states that he passes over the subject, because he could not reduce
the facts to general laws: but Clairaut was more successful, and
Laplace and Poisson have since given great analytical completeness to
his theory. At present our business is, not so much with the
sufficiency of the theory to explain phenomena, as with the mechanical
problem of which this is an example, which is one of a very remarkable
and important character; namely, to determine the effect of
attractions which are exercised by all the particles of bodies, on the
hypothesis that the {378} attraction of each particle, though sensible
when it acts upon another particle at an extremely small distance from
it, becomes insensible and vanishes the moment this distance assumes a
perceptible magnitude. It may easily be imagined that the analysis by
which results are obtained under conditions so general and so
peculiar, is curious and abstract; the problem has been resolved in
some very extensive cases.

[Note 61\6: _Hydrodyn._ Pref. p. 5.]

13. _Motion of Fluids._--The only branch of mathematical mechanics
which remains to be considered, is that which is, we may venture to
say, hitherto incomparably the most incomplete of
all,--Hydrodynamics. It may easily be imagined that the mere
hypothesis of absolute relative mobility in the parts, combined with
the laws of motion and nothing more, are conditions too vague and
general to lead to definite conclusions. Yet such are the conditions
of the problems which relate to the motion of fluids. Accordingly,
the mode of solving them has been, to introduce certain other
hypotheses, often acknowledged to be false, and almost always in
some measure arbitrary, which may assist in determining and
obtaining the solution. The Velocity of a fluid issuing from an
orifice in a vessel, and the Resistance which a solid body suffers
in moving in a fluid, have been the two main problems on which
mathematicians have employed themselves. We have already spoken of
the manner in which Newton attacked both these, and endeavored to
connect them. The subject became a branch of Analytical Mechanics by
the labors of D. Bernoulli, whose _Hydrodynamica_ was published in
1738. This work rests upon the Huyghenian principle of which we have
already spoken in the history of the centre of oscillation; namely,
the equality of the _actual descent_ of the particles and the
_potential ascent_; or, in other words, the conservation of _vis
viva_. This was the first analytical treatise; and the analysis is
declared by Lagrange to be as elegant in its steps as it is simple
in its results. Maclaurin also treated the subject; but is accused
of reasoning in such a way as to show that he had determined upon
his result beforehand; and the method of John Bernoulli, who
likewise wrote upon it, has been strongly objected to by D'Alembert.
D'Alembert himself applied the principle which bears his name to
this subject; publishing a _Treatise on the Equilibrium and Motion
of Fluids_ in 1744, and on the _Resistance of Fluids_ in 1753. His
_Réflexions sur la Cause Générale des Vents_, printed in 1747, are
also a celebrated work, belonging to this part of mathematics.
Euler, in this as in other cases, was one of those who most
contributed to give analytical elegance to the subject. In addition
to the questions which {379} have been mentioned, he and Lagrange
treated the problems of the small vibrations of fluids, both
inelastic and elastic;--a subject which leads, like the question of
vibrating strings, to some subtle and abstruse considerations
concerning the significations of the integrals of partial
differential equations. Laplace also took up the subject of waves
propagated along the surface of water; and deduced a very celebrated
theory of the tides, in which he considered the ocean to be, not in
equilibrium, as preceding writers had supposed, but agitated by a
constant series of undulations, produced by the solar and lunar
forces. The difficulty of such an investigation may be judged of
from this, that Laplace, in order to carry it on, is obliged to
assume a mechanical proposition, unproved, and only conjectured to
be true; namely,[62\6] that, "in a system of bodies acted upon by
forces which are periodical, the state of the system is periodical
like the forces." Even with this assumption, various other arbitrary
processes are requisite; and it appears still very doubtful whether
Laplace's theory is either a better mechanical solution of the
problem, or a nearer approximation to the laws of the phenomena,
than that obtained by D. Bernoulli, following the views of Newton.

[Note 62\6: _Méc. Cél._ t. ii. p. 218.]

In most cases, the solutions of problems of hydrodynamics are not
satisfactorily confirmed by the results of observation. Poisson and
Cauchy have prosecuted the subject of waves, and have deduced very
curious conclusions by a very recondite and profound analysis. The
assumptions of the mathematician here do not represent the
conditions of nature; the rules of theory, therefore, are not a good
standard to which we may refer the aberrations of particular cases;
and the laws which we obtain from experiment are very imperfectly
illustrated by _à priori_ calculation. The case of this department
of knowledge, Hydrodynamics, is very peculiar; we have reached the
highest point of the science,--the laws of extreme simplicity and
generality from which the phenomena flow; we cannot doubt that the
ultimate principles which we have obtained are the true ones, and
those which really apply to the facts; and yet we are far from being
able to apply the principles to explain or find out the facts. In
order to do this, we want, in addition to what we have, true and
useful principles, intermediate between the highest and the
lowest;--between the extreme and almost barren generality of the
laws of motion, and the endless varieties and inextricable
complexity of fluid motions in special cases. {380} The reason of
this peculiarity in the science of Hydrodynamics appears to be, that
its general principles were not discovered with reference to the
science itself, but by extension from the sister science of the
Mechanics of Solids; they were not obtained by ascending gradually
from particulars, to truths more and more general, respecting the
motions of fluids; but were caught at once, by a perception that the
parts of fluids are included in that range of generality which we
are entitled to give to the supreme laws of motions of solids. Thus,
Solid Dynamics and Fluid Dynamics resemble two edifices which have
their highest apartment in common, and though we can explore every
part of the former building, we have not yet succeeded in traversing
the staircase of the latter, either from the top or from the bottom.
If we had lived in a world in which there were no solid bodies, we
should probably not have yet discovered the laws of motion; if we
had lived in a world in which there were no fluids, we should have
no idea how insufficient a complete possession of the general laws
of motion may be, to give us a true knowledge of particular results.

14. _Various General Mechanical Principles._--The generalized laws
of motion, the points to which I have endeavored to conduct my
history, include in them all other laws by which the motions of
bodies can be regulated; and among such, several laws which had been
discovered before the highest point of generalization was reached,
and which thus served as stepping-stones to the ultimate principles.
Such were, as we have seen, the Principles of the Conservation of
_vis viva_, the Principle of the Conservation of the Motion of the
Centre of Gravity, and the like. These principles may, of course, be
deduced from our elementary laws, and were finally established by
mathematicians on that footing. There are other principles which may
be similarly demonstrated; among the rest, I may mention the
Principle of _the Conservation of areas_, which extends to any
number of bodies a law analogous to that which Kepler had observed,
and Newton demonstrated, respecting the areas described by each
planet round the sun. I may mention also, the Principle of the
_Immobility of the plane of maximum areas_, a plane which is not
disturbed by any mutual action of the parts of any system. The
former of these principles was published about the same time by
Euler, D. Bernoulli, and Darcy, under different forms, in 1746 and
1747; the latter by Laplace.

To these may be added a law, very celebrated in its time, and the
occasion of an angry controversy, _the Principle of least action_.
{381} Maupertuis conceived that he could establish _à priori_, by
theological arguments, that all mechanical changes must take place
in the world so as to occasion the least possible quantity of
_action_. In asserting this, it was proposed to measure the Action
by the product of Velocity and Space; and this measure being
adopted, the mathematicians, though they did not generally assent to
Maupertuis' reasonings, found that his principle expressed a
remarkable and useful truth, which might be established on known
mechanical grounds.

15. _Analytical Generality. Connection of Statics and
Dynamics._--Before I quit this subject, it is important to remark
the peculiar character which the science of Mechanics has now
assumed, in consequence of the extreme analytical generality which
has been given it. Symbols, and operations upon symbols, include the
whole of the reasoner's task; and though the relations of space are
the leading subjects in the science, the great analytical treatises
upon it do not contain a single diagram. The _Mécanique Analytique_
of Lagrange, of which the first edition appeared in 1788, is by far
the most consummate example of this analytical generality. "The plan
of this work," says the author, "is entirely new. I have proposed to
myself to reduce the whole theory of this science, and the art of
resolving the problems which it includes, to general formulæ, of
which the simple development gives all the equations necessary for
the solution of the problem."--"The reader will find no figures in
the work. The methods which I deliver do not require either
constructions, or geometrical or mechanical reasonings; but only
algebraical operations, subject to a regular and uniform rule of
proceeding." Thus this writer makes Mechanics a branch of Analysis;
instead of making, as had previously been done, Analysis an
implement of Mechanics.[63\6] The transcendent generalizing genius
of Lagrange, and his matchless analytical skill and elegance, have
made this undertaking as successful as it is striking.

[Note 63\6: Lagrange himself terms Mechanics, "An Analytical
Geometry of four dimensions." Besides the _three co-ordinates_ which
determine the place of a body in _space_, the _time_ enters as a
_fourth co-ordinate_. [Note by Littrow.]]

The mathematical reader is aware that the language of mathematical
symbols is, in its nature, more general than the language of words:
and that in this way truths, translated into symbols, often suggest
their own generalizations. Something of this kind has happened in
Mechanics. The same Formula expresses the general condition of
Statics and that of Dynamics. The tendency to generalization which
is thus introduced by analysis, makes mathematicians unwilling to
{382} acknowledge a plurality of Mechanical principles; and in the
most recent analytical treatises on the subject, all the doctrines
are deduced from the single Law of Inertia. Indeed, if we identify
Forces with the Velocities which produce them, and allow the
Composition of Forces to be applicable to force _so understood_, it
is easy to see that we can reduce the Laws of Motion to the
Principles of Statics; and this conjunction, though it may not be
considered as philosophically just, is verbally correct. If we thus
multiply or extend the meanings of the term Force, we make our
elementary principles simpler and fewer than before; and those
persons, therefore, who are willing to assent to such a use of
words, can thus obtain an additional generalisation of dynamical
principles; and this, as I have stated, has been adopted in several
recent treatises. I shall not further discuss here how far this is a
real advance in science.

Having thus rapidly gone through the history of Force and Attraction
in the abstract, we return to the attempt to interpret the phenomena
of the universe by the aid of these abstractions thus established.

But before we do so, we may make one remark on the history of this
part of science. In consequence of the vast career into which the
Doctrine of Motion has been drawn by the splendid problems proposed to
it by Astronomy, the origin and starting-point of Mechanics, namely
Machines, had almost been lost out of sight. _Machines_ had become the
smallest part of _Mechanics_, as _Land-measuring_ had become the
smallest part of _Geometry_. Yet the application of Mathematics to the
doctrine of Machines has led, at all periods of the Science, and
especially in our own time, to curious and valuable results. Some of
these will be noticed in the _Additions_ to this volume.



{{383}}
BOOK VII.



THE MECHANICAL SCIENCES.
(CONTINUED.)


HISTORY
OF
PHYSICAL ASTRONOMY.


  DESCEND from heaven, Urania, by that name
  If rightly thou art called, whose voice divine
  Following, above the Olympian hill I soar,
  Above the flight of Pegasean wing.
  The meaning, not the name, I call, for thou
  Nor of the muses nine, nor on the top
  Of old Olympus dwell'st: but heavenly-born,
  Before the hills appeared, or fountain flowed,
  Thou with Eternal Wisdom didst converse,
  Wisdom, thy sister.

          _Paradise Lost_, B. vii.



{{385}}
CHAPTER I.

PRELUDE TO THE INDUCTIVE EPOCH OF NEWTON.


WE have now to contemplate the last and most splendid period of the
progress of Astronomy;--the grand completion of the history of the
most ancient and prosperous province of human knowledge;--the steps
which elevated this science to an unrivalled eminence above other
sciences;--the first great example of a wide and complex assemblage
of phenomena indubitably traced to their single simple cause;--in
short, the first example of the formation of a perfect Inductive
Science.

In this, as in other considerable advances in real science, the
complete disclosure of the new truths by the principal discoverer,
was preceded by movements and glimpses, by trials, seekings, and
guesses on the part of others; by indications, in short, that men's
minds were already carried by their intellectual impulses in the
direction in which the truth lay, and were beginning to detect its
nature. In a case so important and interesting as this, it is more
peculiarly proper to give some view of this Prelude to the Epoch of
the full discovery.

(_Francis Bacon._) That Astronomy should become Physical
Astronomy,--that the motions of the heavenly bodies should be traced
to their causes, as well as reduced to rule,--was felt by all
persons of active and philosophical minds as a pressing and
irresistible need, at the time of which we speak. We have already
seen how much this feeling had to do in impelling Kepler to the
train of laborious research by which he made his discoveries.
Perhaps it may be interesting to point out how strongly this
persuasion of the necessity of giving a physical character to
astronomy, had taken possession of the mind of Bacon, who, looking
at the progress of knowledge with a more comprehensive spirit, and
from a higher point of view than Kepler, could have none of his
astronomical prejudices, since on that subject he was of a different
school, and of far inferior knowledge. In his "Description of the
Intellectual Globe," Bacon says that while Astronomy had, up to that
time, had it for her business to inquire into the rules of the
heavenly motions, and Philosophy into their causes, they had both so
far worked without due appreciation of their respective tasks;
Philosophy neglecting facts, and Astronomy claiming assent to her
{386} mathematical hypotheses, which ought to be considered as mere
steps of calculation. "Since, therefore," he continues,[1\7] "each
science has hitherto been a slight and ill-constructed thing, we
must assuredly take a firmer stand; our ground being, that these two
subjects, which on account of the narrowness of men's views and the
traditions of professors have been so long dissevered, are, in fact,
one and the same thing, and compose one body of science." It must be
allowed that, however erroneous might be the points of Bacon's
positive astronomical creed, these general views of the nature and
position of the science are most sound and philosophical.

[Note 1\7: Vol. ix. 221.]

(_Kepler_) In his attempts to suggest a right physical view of the
starry heavens and their relation to the earth, Bacon failed, along
with all the writers of his time. It has already been stated that
the main cause of this failure was the want of a knowledge of the
true theory of motion;--the non-existence of the science of
Dynamics. At the time of Bacon and Kepler, it was only just
beginning to be possible to reduce the heavenly motions to the laws
of earthly motion, because the latter were only just then divulged.
Accordingly, we have seen that the whole of Kepler's physical
speculations proceed upon an ignorance of the first law of motion,
and assume it to be the main problem of the physical astronomer to
assign the cause which _keeps up_ the motions of the planets.
Kepler's doctrine is, that a certain Force or Virtue resides in the
sun, by which all bodies within his influence are carried round him.
He illustrates[2\7] the nature of this Virtue in various ways,
comparing it to Light, and to the Magnetic Power, which it resembles
in the circumstances of operating at a distance, and also in
exercising a feebler influence as the distance becomes greater. But
it was obvious that these comparisons were very imperfect; for they
do not explain how the sun produces in a body at a distance a motion
_athwart_ the line of emanation; and though Kepler introduced an
assumed rotation of the sun on his axis as the cause of this effect,
that such a cause could produce the result could not be established
by any analogy of terrestrial motions. But another image to which he
referred, suggested a much more substantial and conceivable kind of
mechanical action by which the celestial motions might be produced,
namely, a current of fluid matter circulating round the sun, and
carrying the planet with it, like a boat in a stream. In the Table
of Contents of the work on the planet Mars, the purport of the
chapter to which I have alluded is {387} stated as follows: "A
physical speculation, in which it is demonstrated that the vehicle
of that Virtue which urges the planets, circulates through the
spaces of the universe after the manner of a river or whirlpool
(_vortex_), moving quicker than the planets." I think it will be
found, by any one who reads Kepler's phrases concerning the _moving
force,--the magnetic nature,--the immaterial virtue_ of the sun,
that they convey no distinct conception, except so far as they are
interpreted by the expressions just quoted. A vortex of fluid
constantly whirling round the sun, kept in this whirling motion by
the rotation of the sun himself, and carrying the planets round the
sun by its revolution, as a whirlpool carries straws, could be
readily understood; and though it appears to have been held by
Kepler that this current and vortex was immaterial, he ascribes to
it the power of overcoming the inertia of bodies, and of putting
them and keeping them in motion, the only material properties with
which he had any thing to do. Kepler's physical reasonings,
therefore, amount, in fact, to the doctrine of Vortices round the
central bodies, and are occasionally so stated by himself; though by
asserting these vortices to be "an immaterial species," and by the
fickleness and variety of his phraseology on the subject, he leaves
this theory in some confusion;--a proceeding, indeed, which both his
want of sound mechanical conceptions, and his busy and inventive
fancy, might have led us to expect. Nor, we may venture to say, was
it easy for any one at Kepler's time to devise a more plausible
theory than the theory of vortices might have been made. It was only
with the formation and progress of the science of Mechanics that
this theory became untenable.

[Note 2\7: _De Stellâ Martis_, P. 3. c. xxxiv.]

(_Descartes_) But if Kepler might be excused, or indeed admired, for
propounding the theory of Vortices at his time, the case was
different when the laws of motion had been fully developed, and when
those who knew the state of mechanical science ought to have learned
to consider the motions of the stars as a mechanical problem,
subject to the same conditions as other mechanical problems, and
capable of the same exactness of solution. And there was an especial
inconsistency in the circumstance of the Theory of Vortices being
put forwards by Descartes, who pretended, or was asserted by his
admirers, to have been one of the discoverers of the true Laws of
Motion. It certainly shows both great conceit and great shallowness,
that he should have proclaimed with much pomp this crude invention
of the ante-mechanical period, at the time when the best
mathematicians of Europe, as Borelli in Italy, Hooke and Wallis in
England, Huyghens in Holland, {388} were patiently laboring to bring
the mechanical problem of the universe into its most distinct form,
in order that it might be solved at last and forever.

I do not mean to assert that Descartes borrowed his doctrines from
Kepler, or from any of his predecessors, for the theory was
sufficiently obvious; and especially if we suppose the inventor to
seek his suggestions rather in the casual examples offered to the
sense than in the exact laws of motion. Nor would it be reasonable
to rob this philosopher of that credit, of the plausible deduction
of a vast system from apparently simple principles, which, at the
time, was so much admired; and which undoubtedly was the great cause
of the many converts to his views. At the same time we may venture
to say that a system of doctrine thus deduced from assumed
principles by a long chain of reasoning, and not verified and
confirmed at every step by detailed and exact facts, has hardly a
chance of containing any truth. Descartes said that he should think
it little to show how the world _is_ constructed, if he could not
also show that it _must_ of necessity have been so constructed. The
more modest philosophy which has survived the boastings of his
school is content to receive all its knowledge of facts from
experience, and never dreams of interposing its peremptory _must be_
when nature is ready to tell us what _is_. The _à priori_
philosopher has, however, always a strong feeling in his favor among
men. The deductive form of his speculations gives them something of
the charm and the apparent certainty of pure mathematics; and while
he avoids that laborious recurrence to experiments, and measures,
and multiplied observations, which is irksome and distasteful to
those who are impatient to grow wise at once, every fact of which
the theory appears to give an explanation, seems to be an unasked
and almost an infallible witness in its favor.

My business with Descartes here is only with his physical Theory of
Vortices; which, great as was its glory at one time, is now utterly
extinguished. It was propounded in his _Principia Philosophiæ_, in
1644. In order to arrive at this theory, he begins, as might be
expected of him, from reasonings sufficiently general. He lays it
down as a maxim, in the first sentence of his book, that a person
who seeks for truth must, once in his life, doubt of all that he
most believes. Conceiving himself thus to have stripped himself of
all his belief on all subjects, in order to resume that part of it
which merits to be retained, he begins with his celebrated
assertion, "I think, therefore I am;" which appears to him a certain
and immovable principle, by means of {389} which he may proceed to
something more. Accordingly, to this he soon adds the idea, and
hence the certain existence, of God and his perfections. He then
asserts it to be also manifest, that a vacuum in any part of the
universe is impossible; the whole must be filled with matter, and
the matter must be divided into equal angular parts, this being the
most simple, and therefore the most natural supposition.[3\7] This
matter being in motion, the parts are necessarily ground into a
spherical form; and the corners thus rubbed off (like filings or
sawdust) form a second and more subtle matter.[4\7] There is,
besides, a third kind of matter, of parts more coarse and less
fitted for motion. The first matter makes luminous bodies, as the
sun, and the fixed stars; the second is the transparent substance of
the skies; the third is the material of opake bodies, as the earth,
planets, and comets. We may suppose, also,[5\7] that the motions of
these parts take the form of revolving circular currents,[6\7] or
_vortices_. By this means, the first matter will be collected to the
centre of each vortex, while the second, or subtle matter, surrounds
it, and, by its centrifugal effort, constitutes light. The planets
are carried round the sun by the motion of his vortex,[7\7] each
planet being at such a distance from the sun as to be in a part of
the vortex suitable to its solidity and mobility. The motions are
prevented from being exactly circular and regular by various causes;
for instance, a vortex may be pressed into an oval shape by
contiguous vortices. The satellites are, in like manner, carried
round their primary planets by subordinate vortices; while the
comets have sometimes the liberty of gliding out of one vortex into
the one next contiguous, and thus travelling in a sinuous course,
from system to system, through the universe. It is not necessary for
us to speak here of the entire deficiency of this system in
mechanical consistency, and in a correspondency to observation in
details and measures. Its general reception and temporary sway, in
some instances even among intelligent men and good mathematicians,
are the most remarkable facts connected with it. These may be
ascribed, in part, to the circumstance that philosophers were now
ready and eager for a physical astronomy commensurate with the
existing state of knowledge; they may have been owing also, in some
measure, to the character and position of Descartes. He was a man of
high claims in every department of speculation, and, in pure
mathematics, a genuine inventor of great eminence;--a man of family
and a soldier;--an inoffensive philosopher, attacked and persecuted
{390} for his opinions with great bigotry and fury by a Dutch
divine, Voet;--the favorite and teacher of two distinguished
princesses, and, it is said, the lover of one of them. This was
Elizabeth, the daughter of the Elector Frederick, and consequently
grand-daughter of our James the First. His other royal disciple, the
celebrated Christiana of Sweden, showed her zeal for his
instructions by appointing the hour of five in the morning for their
interviews. This, in the climate of Sweden, and in the winter, was
too severe a trial for the constitution of the philosopher, born in
the sunny valley of the Loire; and, after a short residence at
Stockholm, he died of an inflammation of the chest in 1650. He
always kept up an active correspondence with his friend Mersenne,
who was called, by some of the Parisians, "the Resident of Descartes
at Paris;" and who informed him of all that was done in the world of
science. It is said that he at first sent to Mersenne an account of
a system of the universe which he had devised, which went on the
assumption of a vacuum; Mersenne informed him that the _vacuum_ was
no longer the fashion at Paris; upon which he proceeded to remodel
his system, and to re-establish it on the principle of a _plenum_.
Undoubtedly he tried to avoid promulgating opinions which might
bring him into trouble. He, on all occasions, endeavored to explain
away the doctrine of the motion of the earth, so as to evade the
scruples to which the decrees of the pope had given rise; and, in
stating the theory of vortices, he says,[8\7] "There is no doubt
that the world was created at first with all its perfection;
nevertheless, it is well to consider how it might have arisen from
certain principles, although we know that it did not." Indeed, in
the whole of his philosophy, he appears to deserve the character of
being both rash and cowardly, "_pusillanimus simul et audax_," far
more than Aristotle, to whose physical speculations Bacon applies
this description.[9\7]

[Note 3\7: _Prin._ p. 58.]

[Note 4\7: Ib. p. 59.]

[Note 5\7: Ib. p. 56.]

[Note 6\7: Ib. p. 61.]

[Note 7\7: Ib. c. 140, p. 114.]

[Note 8\7: _Prin._ p. 56.]

[Note 9\7: Bacon, _Descriptio Globi Intellectualis_.]

Whatever the causes might be, his system was well received and
rapidly adopted. Gassendi, indeed, says that he found nobody who had
the courage to read the _Principia_ through;[10\7] but the system
was soon embraced by the younger professors, who were eager to
dispute in its favor. It is said[11\7] that the University of Paris
was on the point of publishing an edict against these new doctrines,
and was only prevented from doing so by a pasquinade which is worth
mentioning. It was composed by the poet Boileau (about 1684), and
professed to be a Request in favor of Aristotle, and an Edict issued
from Mount {391} Parnassus in consequence. It is obvious that, at
this time, the cause of Cartesianism was looked upon as the cause of
free inquiry and modern discovery, in opposition to that of bigotry,
prejudice, and ignorance. Probably the poet was far from being a
very severe or profound critic of the truth of such claims. "This
petition of the Masters of Arts, Professors and Regents of the
University of Paris, humbly showeth, that it is of public notoriety
that the sublime and incomparable Aristotle was, without contest,
the first founder of the four elements, fire, air, earth, and water;
that he did, by special grace, accord unto them a simplicity which
belongeth not to them of natural right;" and so on. "Nevertheless,
since, a certain time past, two individuals, named Reason and
Experience, have leagued themselves together to dispute his claim to
the rank which of justice pertains to him, and have tried to erect
themselves a throne on the ruins of his authority; and, in order the
better to gain their ends, have excited certain factious spirits,
who, under the names of Cartesians and Gassendists, have begun to
shake off the yoke of their master, Aristotle; and, contemning his
authority, with unexampled temerity, would dispute the right which
he had acquired of making true pass for false and false for
true;"--In fact, this production does not exhibit any of the
peculiar tenets of Descartes, although, probably, the positive
points of his doctrines obtained a footing in the University of
Paris, under the cover of this assault on his adversaries. The
Physics of Rohault, a zealous disciple of Descartes, was published
at Paris about 1670,[12\7] and was, for a time, the standard book
for students of this subject, both in France and in England. I do
not here speak of the later defenders of the Cartesian system, for,
in their hands, it was much modified by the struggle which it had to
maintain against the Newtonian system.

[Note 10\7: Del. _A. M._ ii. 193.]

[Note 11\7: _Enc. Brit._ art. _Cartesianism._]

[Note 12\7: And a second edition in 1672.]

We are concerned with Descartes and his school only as they form
part of the picture of the intellectual condition of Europe just
before the publication of Newton's discoveries. Beyond this, the
Cartesian speculations are without value. When, indeed, Descartes'
countrymen could no longer refuse their assent and admiration to the
Newtonian theory, it came to be the fashion among them to say that
Descartes had been the necessary precursor of Newton; and to adopt a
favorite saying of Leibnitz, that the Cartesian philosophy was the
antechamber of Truth. Yet this comparison is far from being happy:
it appeared rather as if these suitors had mistaken the door; for
those {392} who first came into the presence of Truth herself, were
those who never entered this imagined antechamber, and those who
were in the antechamber first, were the last in penetrating further.
In partly the same spirit, Playfair has noted it as a service which
Newton perhaps owed to Descartes, that "he had exhausted one of the
most tempting forms of error." We shall see soon that this
temptation had no attraction for those who looked at the problem in
its true light, as the Italian and English philosophers already did.
Voltaire has observed, far more truly, that Newton's edifice rested
on no stone of Descartes' foundations. He illustrates this by
relating that Newton only once read the work of Descartes, and, in
doing so, wrote the word "_error_," repeatedly, on the first seven
or eight pages; after which he read no more. This volume, Voltaire
adds, was for some time in the possession of Newton's nephew.[13\7]

[Note 13\7: _Cartesianism_, Enc. Phil.]

(_Gassendi._) Even in his own country, the system of Descartes was
by no means universally adopted. We have seen that though Gassendi
was coupled with Descartes as one of the leaders of the new
philosophy, he was far from admiring his work. Gassendi's own views
of the causes of the motions of the heavenly bodies are not very
clear, nor even very clearly referrible to the laws of mechanics;
although he was one of those who had most share in showing that
those laws apply to astronomical motions. In a chapter, headed[14\7]
"Quæ sit motrix siderum causa," he reviews several opinions; but the
one which he seems to adopt, is that which ascribes the motion of
the celestial globes to certain fibres, of which the action is
similar to that of the muscles of animals. It does not appear,
therefore, that he had distinctly apprehended, either the
continuation of the movements of the planets by the First Law of
Motion, or their deflection by the Second Law;--the two main steps
on the road to the discovery of the true forces by which they are
made to describe their orbits.

[Note 14\7: Gassendi, _Opera_, vol. i. p. 639.]

(_Leibnitz, &c._) Nor does it appear that in Germany mathematicians
had attained this point of view. Leibnitz, as we have seen, did not
assent to the opinions of Descartes, as containing the complete truth;
and yet his own views of the physics of the universe do not seem to
have any great advantage over these. In 1671 he published _A new
physical hypothesis, by which the causes of most phenomena are deduced
from a certain single universal motion supposed in our globe;--not to
be despised either by the Tychonians or the Copernicans_. He supposes
{393} the particles of the earth to have separate motions, which
produce collisions, and thus propagate[15\7] an "agitation of the
ether," radiating in all directions; and,[16\7] "by the rotation of
the sun on its axis, concurring with its rectilinear action on the
earth, arises the motion of the earth about the sun." The other
motions of the solar system are, as we might expect, accounted for in
a similar manner; but it appears difficult to invest such an
hypothesis with any mechanical consistency.

[Note 15\7: Art. 5.]

[Note 16\7: Ib. 8.]

John Bernoulli maintained to the last the Cartesian hypothesis,
though with several modifications of his own, and even pretended to
apply mathematical calculation to his principles. This, however,
belongs to a later period of our history; to the reception, not to
the prelude, of the Newtonian theory.

(_Borelli._) In Italy, Holland, and England, mathematicians appear
to have looked much more steadily at the problem of the celestial
motions, by the light which the discovery of the real laws of motion
threw upon it. In Borelli's _Theories of the Medicean Planets_,
printed at Florence in 1666, we have already a conception of the
nature of central action, in which true notions begin to appear. The
attraction of a body upon another which revolves about it is spoken
of and likened to magnetic action; not converting the attracting
force into a transverse force, according to the erroneous views of
Kepler, but taking it as a tendency of the bodies to meet. "It is
manifest," says he,[17\7] "that every planet and satellite revolves
round some principal globe of the universe as a fountain of virtue,
which so draws and holds them that they cannot by any means be
separated from it, but are compelled to follow it wherever it goes,
in constant and continuous revolutions." And, further on, he
describes[18\7] the nature of the action, as a matter of conjecture
indeed, but with remarkable correctness.[19\7] "We shall account for
these motions by supposing, that which can hardly be denied, that
the planets have a certain natural appetite for uniting themselves
with the globe round which they revolve, and that they really tend,
with all their efforts, to approach to such globe; the planets, for
instance, to the sun, the Medicean Stars to Jupiter. It is certain,
also, that circular motion gives a body a tendency to recede from
the centre of such revolution, as we find in a wheel, or a stone
whirled in a sling. Let us suppose, then, the planet to endeavor to
approach the sun; since, in the mean time, it requires, by the
circular motion, a force to recede from the same central body, it
comes to pass, that when {394} those two opposite forces are equal,
each compensates the other, and the planet cannot go nearer to the
sun nor further from him than a certain determinate space, and thus
appears balanced and floating about him."

[Note 17\7: Cap. 2.]

[Note 18\7: Ib. 11.]

[Note 19\7: P. 47.]

This is a very remarkable passage; but it will be observed, at the
same time, that the author has no distinct conception of the manner
in which the change of direction of the planet's motion is regulated
from one instant to another; still less do his views lead to any
mode of calculating the distance from the central body at which the
planet would be thus balanced, or the space through which it might
approach to the centre and recede from it. There is a great interval
from Borelli's guesses, even to Huyghens' theorems  and a much
greater to the beginning of Newton's discoveries.

(_England._) It is peculiarly interesting to us to trace the gradual
approach towards these discoveries which took place in the minds of
English mathematicians  and this we can do with tolerable
distinctness. Gilbert, in his work, _De Magnete_, printed in 1600,
has only some vague notions that the magnetic virtue of the earth in
some way determines the direction of the earth's axis, the rate of
its diurnal rotation, and that of the revolution of the moon about
it.[20\7] He died in 1603, and, in his posthumous work, already
mentioned (_De Mundo nostro Sublunari Philosophia nova_, 1651), we
have already a more distinct statement of the attraction of one body
by another.[21\7] "The force which emanates from the moon reaches to
the earth, and, in like manner, the magnetic virtue of the earth
pervades the region of the moon: both correspond and conspire by the
joint action of both, according to a proportion and conformity of
motions; but the earth has more effect, in consequence of its
superior mass; the earth attracts and repels the moon, and the moon,
within certain limits, the earth; not so as to make the bodies come
together, as magnetic bodies do, but so that they may go on in a
continuous course." Though this phraseology is capable of
representing a good deal of the truth, it does not appear to have
been connected, in the author's mind, with any very definite notions
of mechanical action in detail. We may probably say the same of
Milton's language:
                       What if the sun
  Be centre to the world; and other stars,
  By his attractive virtue and their own
  Incited, dance about him various rounds?
          _Par. Lost_, B. viii. {395}

[Note 20\7: Lib. vi. cap. 6, 7.]

[Note 21\7: Ib. ii. c. 19.]

Boyle, about the same period, seems to have inclined to the
Cartesian hypothesis. Thus, in order to show the advantage of the
natural theology which contemplates organic contrivances, over that
which refers to astronomy, he remarks: "It may be said, that in
bodies inanimate,[22\7] the contrivance is very rarely so exquisite
but that the various motions and occurrences of their parts may,
without much improbability, be suspected capable, after many essays,
to cast one another into several of those circumvolutions called by
Epicurus συστροφὰς and by Descartes, _vortices_; which being once
made, may continue a long time after the manner explained by the
latter." Neither Milton nor Boyle, however, can be supposed to have
had an exact knowledge of the laws of mechanics; and therefore they
do not fully represent the views of their mathematical
contemporaries. But there arose about this time a group of
philosophers, who began to knock at the door where Truth was to be
found, although it was left for Newton to force it open. These were
the founders of the Royal Society, Wilkins, Wallis, Seth Ward, Wren,
Hooke, and others. The time of the beginning of the speculations and
association of these men corresponds to the time of the civil wars
between the king and parliament in England  and it does not appear a
fanciful account of their scientific zeal and activity, to say, that
while they shared the common mental ferment of the times, they
sought in the calm and peaceful pursuit of knowledge a contrast to
the vexatious and angry struggles which at that time disturbed the
repose of society. It was well if these dissensions produced any
good to science to balance the obvious evils which flowed from them.
Gascoigne, the inventor of the micrometer, a friend of Horrox, was
killed in the battle of Marston Moor. Milburne, another friend of
Horrox, who like him detected the errors of Lansberg's astronomical
tables, left papers on this subject, which were lost by the coming
of the Scotch army into England in 1639; in the civil war which
ensued, the anatomical collections of Harvey were plundered and
destroyed. Most of these persons of whom I have lately had to speak,
were involved in the changes of fortune of the Commonwealth, some on
one side, and some on the other. Wilkins was made Warden of Wadham
by the committee of parliament appointed for reforming the
University of Oxford; and was, in 1659, made Master of Trinity
College, Cambridge, by Richard Cromwell, but ejected thence the year
following, upon the restoration of the {396} royal sway. Seth Ward,
who was a Fellow of Sidney College, Cambridge, was deprived of his
Fellowship by the parliamentary committee; but at a later period
(1649) he took the engagement to be faithful to the Commonwealth,
and became Savilian Professor of Astronomy at Oxford. Wallis held a
Fellowship of Queen's College, Cambridge, but vacated it by
marriage. He was afterwards much employed by the royal party in
deciphering secret writings, in which art he had peculiar skill. Yet
he was appointed by the parliamentary commissioners Savilian
Professor of Geometry at Oxford, in which situation he was continued
by Charles II. after his restoration. Christopher Wren was somewhat
later, and escaped these changes. He was chosen Fellow of All-Souls
in 1652, and succeeded Ward as Savilian Professor of Astronomy.
These men, along with Boyle and several others, formed themselves
into a club, which they called the Philosophical, or the Invisible
College; and met, from about the year 1645, sometimes in London, and
sometimes in Oxford, according to the changes of fortune and
residence of the members. Hooke went to Christ Church, Oxford, in
1663, where he was patronized by Boyle, Ward, and Wallis; and when
the Philosophical College resumed its meetings in London, after the
Restoration, as the Royal Society, Hooke was made "curator of
experiments." Halley was of the next generation, and comes after
Newton; he studied at Queen's College, Oxford, in 1673; but was at
first a man of some fortune, and not engaged in any official
situation. His talents and zeal, however, made him an active and
effective ally in the promotion of science.

[Note 22\7: Shaw's Boyle's _Works_, ii. 160.]

The connection of the persons of whom we have been speaking has a
bearing on our subject, for it led, historically speaking, to the
publication of Newton's discoveries in physical astronomy. Rightly
to propose a problem is no inconsiderable step to its solution; and
it was undoubtedly a great advance towards the true theory of the
universe to consider the motion of the planets round the sun as a
mechanical question, to be solved by a reference to the laws of
motion, and by the use of mathematics. So far the English
philosophers appear to have gone, before the time of Newton. Hooke,
indeed, when the doctrine of gravitation was published, asserted
that he had discovered it previously to Newton; and though this
pretension could not be maintained, he certainly had perceived that
the thing to be done was, to determine the effect of a central force
in producing curvilinear motion; which effect, as we have already
seen, he illustrated by experiment as early as 1666. Hooke had also
spoken more clearly on this subject {397} in _An Attempt to prove
the Motion of the Earth from Observations_, published in 1674. In
this, he distinctly states that the planets would move in straight
lines, if they were not deflected by central forces; and that the
central attractive power increases in approaching the centre in
certain degrees, dependent on the distance. "Now what these degrees
are," he adds, "I have not yet experimentally verified;" but he
ventures to promise to any one who succeeds in this undertaking, a
discovery of the cause of the heavenly motions. He asserted, in
conversation, to Halley and Wren, that he had solved this problem,
but his solution was never produced. The proposition that the
attractive force of the sun varies inversely as the square of the
distance from the centre, had already been divined, if not fully
established. If the orbits of the planets were circles, this
proportion of the forces might be deduced in the same manner as the
propositions concerning circular motion, which Huyghens published in
1673; yet it does not appear that Huyghens made this application of
his principles. Newton, however, had already made this step some
years before this time. Accordingly, he says in a letter to Halley,
on Hooke's claim to this discovery,[23\7] "When Huygenius put out
his _Horologium Oscillatorium_, a copy being presented to me, in my
letter of thanks I gave those rules in the end thereof a particular
commendation for their usefulness in computing the forces of the
moon from the earth, and the earth from the sun." He says, moreover,
"I am almost confident by circumstances, that Sir Christopher Wren
knew the duplicate proportion when I gave him a visit; and then Mr.
Hooke, by his book _Cometa_, will prove the last of us three that
knew it." Hooke's _Cometa_ was published in 1678. These inferences
were all connected with Kepler's law, that the times are in the
sesquiplicate ratio of the major axes of the orbits. But Halley had
also been led to the duplicate proportion by another train of
reasoning, namely, by considering the force of the sun as an
emanation, which must become more feeble in proportion to the
increased spherical surface over which it is diffused, and therefore
in the inverse proportion of the square of the distances.[24\7] In
this view of the matter, however, the difficulty was to determine
what would be the motion of a body acted on by such a force, when
the orbit is not circular but oblong. The investigation of this case
was a problem which, we can {398} easily conceive, must have
appeared of very formidable complexity while it was unsolved, and
the first of its kind. Accordingly Halley, as his biographer says,
"finding himself unable to make it out in any geometrical way, first
applied to Mr. Hooke and Sir Christopher Wren, and meeting with no
assistance from either of them, he went to Cambridge in August
(1684), to Mr. Newton, who supplied him fully with what he had so
ardently sought."

[Note 23\7: _Biog. Brit._, art. _Hooke._]

[Note 24\7: Bullialdus, in 1645, had asserted that the force by
which the sun "prehendit et harpagat," takes hold of and grapples
the planets, must be as the inverse square of the distance.]

A paper of Halley's in the _Philosophical Transactions_ for January,
1686, professedly inserted as a preparation for Newton's work,
contains some arguments against the Cartesian hypothesis of gravity,
which seem to imply that Cartesian opinions had some footing among
English philosophers; and we are told by Whiston, Newton's successor
in his professorship at Cambridge, that Cartesianism formed a part
of the studies of that place. Indeed, Rohault's _Physics_ was used
as a classbook at that University long after the time of which we
are speaking; but the peculiar Cartesian doctrines which it
contained were soon superseded by others.

With regard, then, to this part of the discovery, that the force of
the sun follows the inverse duplicate proportion of the distances,
we see that several other persons were on the verge of it at the
same time with Newton; though he alone possessed that combination of
distinctness of thought and power of mathematical invention, which
enabled him to force his way across the barrier. But another, and so
far as we know, an earlier train of thought, led by a different path
to the same result; and it was the convergence of these two lines of
reasoning that brought the conclusion to men's minds with
irresistible force. I speak now of the identification of the force
which retains the moon in her orbit with the force of gravity by
which bodies fall at the earth's surface. In this comparison Newton
had, so far as I am aware, no forerunner. We are now, therefore,
arrived at the point at which the history of Newton's great
discovery properly begins. {399}




CHAPTER II.

THE INDUCTIVE EPOCH OF NEWTON.--DISCOVERY OF THE UNIVERSAL
GRAVITATION OF MATTER, ACCORDING TO THE LAW OF THE INVERSE SQUARE OF
THE DISTANCE.


IN order that we may the more clearly consider the bearing of this,
the greatest scientific discovery ever made, we shall resolve it
into the partial propositions of which it consists. Of these we may
enumerate five. The doctrine of universal gravitation asserts,

1. That the force by which the _different_ planets are attracted to
the sun is in the inverse proportion of the squares of their
distances;

2. That the force by which the _same_ planet is attracted to the
sun, in different parts of its orbit, is also in the inverse
proportion of the squares of the distances;

3. That the _earth_ also exerts such a force on the _moon_, and that
this force is identical with the force of _gravity_;

4. That bodies thus act on _other_ bodies, besides those which
revolve round them; thus, that the sun exerts such a force on the
moon and satellites, and that the planets exert such forces on _one
another_;

5. That this force, thus exerted by the general masses of the sun,
earth, and planets, arises from the attraction of _each particle_ of
these masses; which attraction follows the above law, and belongs to
all matter alike.

The history of the establishment of these five truths will be given
in order.

1. _Sun's Force on Different Planets._--With regard to the first of
the above five propositions, that the different planets are
attracted to the sun by a force which is inversely as the square of
the distance, Newton had so far been anticipated, that several
persons had discovered it to be true, or nearly true; that is, they
had discovered that if the orbits of the planets were circles, the
proportions of the central force to the inverse square of the
distance would follow from Kepler's third law, of the sesquiplicate
proportion of the periodic times. As we have seen, Huyghens'
theorems would have proved this, if they had been so applied; Wren
knew it; Hooke not only knew it, but claimed a prior knowledge to
Newton; and Halley had satisfied himself that it was at {400} least
nearly true, before he visited Newton. Hooke was reported to Newton
at Cambridge, as having applied to the Royal Society to do him
justice with regard to his claims; but when Halley wrote and
informed Newton (in a letter dated June 29, 1686), that Hooke's
conduct "had been represented in worse colors than it ought," Newton
inserted in his book a notice of these his predecessors, in order,
as he said, "to compose the dispute."[25\7] This notice appears in a
Scholium to the fourth Proposition of the _Principia_, which states
the general law of revolutions in circles. "The case of the sixth
corollary," Newton there says, "obtains in the celestial bodies, as
has been separately inferred by our countrymen, Wren, Hooke, and
Halley;" he soon after names Huyghens, "who, in his excellent
treatise _De Horologio Oscillatorio_, compares the force of gravity
with the centrifugal forces of revolving bodies."

[Note 25\7: _Biog. Brit._ folio, art. _Hooke._]

The two steps requisite for this discovery were, to propose the
motions of the planets as simply a mechanical problem, and to apply
mathematical reasoning so as to solve this problem, with reference to
Kepler's third law considered as a fact. The former step was a
consequence of the mechanical discoveries of Galileo and his school;
the result of the firm and clear place which these gradually obtained
in men's mind, and of the utter abolition of all the notions of solid
spheres by Kepler. The mathematical step required no small
mathematical powers; as appears, when we consider that this was the
first example of such a problem, and that the method of limits, under
all its forms, was at this time in its infancy, or rather, at its
birth. Accordingly, even this step, though much the easiest in the
path of deduction, no one before Newton completely executed.

2. _Force in different Points of an Orbit._--The inference of the
law of the force from Kepler's two laws concerning the elliptical
motion, was a problem quite different from the preceding, and much
more difficult; but the dispute with respect to priority in the two
propositions was intermingled. Borelli, in 1666, had, as we have
seen, endeavored to reconcile the general form of the orbit with the
notion of a central attractive force, by taking centrifugal force
into the account; and Hooke, in 1679, had asserted that the result
of the law of the inverse square in the force of the earth would be
an ellipse,[26\7] or a curve like an ellipse.[27\7] But it does not
appear that this was any thing more than {401} a conjecture. Halley
says[28\7] that "Hooke, in 1683, told him he had demonstrated all
the laws of the celestial motions by the reciprocally duplicate
proportion of the force of gravity; but that, being offered forty
shillings by Sir Christopher Wren to produce such a demonstration,
his answer was, that he had it, but would conceal it for some time,
that others, trying and failing, might know how to value it when he
should make it public." Halley, however, truly observes, that after
the publication of the demonstration in the _Principia_, this reason
no longer held; and adds, "I have plainly told him, that unless he
produce another differing demonstration, and let the world judge of
it, neither I nor any one else can believe it."

[Note 26\7: Newton's Letter, _Biog. Brit._, Hooke, p. 2660.]

[Note 27\7: Birch's _Hist. R. S._, Wallis's Life.]

[Note 28\7: _Enc. Brit._, Hooke, p. 2660.]

Newton allows that Hooke's assertions in 1679 gave occasion to his
investigation on this point of the theory. His demonstration is
contained in the second and third Sections of the _Principia_. He
first treats of the general law of central forces in any curve; and
then, on account, as he states, of the application to the motion of
the heavenly bodies, he treats of the case of force varying
inversely as the square of the distance, in a more diffuse manner.

In this, as in the former portion of his discovery, the two steps
were, the proposing the heavenly motions as a mechanical problem,
and the solving this problem. Borelli and Hooke had certainly made
the former step, with considerable distinctness; but the
mathematical solution required no common inventive power.

Newton seems to have been much ruffled by Hooke's speaking slightly
of the value of this second step; and is moved in return to deny
Hooke's pretensions with some asperity, and to assert his own. He
says, in a letter to Halley, "Borelli did something in it, and wrote
modestly; he (Hooke) has done nothing; and yet written in such a way
as if he knew, and had sufficiently hinted all but what remained to
be determined by the drudgery of calculations and observations;
excusing himself from that labor by reason of his other business;
whereas he should rather have excused himself by reason of his
inability; for it is very plain, by his words, he knew not how to go
about it. Now is not this very fine? Mathematicians that find out,
settle, and do all the business, must content themselves with being
nothing but dry calculators and drudges; and another that does
nothing but pretend and grasp at all things, must carry away all the
inventions, as well of those that were to follow him as of those
that {402} went before." This was written, however, under the
influence of some degree of mistake; and in a subsequent letter,
Newton says, "Now I understand he was in some respects
misrepresented to me, I wish I had spared the postscript to my
last," in which is the passage just quoted. We see, by the melting
away of rival claims, the undivided honor which belongs to Newton,
as the real discoverer of the proposition now under notice. We may
add, that in the sequel of the third Section of the _Principia_, he
has traced its consequences, and solved various problems flowing
from it with his usual fertility and beauty of mathematical
resource; and has there shown the necessary connection of Kepler's
third law with his first and second.

3. _Moon's Gravity to the Earth._--Though others had considered
cosmical forces as governed by the general laws of motion, it does not
appear that they had identified such forces with the force of
terrestrial gravity. This step in Newton's discoveries has generally
been the most spoken of by superficial thinkers; and a false kind of
interest has been attached to it, from the story of its being
suggested by the fall of an apple. The popular mind is caught by the
character of an eventful narrative which the anecdote gives to this
occurrence; and by the antithesis which makes a profound theory appear
the result of a trivial accident. How inappropriate is such a view of
the matter we shall soon see. The narrative of the progress of
Newton's thoughts, is given by Pemberton (who had it from Newton
himself) in his preface to his _View of Newton's Philosophy_, and by
Voltaire, who had it from Mrs. Conduit, Newton's niece.[29\7] "The
first thoughts," we are told, "which gave rise to his _Principia_, he
had when he retired from Cambridge, in 1666, on account of the plague
(he was then twenty-four years of age). As he sat alone in a garden,
he fell into a speculation on the power of gravity; that as this power
is not found sensibly diminished at the remotest distance from the
centre of the earth to which we can rise, neither at the tops of the
loftiest buildings, nor even on the summits of the highest mountains,
it appeared to him reasonable to conclude that this power must extend
much further than was usually thought: Why not as high as the moon?
said he to himself; and if so, her motion must be influenced by it;
perhaps she is retained in her orbit thereby."

[Note 29\7: _Elémens de Phil. de Newton_, 3me partie, chap. iii.]

The thought of cosmical gravitation was thus distinctly brought into
being; and Newton's superiority here was, that he conceived the
{403} celestial motions as distinctly as the motions which took
place close to him;--considered them as of the same kind, and
applied the same rules to each, without hesitation or obscurity. But
so far, this thought was merely a guess: its occurrence showed the
activity of the thinker; but to give it any value, it required much
more than a "why not?"--a "perhaps." Accordingly, Newton's "why not?"
was immediately succeeded by his "if so, what then?" His reasoning
was, that if gravity reach to the moon, it is probably of the same
kind as the central force of the sun, and follows the same rule with
respect to the distance. What is this rule? We have already seen
that, by calculating from Kepler's laws, and supposing the orbits to
be circles, the rule of the force appears to be the inverse
duplicate proportion of the distance; and this, which had been
current as a conjecture among the previous generation of
mathematicians, Newton had already proved by indisputable
reasonings, and was thus prepared to proceed in his train of
inquiry. If, then, he went on, pursuing his train of thought, the
earth's gravity extend to the moon, diminishing according to the
inverse square of the distance, will it, at the moon's orbit, be of
the proper magnitude for retaining her in her path? Here again came
in calculation, and a calculation of extreme interest; for how
important and how critical was the decision which depended on the
resulting numbers? According to Newton's calculations, made at this
time, the moon by her motion in her orbit, was deflected from the
tangent every minute through a space of thirteen feet. But by
noticing the space through which bodies would fall in one minute at
the earth's surface, and supposing this to be diminished in the
ratio of the inverse square, it appeared that gravity would, at the
moon's orbit, draw a body through more than fifteen feet. The
difference seems small, the approximation encouraging, the theory
plausible; a man in love with his own fancies would readily have
discovered or invented some probable cause of this difference. But
Newton acquiesced in it as a disproof of his conjecture, and "laid
aside at that time any further thoughts of this matter;**" thus
resigning a favorite hypothesis, with a candor and openness to
conviction not inferior to Kepler, though his notion had been taken
up on far stronger and sounder grounds than Kepler dealt in; and
without even, so far as we know, Kepler's regrets and struggles. Nor
was this levity or indifference; the idea, though thus laid aside,
was not finally condemned and abandoned. When Hooke, in 1679,
contradicted Newton on the subject of the curve described by a
falling body, and asserted it to be an ellipse, Newton {404} was led
to investigate the subject, and was then again conducted, by another
road, to the same law of the inverse square of the distance. This
naturally turned his thoughts to his former speculations. Was there
really no way of explaining the discrepancy which this law gave,
when he attempted to reduce the moon's motion to the action of
gravity? A scientific operation then recently completed, gave the
explanation at once. He had been mistaken in the magnitude of the
earth, and consequently in the distance of the moon, which is
determined by measurements of which the earth's radius is the base.
He had taken the common estimate, current among geographers and
seamen, that sixty English miles are contained in one degree of
latitude. But Picard, in 1670, had measured the length of a certain
portion of the meridian in France, with far greater accuracy than
had yet been attained  and this measure enabled Newton to repeat his
calculations with these amended data. We may imagine the strong
curiosity which he must have felt as to the result of these
calculations. His former conjecture was now found to agree with the
phenomena to a remarkable degree of precision. This conclusion, thus
coming after long doubts and delays, and falling in with the other
results of mechanical calculation for the solar system, gave a stamp
from that moment to his opinions, and through him to those of the
whole philosophical world.

[2d Ed.] [Dr. Robison (_Mechanical Philosophy_, p. 288) says that
Newton having become a member of the Royal Society, there learned
the accurate measurement of the earth by Picard, differing very much
from the estimation by which he had made his calculations in 1666.
And M. Biot, in his Life of Newton, published in the _Biographie
Universelle_, says, "According to conjecture, about the month of
June, 1682, Newton being in London at a meeting of the Royal
Society, mention was made of the new measure of a degree of the
earth's surface, recently executed in France by Picard; and great
praise was given to the care which had been employed in making this
measure exact."

I had adopted this conjecture as a fact in my first edition; but it
has been pointed out by Prof. Rigaud (_Historical Essay on the First
Publication of the Principia_, 1838), that Picard's measurement was
probably well known to the Fellows of the Royal Society as early as
1675, there being an account of the results of it given in the
_Philosophical Transactions_ for that year. Newton appears to have
discovered the method of determining that a body might describe an
ellipse when acted upon by a force residing in the focus, and
varying {405} inversely as the square of the distance, in 1679, upon
occasion of his correspondence with Hooke. In 1684, at Halley's
request, he returned to the subject, and in February, 1685, there
was inserted in the Register of the Royal Society a paper of
Newton's (_Isaaci Newtoni Propositiones de Motu_) which contained
some of the principal Propositions of the first two Books of the
_Principia_. This paper, however, does not contain the Proposition
"Lunam gravitare in terram," nor any of the other propositions of
the third Book. The _Principia_ was printed in 1686 and 7,
apparently at the expense of Halley. On the 6th of April, 1687, the
third Book was presented to the Royal Society.]

It does not appear, I think, that before Newton, philosophers in
general had supposed that terrestrial gravity was the very force by
which the moon's motions are produced. Men had, as we have seen,
taken up the conception of such forces, and had probably called them
gravity: but this was done only to explain, by analogy, what _kind_
of forces they were, just as at other times they compared them with
magnetism; and it did not imply that terrestrial gravity was a force
which acted in the celestial spaces. After Newton had discovered
that this was so, the application of the term "gravity" did
undoubtedly convey such a suggestion; but we should err if we
inferred from this coincidence of expression that the notion was
commonly entertained before him. Thus Huyghens appears to use
language which may be mistaken, when he says,[30\7] that Borelli was
of opinion that the primary planets were urged by "gravity" towards
the sun, and the satellites towards the primaries. The notion of
terrestrial gravity, as being actually a cosmical force, is foreign
to all Borelli's speculations.[31\7] But Horrox, as early as 1635,
appears to have entertained the true view on this subject, although
vitiated by Keplerian errors concerning the connection between the
rotation of the central body and its effect on the body which
revolves about it. Thus he says,[32\7] that the emanation of the
earth carries a projected stone along with the motion of the earth,
just in the same way as it carries the moon in her orbit; and that
this force is greater on the stone than on the moon, because the
distance is less.

[Note 30\7: _**Cosmotheoros_, l. 2. p. 720.]

[Note 31\7: I have found no instance in which the word is so used by
him.]

[Note 32\7: _Astronomia Kepleriana defensa et promota_, cap. 2. See
further on this subject in the _Additions_ to this volume.]

The Proposition in which Newton has stated the discovery of which we
are now speaking, is the fourth of his third Book: "That the moon
gravitates to the earth, and by the force of gravity is perpetually
{406} deflected from a rectilinear motion, and retained in her
orbit." The proof consists in the numerical calculation, of which he
only gives the elements, and points out the method; but we may
observe, that no small degree of knowledge of the way in which
astronomers had obtained these elements, and judgment in selecting
among them, were necessary: thus, the mean distance of the moon had
been made as little as fifty-six and a half semidiameters of the
earth by Tycho, and as much as sixty-two and a half by Kircher:
Newton gives good reasons for adopting sixty-one.

The term "gravity," and the expression "to gravitate," which, as we
have just seen, Newton uses of the moon, were to receive a still
wider application in consequence of his discoveries; but in order to
make this extension clearer, we consider it as a separate step.

4. _Mutual Attraction of all the Celestial Bodies._--If the
preceding parts of the discovery of gravitation were comparatively
easy to conjecture, and difficult to prove, this was much more the
case with the part of which we have now to speak, the attraction of
other bodies, besides the central ones, upon the planets and
satellites. If the mathematical calculation of the unmixed effect of
a central force required transcendent talents, how much must the
difficulty be increased, when other influences prevented those first
results from being accurately verified, while the deviations from
accuracy were far more complex than the original action! If it had
not been that these deviations, though surprisingly numerous and
complicated in their nature, were very small in their quantity, it
would have been impossible for the intellect of man to deal with the
subject; as it was, the struggle with its difficulties is even now a
matter of wonder.

The conjecture that there is some mutual action of the planets, had
been put forth by Hooke in his _Attempt to prove the Motion of the
Earth_ (1674). It followed, he said, from his doctrine, that not
only the sun and moon act upon the course and motion of the earth,
but that Mercury, Venus, Mars, Jupiter, and Saturn, have also, by
their attractive power, a considerable influence upon the motion of
the earth, and the earth in like manner powerfully affects the
motions of those bodies. And Borelli, in attempting to form
"theories" of the satellites of Jupiter, had seen, though dimly and
confusedly, the probability that the sun would disturb the motions
of these bodies. Thus he says (cap. 14), "How can we believe that
the Medicean globes are not, like other planets, impelled with a
greater velocity when they approach the sun: and thus they are acted
upon by two moving forces, one of {407} which produces their proper
revolution about Jupiter, the other regulates their motion round the
sun." And in another place (cap. 20), he attempts to show an effect
of this principle upon the inclination of the orbit; though, as
might be expected, without any real result.

The case which most obviously suggests the notion that the sun
exerts a power to disturb the motions of secondary planets about
primary ones, might seem to be our own moon; for the great
inequalities which had hitherto been discovered, had all, except the
first, or elliptical anomaly, a reference to the position of the
sun. Nevertheless, I do not know that any one had attempted thus to
explain the curiously irregular course of the earth's attendant. To
calculate, from the disturbing agency, the amount of the
irregularities, was a problem which could not, at any former period,
have been dreamt of as likely to be at any time within the verge of
human power.

Newton both made the step of inferring that there were such forces,
and, to a very great extent, calculated the effects of them. The
inference is made on mechanical principles, in the sixth Theorem of
the third Book of the _Principia_;--that the moon is attracted by
the sun, as the earth is;--that the satellites of Jupiter and Saturn
are attracted as the primaries are; in the same manner, and with the
same forces. If this were not so, it is shown that these attendant
bodies could not accompany the principal ones in the regular manner
in which they do. All those bodies at equal distances from the sun
would be equally attracted.

But the complexity which must occur in tracing the results of this
principle will easily be seen. The satellite and the primary, though
nearly at the same distance, and in the same direction, from the
sun, are not exactly so. Moreover the difference of the distances
and of the directions is perpetually changing; and if the motion of
the satellite be elliptical, the cycle of change is long and
intricate: on this account alone the effects of the sun's action
will inevitably follow cycles as long and as perplexed as those of
the positions. But on another account they will be still more
complicated; for in the continued action of a force, the effect
which takes place at first, modifies and alters the effect
afterwards. The result at any moment is the sum of the results in
preceding instants: and since the terms, in this series of
instantaneous effects, follow very complex rules, the sums of such
series will be, it might be expected, utterly incapable of being
reduced to any manageable degree of simplicity.

It certainly does not appear that any one but Newton could make
{408} any impression on this problem, or course of problems. No one
for sixty years after the publication of the _Principia_, and, with
Newton's methods, no one up to the present day, had added any thing
of any value to his deductions. We know that he calculated all the
principal lunar inequalities; in many of the cases, he has given us
his processes; in others, only his results. But who has presented,
in his beautiful geometry, or deduced from his simple principles,
any of the inequalities which he left untouched? The ponderous
instrument of synthesis, so effective in his hands, has never since
been grasped by one who could use it for such purposes; and we gaze
at it with admiring curiosity, as on some gigantic implement of war,
which stands idle among the memorials of ancient days, and makes us
wonder what manner of man he was who could wield as a weapon what we
can hardly lift as a burden.

It is not necessary to point out in detail the sagacity and skill
which mark this part of the _Principia_. The mode in which the
author obtains the effect of a disturbing force in producing a
motion of the apse of an elliptical orbit (the ninth Section of the
first Book), has always been admired for its ingenuity and elegance.
The general statement of the nature of the principal inequalities
produced by the sun in the motion of a satellite, given in the
sixty-sixth Proposition, is, even yet, one of the best explanations
of such action; and the calculations of the quantity of the effects
in the third Book, for instance, the _variation_ of the moon, the
_motion of the nodes_ and its inequalities, the _change of
inclination_ of the orbit,--are full of beautiful and efficacious
artifices. But Newton's inventive faculty was exercised to an extent
greater than these published investigations show. In several cases
he has suppressed the demonstration of his method, and given us the
result only; either from haste or from mere weariness, which might
well overtake one who, while he was struggling with facts and
numbers, with difficulties of conception and practice, was aiming
also at that geometrical elegance of exposition, which he considered
as alone fit for the public eye. Thus, in stating the effect of the
eccentricity of the moon's orbit upon the motion of the apogee, he
says,[33\7] "The computations, as too intricate and embarrassed with
approximations, I do not choose to introduce."

[Note 33\7: Schol. to Prop. 35, first edit.]

The computations of the theoretical motion of the moon being thus
difficult, and its irregularities numerous and complex, we may ask
{409} whether Newton's reasoning was sufficient to establish this
part of his theory; namely, that her actual motions arise from her
gravitation to the sun. And to this we may reply, that it was
sufficient for that purpose,--since it showed that, from Newton's
hypothesis, inequalities must result, following the laws which the
moon's inequalities were known to follow;--since the amount of the
inequalities given by the theory agreed nearly with the rules which
astronomers had collected from observation;--and since, by the very
intricacy of the calculation, it was rendered probable, that the
first results might be somewhat inaccurate, and thus might give rise
to the still remaining differences between the calculations and the
facts. A _Progression of the Apogee_; a _Regression of the Nodes_;
and, besides the Elliptical, or first Inequality, an inequality,
following the law of the _Evection_, or second inequality discovered
by Ptolemy; another, following the law of the _Variation_ discovered
by Tycho;--were pointed out in the first edition of the _Principia_,
as the consequences of the theory. Moreover, the quantities of these
inequalities were calculated and compared with observation with the
utmost confidence, and the agreement in most instances was striking.
The Variation agreed with Halley's recent observations within a
minute of a degree.[34\7] The Mean Motion of the Nodes in a year
agreed within less than one-hundredth of the whole.[35\7] The
Equation of the Motion of the Nodes also agreed well.[36\7] The
Inclination of the Plane of the Orbit to the ecliptic, and its
changes, according to the different situations of the nodes,
likewise agreed.[37\7] The Evection has been already noticed as
encumbered with peculiar difficulties: here the accordance was less
close. The Difference of the daily progress of the Apogee in syzygy,
and its daily Regress in Quadratures, is, Newton says, "4¼ minutes
by the Tables, 6⅔ by our calculation." He boldly adds, "I suspect
this difference to be due to the fault of the Tables." In the second
edition (1711) he added the calculation of several other
inequalities, as the _Annual Equation_, also discovered by Tycho;
and he compared them with more recent observations made by Flamsteed
at Greenwich; but even in what has already been stated, it must be
allowed that there is a wonderful accordance of theory with
phenomena, both being very complex in the rules which they educe.

[Note 34\7: B. iii. Prop. 29.]

[Note 35\7: Prop. 32.]

[Note 36\7: Prop. 33.]

[Note 37\7: Prop. 35.]

The same theory which gave these Inequalities in the motion of the
Moon produced by the disturbing force of the sun, gave also {410}
corresponding Inequalities in the motions of the Satellites of other
planets, arising from the same cause; and likewise pointed out the
necessary existence of irregularities in the motions of the Planets
arising from their mutual attraction. Newton gave propositions by
which the Irregularities of the motion of Jupiter's moons might be
deduced from those of our own;[38\7] and it was shown that the
motions of their nodes would be slow by theory, as Flamsteed had
found it to be by observation.[39\7] But Newton did not attempt to
calculate the effect of the mutual action of the planets, though he
observes, that in the case of Jupiter and Saturn this effect is too
considerable to be neglected;[40\7] and he notices in the second
edition,[41\7] that it follows from the theory of gravity, that the
aphelia of Mercury, Venus, the Earth, and Mars, slightly progress.

[Note 38\7: B. i. Prop. 66.]

[Note 39\7: B. iii. Prop. 23.]

[Note 40\7: B. iii. Prop. 13.]

[Note 41\7: Scholium to Prop. 14. B. iii.]

In one celebrated instance, indeed, the deviation of the theory of
the _Principia_ from observation was wider, and more difficult to
explain; and as this deviation for a time resisted the analysis of
Euler and Clairaut, as it had resisted the synthesis of Newton, it
at one period staggered the faith of mathematicians in the exactness
of the law of the inverse square of the distance. I speak of the
Motion of the Moon's Apogee, a problem which has already been
referred to; and in which Newton's method, and all the methods which
could be devised for some time afterwards, gave only half the
observed motion; a circumstance which arose, as was discovered by
Clairaut in 1750, from the insufficiency of the method of
approximation. Newton does not attempt to conceal this discrepancy.
After calculating what the motion of apse would be, upon the
assumption of a disturbing force of the same amount as that which
the sun exerts on the moon, he simply says,[42\7] "the apse of the
moon moves about twice as fast."

[Note 42\7: B. i. Prop. 44, second edit. There is reason to believe,
however, that Newton had, in his unpublished calculations, rectified
this discrepancy.]

The difficulty of doing what Newton did in this branch of the
subject, and the powers it must have required, may be judged of from
what has already been stated;--that no one, with his methods, has
yet been able to add any thing to his labors: few have undertaken to
illustrate what he has written, and no great number have understood
it throughout. The extreme complication of the forces, and of the
conditions under which they act, makes the subject by far the most
thorny walk of mathematics. It is necessary to resolve the action
{411} into many elements, such as can be separated; to invent
artifices for dealing with each of these; and then to recompound the
laws thus obtained into one common conception. The moon's motion
cannot be conceived without comprehending a scheme more complex than
the Ptolemaic epicycles and eccentrics in their worst form; and the
component parts of the system are not, in this instance, mere
geometrical ideas, requiring only a distinct apprehension of
relations of space in order to hold them securely; they are the
foundations of mechanical notions, and require to be grasped so that
we can apply to them sound mechanical reasonings. Newton's
successors, in the next generation, abandoned the hope of imitating
him in this intense mental effort; they gave the subject over to the
operation of algebraical reasoning, in which symbols think for us,
without our dwelling constantly upon their meaning, and obtain for
us the consequences which result from the relations of space and the
laws of force, however complicated be the conditions under which
they are combined. Even Newton's countrymen, though they were long
before they applied themselves to the method thus opposed to his,
did not produce any thing which showed that they had mastered, or
could retrace, the Newtonian investigations.

Thus the Problem of Three Bodies,[43\7] treated geometrically,
belongs exclusively to Newton; and the proofs of the mutual action
of the sun, planets, and satellites, which depend upon such
reasoning, could not be discovered by any one but him.

[Note 43\7: See the history of the _Problem of Three Bodies_,
_ante_, in Book vi. Chap. vi. Sect. 7.]

But we have not yet done with his achievements on this subject; for
some of the most remarkable and beautiful of the reasonings which he
connected with this problem, belong to the next step of his
generalization.

5. _Mutual Attraction of all Particles of Matter._--That all the
parts of the universe are drawn and held together by love, or
harmony, or some affection to which, among other names, that of
attraction may have been given, is an assertion which may very
possibly have been made at various times, by speculators writing at
random, and taking their chance of meaning and truth. The authors of
such casual dogmas have generally nothing accurate or substantial,
either in their conception of the general proposition, or in their
reference to examples of it; and, therefore, their doctrines are no
concern of ours at present. But among those who were really the
first to think of the mutual {412} attraction of matter, we cannot
help noticing Francis Bacon; for his notions were so far from being
chargeable with the looseness and indistinctness to which we have
alluded, that he proposed an experiment[44\7] which was to decide
whether the facts were so or not;--whether the gravity of bodies to
the earth arose from an attraction of the parts of matter towards
each other, or was a tendency towards the centre of the earth. And
this experiment is, even to this day, one of the best which can be
devised, in order to exhibit the universal gravitation of matter: it
consists in the comparison of the rate of going of a clock in a deep
mine, and on a high place. Huyghens, in his book _De Causâ
Gravitatis_, published in 1690, showed that the earth would have an
oblate form, in consequence of the action of the centrifugal force;
but his reasoning does not suppose gravity to arise from the mutual
attraction of the parts of the earth. The apparent influence of the
moon upon the tides had long been remarked; but no one had made any
progress in truly explaining the mechanism of this influence; and
all the analogies to which reference had been made, on this and
similar subjects, as magnetic and other attractions, were rather
delusive than illustrative, since they represented the attraction as
something peculiar in particular bodies, depending upon the nature
of each body.

[Note 44\7:  _Nov. Org._ Lib. ii. Aph. 36.]

That all such forces, cosmical and terrestrial, were the same single
force, and that this was nothing more than the insensible attraction
which subsists between one stone and another, was a conception
equally bold and grand; and would have been an incomprehensible
thought, if the views which we have already explained had not
prepared the mind for it. But the preceding steps having disclosed,
between all the bodies of the universe, forces of the same kind as
those which produce the weight of bodies at the earth, and,
therefore, such as exist in every particle of terrestrial matter; it
became an obvious question, whether such forces did not also belong
to all particles of planetary matter, and whether this was not, in
fact, the whole account of the forces of the solar system. But,
supposing this conjecture to be thus suggested, how formidable, on
first appearance at least, was the undertaking of verifying it! For
if this be so, every finite mass of matter exerts forces which are
the result of the infinitely numerous forces of its particles, these
forces acting in different directions. It does not appear, at first
sight, that the law by which the force is related to the distance,
will be the same for the particles as it is for the masses; and, in
reality, it {413} is not so, except in special cases. And, again, in
the instance of any effect produced by the force of a body, how are
we to know whether the force resides in the whole mass as a unit, or
in the separate particles? We may reason, as Newton does,[45\7] that
the rule which proves gravity to belong universally to the planets,
proves it also to belong to their parts; but the mind will not be
satisfied with this extension of the rule, except we can find
decisive instances, and calculate the effects of both suppositions,
under the appropriate conditions. Accordingly, Newton had to solve a
new series of problems suggested by this inquiry; and this he did.

[Note 45\7: _Princip._ B. iii. Prop. 7.]

These solutions are no less remarkable for the mathematical power
which they exhibit, than the other parts of the _Principia_. The
propositions in which it is shown that the law of the inverse square
for the particles gives the same law for spherical masses, have that
kind of beauty which might well have justified their being published
for their mathematical elegance alone, even if they had not applied to
any real case. Great ingenuity is also employed in other instances, as
in the case of spheroids of small eccentricity. And when the amount of
the mechanical action of masses of various forms has thus been
assigned, the sagacity shown in tracing the results of such action in
the solar system is truly admirable; not only the general nature of
the effect being pointed out, but its quantity calculated. I speak in
particular of the reasonings concerning the Figure of the Earth, the
Tides, the Precession of the Equinoxes, the Regression of the Nodes of
a ring such as Saturn's; and of some effects which, at that time, had
not been ascertained even as facts of observation; for instance, the
difference of gravity in different latitudes, and the Nutation of the
earth's axis. It is true, that in most of these cases, Newton's
process could be considered only as a rude approximation. In one (the
Precession) he committed an error, and in all, his means of
calculation were insufficient. Indeed these are much more difficult
investigations than the Problem of Three Bodies, in which three points
act on each other by explicit laws. Up to this day, the resources of
modern analysis have been employed upon some of them with very partial
success; and the facts, in all of them, required to be accurately
ascertained and measured, a process which is not completed even now.
Nevertheless the form and nature of the conclusions which Newton did
obtain, were such as to inspire a strong confidence in the competency
of his theory to explain {414} all such phenomena as have been spoken
of. We shall afterwards have to speak of the labors, undertaken in
order to examine the phenomena more exactly, to which the theory gave
occasion.

Thus, then, the theory of the universal mutual gravitation of all
the particles of matter, according to the law of the inverse square
of the distances, was conceived, its consequences calculated, and
its results shown to agree with phenomena. It was found that this
theory took up all the facts of astronomy as far as they had
hitherto been ascertained; while it pointed out an interminable
vista of new facts, too minute or too complex for observation alone
to disentangle, but capable of being detected when theory had
pointed out their laws, and of being used as criteria or
confirmations of the truth of the doctrine. For the same reasoning
which explained the evection, variation, and annual equation of the
moon, showed that there must be many other inequalities besides
these; since these resulted from approximate methods of calculation,
in which small quantities were neglected. And it was known that, in
fact, the inequalities hitherto detected by astronomers did not give
the place of the moon with satisfactory accuracy; so that there was
room, among these hitherto untractable irregularities, for the
additional results of the theory. To work out this comparison was
the employment of the succeeding century; but Newton began it. Thus,
at the end of the proposition in which he asserts,[46\7] that "all
the lunar motions and their irregularities follow from the
principles here stated," he makes the observation which we have just
made; and gives, as examples, the different motions of the apogee
and nodes, the difference of the change of the eccentricity, and the
difference of the moon's variation, according to the different
distances of the sun. "But this inequality," he says, "in
astronomical calculations, is usually referred to the prosthaphæresis
of the moon, and confounded with it."

[Note 46\7: B. iii. Prop. 22.]

_Reflections on the Discovery._--Such, then, is the great Newtonian
Induction of Universal Gravitation, and such its history. It is
indisputably and incomparably the greatest scientific discovery ever
made, whether we look at the advance which it involved, the extent
of the truth disclosed, or the fundamental and satisfactory nature
of this truth. As to the first point, we may observe that any one of
the five steps into which we have separated the doctrine, would, of
itself, have been considered as an important advance;--would have
conferred distinction on the persons who made it, and the time to
which it belonged. All {415} the five steps made at once, formed not
a leap, but a flight,--not an improvement merely, but a
metamorphosis,--not an epoch, but a termination. Astronomy passed at
once from its boyhood to mature manhood. Again, with regard to the
extent of the truth, we obtain as wide a generalization as our
physical knowledge admits, when we learn that every particle of
matter, in all times, places, and circumstances, attracts every
other particle in the universe by one common law of action. And by
saying that the truth was of a fundamental and satisfactory nature,
I mean that it assigned, not a rule merely, but a cause, for the
heavenly motions; and that kind of cause which most eminently and
peculiarly we distinctly and thoroughly conceive, namely, mechanical
force. Kepler's laws were merely _formal_ rules, governing the
celestial motions according to the relations of space, time, and
number; Newton's was a _**causal_ law, referring these motions to
mechanical reasons. It is no doubt conceivable that future
discoveries may both extend and further explain Newton's
doctrines;--may make gravitation a case of some wider law, and may
disclose something of the mode in which it operates; questions with
which Newton himself struggled. But, in the mean time, few persons
will dispute, that both in generality and profundity, both in width
and depth, Newton's theory is altogether without a rival or
neighbor.[47\7]

[Note 47\7: The value and nature of this step have long been
generally acknowledged wherever science is cultivated. Yet it would
appear that there is, in one part of Europe, a school of
philosophers who contest the merit of this part of Newton's
discoveries. "Kepler," says a celebrated German metaphysician,*
"discovered the laws of free motion; a discovery of immortal glory.
It has since been the fashion to say that Newton first found out the
proof of these rules. It has seldom happened that the glory of the
first discoverer has been more unjustly transferred to another
person." It may appear strange that any one in the present day
should hold such language; but if we examine the reasons which this
author gives, they will be found, I think, to amount to this: that
his mind is in the condition in which Kepler's was; and that the
whole range of mechanical ideas and modes of conception which made
the transition from Kepler and Newton possible, are extraneous to
the domain of his philosophy. Even this author, however, if I
understand him rightly, recognizes Newton as the author of the
doctrine of Perturbations.

I have given a further account of these views, in a Memoir _On Hegel's
Criticism of Newton's Principia_. Cambridge Transactions, 1849.

* Hegel, _Encyclopædia_, § 270.]

The requisite conditions of such a discovery in the mind of its author
were, in this as in other cases, the idea, and its comparison with
facts;--the conception of the law, and the moulding this conception in
such a form as to correspond with known realities. The idea of
mechanical {416} force as the cause of the celestial motions, had, as
we have seen, been for some time growing up in men's minds; had gone
on becoming more distinct and more general; and had, in some persons,
approached the form in which it was entertained by Newton. Still, in
the mere conception of universal gravitation, Newton must have gone
far beyond his predecessors and contemporaries, both in generality and
distinctness; and in the inventiveness and sagacity with which he
traced the consequences of this conception, he was, as we have shown,
without a rival, and almost without a second. As to the facts which he
had to include in his law, they had been accumulating from the very
birth of astronomy; but those which he had more peculiarly to take
hold of were the facts of the planetary motions as given by Kepler,
and those of the moon's motions as given by Tycho Brahe and Jeremy
Horrox.

We find here occasion to make a remark which is important in its
bearing on the nature of progressive science. What Newton thus used
and referred to as _facts_, were the _laws_ which his predecessors had
established. What Kepler and Horrox had put forth as "theories," were
now established truths, fit to be used in the construction of other
theories. It is in this manner that one theory is built upon
another;--that we rise from particulars to generals, and from one
generalization to another;--that we have, in short, successive steps
of induction. As Newton's laws assumed Kepler's, Kepler's laws assumed
as facts the results of the planetary theory of Ptolemy; and thus the
theories of each generation in the scientific world are (when
thoroughly verified and established,**) the facts of the next
generation. Newton's theory is the circle of generalization which
includes all the others;--the highest point of the inductive
ascent;--the catastrophe of the philosophic drama to which Plato had
prologized;--the point to which men's minds had been journeying for
two thousand years.

_Character of Newton._--It is not easy to anatomize the constitution
and the operations of the mind which makes such an advance in
knowledge. Yet we may observe that there must exist in it, in an
eminent degree, the elements which compose the mathematical talent. It
must possess distinctness of intuition, tenacity and facility in
tracing logical connection, fertility of invention, and a strong
tendency to generalization. It is easy to discover indications of
these characteristics in Newton. The distinctness of his intuitions of
space, and we may add of force also, was seen in the amusements of his
youth; in his constructing clocks and mills, carts and dials, as well
as the facility with which he {417} mastered geometry. This fondness
for handicraft employments, and for making models and machines,
appears to be a common prelude of excellence in physical
science;[48\7] probably on this very account, that it arises from the
distinctness of intuitive power with which the child conceives the
shapes and the working of such material combinations. Newton's
inventive power appears in the number and variety of the mathematical
artifices and combinations which he devised, and of which his books
are full. If we conceive the operation of the inventive faculty in the
only way in which it appears possible to conceive it;--that while some
hidden source supplies a rapid stream of possible suggestions, the
mind is on the watch to seize and detain any one of these which will
suit the case in hand, allowing the rest to pass by and be
forgotten;--we shall see what extraordinary fertility of mind is
implied by so many successful efforts; what an innumerable host of
thoughts must have been produced, to supply so many that deserved to
be selected. And since the selection is performed by tracing the
consequences of each suggestion, so as to compare them with the
requisite conditions, we see also what rapidity and certainty in
drawing conclusions the mind must possess as a talent, and what
watchfulness and patience as a habit.

[Note 48\7: As in Galileo, Hooke, Huyghens, and others.]

The hidden fountain of our unbidden thoughts is for us a mystery;
and we have, in our consciousness, no standard by which we can
measure our own talents; but our acts and habits are something of
which we are conscious; and we can understand, therefore, how it was
that Newton could not admit that there was any difference between
himself and other men, except in his possession of such habits as we
have mentioned, perseverance and vigilance. When he was asked how he
made his discoveries, he answered, "by always thinking about them;"
and at another time he declared that if he had done any thing, it
was due to nothing but industry and patient thought: "I keep the
subject of my inquiry constantly before me, and wait till the first
dawning opens gradually, by little and little, into a full and clear
light." No better account can be given of the nature of the mental
_effort_ which gives to the philosopher the full benefit of his
powers; but the natural _powers_ of men's minds are not on that
account the less different. There are many who might wait through
ages of darkness without being visited by any dawn.

The habit to which Newton thus, in some sense, owed his {418}
discoveries, this constant attention to the rising thought, and
development of its results in every direction, necessarily engaged
and absorbed his spirit, and made him inattentive and almost
insensible to external impressions and common impulses. The stories
which are told of his extreme absence of mind, probably refer to the
two years during which he was composing his _Principia_, and thus
following out a train of reasoning the most fertile, the most
complex, and the most important, which any philosopher had ever had
to deal with. The magnificent and striking questions which, during
this period, he must have had daily rising before him; the perpetual
succession of difficult problems of which the solution was necessary
to his great object; may well have entirely occupied and possessed
him. "He existed only to calculate and to think."[49\7] Often, lost
in meditation, he knew not what he did, and his mind appeared to
have quite forgotten its connection with the body. His servant
reported that, on rising in a morning, he frequently sat a large
portion of the day, half-dressed, on the side of his bed  and that
his meals waited on the table for hours before he came to take them.
Even with his transcendent powers, to do what he did was almost
irreconcilable with the common conditions of human life; and
required the utmost devotion of thought, energy of effort, and
steadiness of will--the strongest character, as well as the highest
endowments, which belong to man.

[Note 49\7:  Biot.]

Newton has been so universally considered as the greatest example of
a natural philosopher, that his moral qualities, as well as his
intellect, have been referred to as models of the philosophical
character; and those who love to think that great talents are
naturally associated with virtue, have always dwelt with pleasure
upon the views given of Newton by his contemporaries; for they have
uniformly represented him as candid and humble, mild and good. We
may take as an example of the impressions prevalent about him in his
own time, the expressions of Thomson, in the Poem on his
Death.[50\7] {419}
  Say ye who best can tell, ye happy few,
  Who saw him in the softest lights of life,
  All unwithheld, indulging to his friends
  The vast unborrowed treasures of his mind,
  Oh, speak the wondrous man! how mild, how calm
  How greatly humble, how divinely good,
  How firm established on eternal truth!
  Fervent in doing well, with every nerve
  Still pressing on, forgetful of the past,
  And panting for perfection; far above
  Those little cares and visionary joys
  That so perplex the fond impassioned heart
  Of ever-cheated, ever-trusting man.

[Note 50\7: In the same strain we find the general voice of the
time. For instance, one of Loggan's "Views of Cambridge" is
dedicated "Isaaco Newtono . . Mathematico, Physico, Chymico
consummatissimo; nec minus suavitate morum  et candore animi . . .
spectabili."

In opposition to the general current of such testimony, we have the
complaints of Flamsteed, who ascribes to Newton angry language and
harsh conduct in the matter of the publication of the Greenwich
Observations, and of Whiston. Yet even Flamsteed speaks well of his
general disposition. Whiston was himself so weak and prejudiced that
his testimony is worth very little.]

[2d Ed.] [In the first edition of the _Principia_, published in
1687, Newton showed that the nature of all the then known
inequalities of the moon, and in some cases, their quantities, might
be deduced from the principles which he laid down  but the
determination of the amount and law of most of the inequalities was
deferred to a more favorable opportunity, when he might be furnished
with better astronomical observations. Such observations as he
needed for this purpose had been made by Flamsteed, and for these he
applied, representing how much value their use would add to the
observations. "If," he says, in 1694, "you publish them without such
a theory to recommend them, they will only be thrown into the heap
of the observations of former astronomers, till somebody shall arise
that by perfecting the theory of the moon shall discover your
observations to be exacter than the rest; but when that shall be,
God knows: I fear, not in your lifetime, if I should die before it
is done. For I find this theory so very intricate, and the theory of
gravity so necessary to it, that I am satisfied it will never be
perfected but by somebody who understands the theory of gravity as
well, or better than I do." He obtained from Flamsteed the lunar
observations for which he applied, and by using these he framed the
Theory of the Moon which is given as his in David Gregory's
_Astronomiæ Elementa_.[51\7] He also obtained from Flamsteed the
diameters of the planets as observed at various times, and the
greatest elongation of Jupiter's Satellites, both of which,
Flamsteed says, he made use of in his _Principia_.

[Note 51\7: In the Preface to a _Treatise on Dynamics_, Part i.,
published in 1836, I have endeavored to show that Newton's modes of
determining several of the lunar inequalities admitted of an
accuracy not very inferior to the modern analytical methods.]

Newton, in his letters to Flamsteed in 1694 and 5, acknowledges this
service.[52\7]**] {420}

[Note 52\7: The quarrel on the subject of the publication of
Flamsteed's Observations took place at a later period. Flamsteed
wished to have his Observations printed complete and entire. Halley,
who, under the authority of Newton and others, had the management of
the printing, made many alterations and omissions, which Flamsteed
considered as deforming and spoiling the work. The advantages of
publishing a _complete_ series of observations, now generally
understood, were not then known to astronomers in general, though
well known to Flamsteed, and earnestly insisted upon in his
remonstrances. The result was that Flamsteed published his
Observations at his own expense, and finally obtained permission to
destroy the copies printed by Halley, which he did. In 1726, after
Flamsteed's death, his widow applied to the Vice-Chancellor of
Oxford, requesting that the volume printed by Halley might be
removed out of the Bodleian Library, where it exists, as being
"nothing more than an erroneous abridgment of Mr. Flamsteed's
works," and unfit to see the light.]




CHAPTER III.

SEQUEL TO THE EPOCH OF NEWTON.--RECEPTION OF THE NEWTONIAN THEORY.


_Sect._ 1.--_General Remarks._

THE doctrine of universal gravitation, like other great steps in
science, required a certain time to make its way into men's minds;
and had to be confirmed, illustrated, and completed, by the labors
of succeeding philosophers. As the discovery itself was great beyond
former example, the features of the natural sequel to the discovery
were also on a gigantic scale; and many vast and laborious trains of
research, each of which might, in itself, be considered as forming a
wide science, and several of which have occupied many profound and
zealous inquirers from that time to our own day, come before us as
parts only of the verification of Newton's Theory. Almost every
thing that has been done, and is doing, in astronomy, falls
inevitably under this description; and it is only when the
astronomer travels to the very limits of his vast field of labor,
that he falls in with phenomena which do not acknowledge the
jurisdiction of the Newtonian legislation. We must give some account
of the events of this part of the history of astronomy; but our
narrative must necessarily be extremely brief and imperfect; for the
subject is most large and copious, and our limits are fixed and
narrow. We have here to do with the history of discoveries, only so
far as it illustrates their philosophy. And though the {421}
astronomical discoveries of the last century are by no means poor,
even in interest of this kind, the generalizations which they
involve are far less important for our object, in consequence of
being included in a previous generalization. Newton shines out so
brightly, that all who follow seem faint and dim. It is not
precisely the case which the poet describes--
  As in a theatre the eyes of men,
  After some well-graced actor leaves the stage,
  Are idly bent on him that enters next,
  Thinking his prattle to be tedious:
but our eyes are at least less intently bent on the astronomers who
succeeded, and we attend to their communications with less
curiosity, because we know the end, if not the course of their
story; we know that their speeches have all closed with Newton's
sublime declaration, asserted in some new form.

Still, however, the account of the verification and extension of any
great discovery is a highly important part of its history. In this
instance it is most important; both from the weight and dignity of
the theory concerned, and the ingenuity and extent of the methods
employed: and, of course, so long as the Newtonian theory still
required verification, the question of the truth or falsehood of
such a grand system of doctrines could not but excite the most
intense curiosity. In what I have said, I am very far from wishing
to depreciate the value of the achievements of modern astronomers,
but it is essential to my purpose to mark the subordination of
narrower to wider truths--the different character and import of the
labors of those who come before and after the promulgation of a
master-truth. With this warning I now proceed to my narrative.


_Sect._ 2.--_Reception of the Newtonian Theory in England._

THERE appears to be a popular persuasion that great discoveries are
usually received with a prejudiced and contentious opposition, and
the authors of them neglected or persecuted. The reverse of this was
certainly the case in England with regard to the discoveries of
Newton. As we have already seen, even before they were published,
they were proclaimed by Halley to be something of transcendent
value; and from the moment of their appearance, they rapidly made
their way from one class of thinkers to another, nearly as fast as
the nature of men's intellectual capacity allows. Halley, Wren, and
all the leading {422} members of the Royal Society, appear to have
embraced the system immediately and zealously. Men whose pursuits
had lain rather in literature than in science, and who had not the
knowledge and habits of mind which the strict study of the system
required, adopted, on the credit of their mathematical friends, the
highest estimation of the _Principia_, and a strong regard for its
author, as Evelyn, Locke, and Pepys. Only five years after the
publication, the principles of the work were referred to from the
pulpit, as so incontestably proved that they might be made the basis
of a theological argument. This was done by Dr. Bentley, when he
preached the Boyle's Lectures in London, in 1692. Newton himself,
from the time when his work appeared, is never mentioned except in
terms of profound admiration; as, for instance, when he is called by
Dr. Bentley, in his sermon,[53\7] "That very excellent and divine
theorist, Mr. Isaac Newton." It appears to have been soon suggested,
that the Government ought to provide in some way for a person who
was so great an honor to the nation. Some delay took place with
regard to this; but, in 1695, his friend Mr. Montague, afterwards
Earl of Halifax, at that time Chancellor of the Exchequer, made him
Warden of the Mint; and in 1699, he succeeded to the higher office
of Master of the Mint, a situation worth £1200 or £1500 a year,
which he filled to the end of his life. In 1703, he became President
of the Royal Society, and was annually re-elected to this office
during the remaining twenty-five years of his life. In 1705, he was
knighted in the Master's Lodge, at Trinity College, by Queen Anne,
then on a visit to the University of Cambridge. After the accession
of George the First, Newton's conversation was frequently sought by
the Princess, afterwards Queen Caroline, who had a taste for
speculative studies, and was often heard to declare in public, that
she thought herself fortunate in living at a time which enabled her
to enjoy the society of so great a genius. His fame, and the respect
paid him, went on increasing to the end of his life; and when, in
1727, full of years and glory, his earthly career was ended, his
death was mourned as a national calamity, with the forms usually
confined to royalty. His body lay in state in the Jerusalem chamber;
his pall was borne by the first nobles of the land  and his earthly
remains were deposited in the centre of Westminster Abbey, in the
midst of the memorials of the greatest and wisest men whom England
has produced.

[Note 53\7: Serm. vii. 221.]

It cannot be superfluous to say a word or two on the reception of
{423} his philosophy in the universities of England. These are often
represented as places where bigotry and ignorance resist, as long as
it is possible to resist, the invasion of new truths. We cannot
doubt that such opinions have prevailed extensively, when we find an
intelligent and generally temperate writer, like the late Professor
Playfair of Edinburgh, so far possessed by them, as to be incapable
of seeing, or interpreting, in any other way, any facts respecting
Oxford and Cambridge. Yet, notwithstanding these opinions, it will
be found that, in the English universities, new views, whether in
science or in other subjects, have been introduced as soon as they
were clearly established;--that they have been diffused from the few
to the many more rapidly there than elsewhere occurs;--and that from
these points, the light of newly-discovered truths has most usually
spread over the land. In most instances undoubtedly there has been
something of a struggle, on such occasions, between the old and the
new opinions. Few men's minds can at once shake off a familiar and
consistent system of doctrines, and adopt a novel and strange set of
principles as soon as presented; but all can see that one change
produces many, and that change, in itself, is a source of
inconvenience and danger. In the case of the admission of the
Newtonian opinions into Cambridge and Oxford, however, there are no
traces even of a struggle. Cartesianism had never struck its roots
deep in this country; that is, the peculiar hypotheses of Descartes.
The Cartesian books, such, for instance, as that of Rohault, were
indeed in use; and with good reason, for they contained by far the
best treatises on most of the physical sciences, such as Mechanics,
Hydrostatics, Optics, and Formal Astronomy, which could then be
found. But I do not conceive that the Vortices were ever dwelt upon
as a matter of importance in our academic teaching. At any rate, if
they were brought among us, they were soon dissipated. Newton's
College, and his University, exulted in his fame, and did their
utmost to honor and aid him. He was exempted by the king from the
obligation of taking orders, under which the fellows of Trinity
College in general are; by his college he was relieved from all
offices which might interfere, however slightly, with his studious
employments, though he resided within the walls of the society
thirty-five years, almost without the interruption of a month.[54\7]
By the University he was elected their representative in parliament
in 1688, {424} and again in 1701; and though he was rejected in the
dissolution of 1705, those who opposed him acknowledged him[55\7] to
be "the glory of the University and nation," but considered the
question as a political one, and Newton as sent "to tempt them from
their duty, by the great and just veneration they had for him."
Instruments and other memorials, valued because they belonged to
him, are still preserved in his college, along with the tradition of
the chambers which he occupied.

[Note 54\7: His name is nowhere found on the college-books, as
appointed to any of the offices which usually pass down the list of
resident fellows in rotation. This might be owing in part, however,
to his being Lucasian Professor. The constancy of his residence in
college appears from the _exit_ and _redit_ book of that time, which
is still preserved.]

[Note 55\7: A pamphlet by Styan Thurlby.]

The most active and powerful minds at Cambridge became at once
disciples and followers of Newton. Samuel Clarke, afterwards his
friend, defended in the public schools a thesis taken from his
philosophy, as early as 1694; and in 1697 published an edition of
Rohault's _Physics_, with notes, in which Newton is frequently
referred to with expressions of profound respect, though the leading
doctrines of the _Principia_ are not introduced till a later
edition, in 1703. In 1699, Bentley, whom we have already mentioned
as a Newtonian, became Master of Trinity College; and in the same
year, Whiston, another of Newton's disciples, was appointed his
deputy as professor of mathematics. Whiston delivered the Newtonian
doctrines, both from the professor's chair, and in works written for
the use of the University; yet it is remarkable that a taunt
respecting the late introduction of the Newtonian system into the
Cambridge course of education, has been founded on some peevish
expressions which he uses in his Memoirs, written at a period when,
having incurred expulsion from his professorship and the University,
he was naturally querulous and jaundiced in his views. In 1709-10,
Dr. Laughton, who was tutor in Clare Hall, procured himself to be
appointed moderator of the University disputations, in order to
promote the diffusion of the new mathematical doctrines. By this
time the first edition of the _Principia_ was become rare, and
fetched a great price. Bentley urged Newton to publish a new one;
and Cotes, by far the first, at that time, of the mathematicians of
Cambridge, undertook to superintend the printing, and the edition
was accordingly published in 1713.

[2d Ed.] [I perceive that my accomplished German translator,
Littrow, has incautiously copied the insinuations of some modern
writers to the effect that Clarke's reference to Newton, in his
Edition of Rohault's _Physics_, was a mode of introducing Newtonian
doctrines covertly, when it was not allowed him to introduce such
novelties {425} openly. I am quite sure that any one who looks into
this matter will see that this supposition of any unwillingness at
Cambridge to receive Newton's doctrine is quite absurd, and can
prove nothing but the intense prejudices of those who maintain such
an opinion. Newton received and held his professorship amid the
unexampled admiration of all contemporary members of the University.
Whiston, who is sometimes brought as an evidence against Cambridge
on this point, says, "I with immense pains set myself with the
utmost zeal to the study of Sir Isaac Newton's wonderful discoveries
in his _Philosophiæ Naturalis Principia Mathematica_, one or two of
which _lectures I had heard him read in the public schools_, though
I understood them not at the time." As to Rohault's _Physics_, it
really did contain the best mechanical philosophy of the time;--the
doctrines which were held by Descartes in common with Galileo, and
with all the sound mathematicians who succeeded them. Nor does it
look like any great antipathy to novelty in the University of
Cambridge, that this book, which was quite as novel in its doctrines
as Newton's _Principia_, and which had only been published at Paris
in 1671, had obtained a firm hold on the University in less than
twenty years. Nor is there any attempt made in Clarke's notes to
conceal the novelty of Newton's discoveries, but on the contrary,
admiration is claimed for them as new.

The promptitude with which the Mathematicians of the University of
Cambridge adopted the best parts of the mechanical philosophy of
Descartes, and the greater philosophy of Newton, in the seventeenth
century, has been paralleled in our own times, in the promptitude
with which they have adopted and followed into their consequences
the Mathematical Theory of Heat of Fourier and Laplace, and the
Undulatory Theory of Light of Young and Fresnel.

In Newton's College, we possess, besides the memorials of him
mentioned above (which include two locks of his silver-white hair),
a paper in his own handwriting, describing the preparatory reading
which was necessary in order that our College students might be able
to read the _Principia_. I have printed this paper in the Preface to
my Edition of the First Three Sections of the _Principia_ in the
original Latin (1846).

Bentley, who had expressed his admiration for Newton in his Boyle's
Lectures in 1692, was made Master of the College in 1699, as I have
stated; and partly, no doubt, in consequence of the Newtonian
sermons which he had preached. In his administration of the College,
he zealously stimulated and assisted the exertions of Cotes,
Whiston, and other disciples of Newton. Smith, Bentley's successor
as Master of {426} the College, erected a statue of Newton in the
College Chapel (a noble work of Roubiliac), with the inscription,
_Qui genus humanum ingenio superavit._]

At Oxford, David Gregory and Halley, both zealous and distinguished
disciples of Newton, obtained the Savilian professorships of
astronomy and geometry in 1691 and 1703.

David Gregory's _Astronomiæ Physicæ et Geometricæ Elementa_ issued
from the Oxford Press in 1702. The author, in the first sentence of
the Preface, states his object to be to explain the mechanics of the
universe (Physica Cœlestis), which Isaac Newton, the Prince of
Geometers, has carried to a point of elevation which all look up to
with admiration. And this design is executed by a full exposition of
the Newtonian doctrines and their results. Keill, a pupil of
Gregory, followed his tutor to Oxford, and taught the Newtonian
philosophy there in 1700, being then Deputy Sedleian Professor. He
illustrated his lectures by experiments, and published an
Introduction to the _Principia_ which is not out of use even yet.

In Scotland, the Newtonian philosophy was accepted with great
alacrity, as appears by the instances of David Gregory and Keill.
David Gregory was professor at Edinburgh before he removed to Oxford,
and was succeeded there by his brother James. The latter had, as early
as 1690, printed a thesis, containing in twenty-two propositions, a
compend of Newton's _Principia_.[56\7] Probably these were intended as
theses for academical disputations; as Laughton at Cambridge
introduced the Newtonian philosophy into these exercises. The formula
at Cambridge, in use till very recently in these disputations, was
"_Rectè statuit Newtonus de Motu Lunæ_;" or the like.

[Note 56\7: See Hutton's _Math. Dict._, art. _James Gregory_. If it
fell in with my plan to notice derivative works, I might speak of
Maclaurin's admirable _Account of Sir Isaac Newton's Discoveries_,
published in 1748. This is still one of the best books on the
subject. The late Professor Rigaud's _Historical Essay on the First
Publication of Sir Isaac Newton's "Principia"_ (Oxf. 1838) contains
a careful and candid view of the circumstances of that event.]

The general diffusion of these opinions in England took place, not
only by means of books, but through the labors of various
experimental lecturers, like Desaguliers, who removed from Oxford to
London in 1713; when he informs us,[57\7] that "he found the
Newtonian philosophy generally received among persons of all ranks
and professions, and even among the ladies by the help of
experiments." {427}

[Note 57\7: Desag. _Pref._]

We might easily trace in our literature indications of the gradual
progress of the Newtonian doctrines. For instance, in the earlier
editions of Pope's _Dunciad_, this couplet occurred, in the
description of the effects of the reign of Dulness:
  Philosophy, that reached the heavens before,
  Shrinks to her hidden cause, and is no more.
"And this," says his editor, Warburton, "was intended as a censure
on the Newtonian philosophy. For the poet had been misled by the
prejudices of foreigners, as if that philosophy had recurred to the
occult qualities of Aristotle. This was the idea he received of it
from a man educated much abroad, who had read every thing, but every
thing superficially.[58\7] When I hinted to him how he had been
imposed upon, he changed the lines with great pleasure into a
compliment (as they now stand) on that divine genius, and a satire
on that very folly by which he himself had been misled." In 1743 it
was printed,
  Philosophy, that leaned on heaven before,
  Shrinks to her second cause, and is no more.
The Newtonians repelled the charge of dealing in occult
causes;[59\7] and, referring gravity to the will of the Deity, as
the First Cause, assumed a superiority over those whose philosophy
rested in second causes.

[Note 58\7: I presume Bolingbroke is here meant.]

[Note 59\7: See Cotes's Pref. to the _Principia_.]

To the cordial reception of the Newtonian theory by the English
astronomers, there is only one conspicuous exception; which is,
however, one of some note, being no other than Flamsteed, the
Astronomer Royal, a most laborious and exact observer. Flamsteed at
first listened with complacency to the promises of improvements in
the Lunar Tables, which the new doctrines held forth, and was
willing to assist Newton, and to receive assistance from him. But
after a time, he lost his respect for Newton's theory, and ceased to
take any interest in it. He then declared to one of his
correspondents,[60\7] "I have determined to lay these crotchets of
Sir Isaac Newton's wholly aside." We need not, however, find any
difficulty in this, if we recollect that Flamsteed, though a good
observer, was no philosopher;--never understood by a Theory any
thing more than a Formula which should predict results;--and was
incapable of comprehending the object of Newton's theory, which was
to assign causes as well as rules, and to satisfy the conditions of
Mechanics as well as of Geometry. {428}

[Note 60\7: Baily's _Account of Flamsteed, &c._, p. 309.]

[2d Ed.] [I do not see any reason to retract what was thus said; but
it ought perhaps to be distinctly said that on these very accounts
Flamsteed's rejection of Newton's rules did not imply a denial of
the doctrine of gravitation. In the letter above quoted, Flamsteed
says that he has been employed upon the Moon, and that "the heavens
reject that equation of Sir I. Newton which Gregory and Newton
called his sixth: I had then [when he wrote before] compared but 72
of my observations with the tables, now I have examined above 100
more. I find them all firm in the same, and the seventh [equation]
too." And thereupon he comes to the determination above stated.

At an earlier period Flamsteed, as I have said, had received
Newton's suggestions with great deference, and had regulated his own
observations and theories with reference to them. The calculation of
the lunar inequalities upon the theory of gravitation was found by
Newton and his successors to be a more difficult and laborious task
than he had anticipated, and was not performed without several
trials and errors. One of the equations was at first published (in
Gregory's _Astronomiæ Elementa_) with a wrong sign. And when Newton
had done all, Flamsteed found that the rules were far from coming up
to the degree of accuracy which had been claimed for them, that they
could give the moon's place true to 2 or 3 minutes. It was not till
considerably later that this amount of exactness was attained.

The late Mr. Baily, to whom astronomy and astronomical literature
are so deeply indebted, in his _Supplement to the Account of
Flamsteed_, has examined with great care and great candor the
assertion that Flamsteed did not understand Newton's Theory. He
remarks, very justly, that what Newton himself at first presented as
his Theory, might more properly be called Rules for computing lunar
tables, than a physical Theory in the modern acceptation of the
term. He shows, too, that Flamsteed had read the _Principia_ with
attention.[61\7] Nor do I doubt that many considerable
mathematicians gave the same imperfect assent to Newton's doctrine
which Flamsteed did. But when we find that others, as Halley, David
Gregory, and Cotes, at once not only saw in the doctrine a source of
true formulæ, but also a magnificent physical discovery, we are
obliged, I think, to make Flamsteed, in this respect, an exception
to the first class of astronomers of his own time.

[Note 61\7: _Supp._ p. 691.]

Mr. Baily's suggestion that the annual equations for the corrections
of the lunar apogee and node were collected from Flamsteed's tables
{429} and observations independently of their suggestion by Newton
as the results of Theory (_Supp._ p. 692, Note, and p. 698), appears
to me not to be adequately supported by the evidence given.]


_Sect._ 3.--_Reception of the Newtonian Theory abroad._

THE reception of the Newtonian theory on the Continent, was much
more tardy and unwilling than in its native island. Even those whose
mathematical attainments most fitted them to appreciate its proofs,
were prevented by some peculiarity of view from adopting it as a
system; as Leibnitz, Bernoulli, Huyghens; who all clung to one
modification or other of the system of vortices. In France, the
Cartesian system had obtained a wide and popular reception, having
been recommended by Fontenelle with the graces of his style; and its
empire was so firm and well established in that country, that it
resisted for a long time the pressure of Newtonian arguments.
Indeed, the Newtonian opinions had scarcely any disciples in France,
till Voltaire asserted their claims, on his return from England in
1728: until then, as he himself says, there were not twenty
Newtonians out of England.

The hold which the Philosophy of Descartes had upon the minds of his
countrymen is, perhaps, not surprising. He really had the merit, a
great one in the history of science, of having completely overturned
the Aristotelian system, and introduced the philosophy of matter and
motion. In all branches of mixed mathematics, as we have already
said, his followers were the best guides who had yet appeared. His
hypothesis of vortices, as an explanation of the celestial motions,
had an apparent advantage over the Newtonian doctrine, in this
respect;--that it referred effects to the most intelligible, or at
least most familiar kinds of mechanical causation, namely, pressure
and impulse. And above all, the system was acceptable to most minds,
in consequence of being, as was pretended, deduced from a few simple
principles by necessary consequences; and of being also directly
connected with metaphysical and theological speculations. We may
add, that it was modified by its mathematical adherents in such a
way as to remove most of the objections to it. A vortex revolving
about a centre could be constructed, or at least it was supposed
that it could be constructed, so as to produce a tendency of bodies
to the centre. In all cases, therefore, where a central force acted,
a vortex was supposed; but in reasoning to the results of this
hypothesis, it was {430} easy to leave out of sight all other
effects of the vortex, and to consider only the central force; and
when this was done, the Cartesian mathematician could apply to his
problems a mechanical principle of some degree of consistency. This
reflection will, in some degree, account for what at first seems so
strange;--the fact that the language of the French mathematicians is
Cartesian, for almost half a century after the publication of the
_Principia_ of Newton.

There was, however, a controversy between the two opinions going on
all this time, and every day showed the insurmountable difficulties
under which the Cartesians labored. Newton, in the _Principia_, had
inserted a series of propositions, the object of which was to prove,
that the machinery of vortices could not be accommodated to one part
of the celestial phenomena, without contradicting another part. A
more obvious difficulty was the case of gravity of the earth; if
this force arose, as Descartes asserted, from the rotation of the
earth's vortex about its axis, it ought to tend directly to the
axis, and not to the centre. The asserters of vortices often tried
their skill in remedying this vice in the hypothesis, but never with
much success. Huyghens supposed the ethereal matter of the vortices
to revolve about the centre in all directions; Perrault made the
strata of the vortex increase in velocity of rotation as they recede
from the centre; Saurin maintained that the circumambient resistance
which comprises the vortex will produce a pressure passing through
the centre. The elliptic form of the orbits of the planets was
another difficulty. Descartes had supposed the vortices themselves
to be oval  but others, as John Bernoulli, contrived ways of having
elliptical motion in a circular vortex.

The mathematical prize-questions proposed by the French Academy,
naturally brought the two sets of opinions into conflict. The
Cartesian memoir of John Bernoulli, to which we have just referred,
was the one which gained the prize in 1730. It not unfrequently
happened that the Academy, as if desirous to show its impartiality,
divided the prize between the Cartesians and Newtonians. Thus in
1734, the question being, the cause of the inclination of the orbits
of the planets, the prize was shared between John Bernoulli, whose
Memoir was founded on the system of vortices, and his son Daniel,
who was a Newtonian. The last act of homage of this kind to the
Cartesian system was performed in 1740, when the prize on the
question of the Tides was distributed between Daniel Bernoulli,
Euler, Maclaurin, and Cavallieri; the last of whom had tried to
patch up and amend the Cartesian hypothesis on this subject. {431}

Thus the Newtonian system was not adopted in France till the
Cartesian generation had died off; Fontenelle, who was secretary to
the Academy of Sciences, and who lived till 1756, died a Cartesian.
There were exceptions; for instance, Delisle, an astronomer who was
selected by Peter the Great of Russia, to found the Academy of St
Petersburg; who visited England in 1724, and to whom Newton then
gave his picture, and Halley his Tables. But in general, during the
interval, that country and this had a national difference of creed
on physical subjects. Voltaire, who visited England in 1727, notices
this difference in his lively manner. "A Frenchman who arrives in
London, finds a great alteration in philosophy, as in other things.
He left the world full [**a _plenum_], he finds it empty. At Paris
you see the universe composed of vortices of subtle matter, in
London we see nothing of the kind. With you it is the pressure of
the moon which causes the tides of the sea, in England it is the sea
which gravitates towards the moon; so that when you think the moon
ought to give us high water, these gentlemen believe that you ought
to have low water; which unfortunately we cannot test by experience;
for in order to do that, we should have examined the Moon and the
Tides at the moment of the creation. You will observe also that the
sun, which in France has nothing to do with the business, here comes
in for a quarter of it. Among you Cartesians, all is done by an
impulsion which one does not well understand; with the Newtonians,
it is done by an attraction of which we know the cause no better. At
Paris you fancy the earth shaped like a melon, at London it is
flattened on the two sides."

It was Voltaire himself as we have said, who was mainly instrumental
in giving the Newtonian doctrines currency in France. He was at first
refused permission to print his _Elements of the Newtonian
Philosophy_, by the Chancellor, D'Aguesseaux, who was a Cartesian; but
after the appearance of this work in 1738, and of other writings by
him on the same subject, the Cartesian edifice, already without real
support or consistency, crumbled to pieces and disappeared. The first
Memoir in the _Transactions of the French Academy_ in which the
doctrine of central force is applied to the solar system, is one by
the Chevalier de Louville in 1720, _On the Construction and Theory of
Tables of the Sun_. In this, however, the mode of explaining the
motions of the planets by means of an original impulse and an
attractive force is attributed to Kepler, not to Newton. The first
Memoir which refers to the universal gravitation of matter is by
Maupertuis, in {432} 1736. But Newton was not unknown or despised in
France till this time. In 1699 he was admitted one of the very small
number of foreign associates of the French Academy of Sciences. Even
Fontenelle, who, as we have said, never adopted his opinions, spoke of
him in a worthy manner, in the _Eloge_ which he composed on the
occasion of his death. At a much earlier period too, Fontenelle did
homage to his fame. The following passage refers, I presume, to
Newton. In the _History_ of the Academy for 1708, which is written by
the secretary, he says,[62\7] in referring to the difficulty which the
comets occasion in the Cartesian hypothesis: "We might relieve
ourselves at once from all the embarrassment which arises from the
directions of these motions, by suppressing, as has been done _by one
of the greatest geniuses of the age_, all this immense fluid matter,
which we commonly suppose between the planets, and conceiving them
suspended in a perfect void."

[Note 62\7: _Hist. Ac. Sc._ 1708. p. 103.]

Comets, as the above passage implies, were a kind of artillery which
the Cartesian _plenum_ could not resist. When it appeared that the
paths of such wanderers traversed the vortices in all directions, it
was impossible to maintain that these imaginary currents governed
the movements of bodies immersed in them  and the mechanism ceased
to have any real efficacy. Both these phenomena of comets, and many
others, became objects of a stronger and more general interest, in
consequence of the controversy between the rival parties; and thus
the prevalence of the Cartesian system did not seriously impede the
progress of sound knowledge. In some cases, no doubt, it made men
unwilling to receive the truth, as in the instance of the deviation
of the comets from the zodiacal motion; and again, when Römer
discovered that light was not instantaneously propagated. But it
encouraged observation and calculation, and thus forwarded the
verification and extension of the Newtonian system; of which process
we must now consider some of the incidents. {433}




CHAPTER IV.

SEQUEL TO THE EPOCH OF NEWTON, CONTINUED.--VERIFICATION AND
COMPLETION OF THE NEWTONIAN THEORY.


_Sect._ 1.--_Division of the Subject._

THE verification of the Law of Universal Gravitation as the
governing principle of all cosmical phenomena, led, as we have
already stated, to a number of different lines of research, all long
and difficult. Of these we may treat successively, the motions of
the Moon, of the Sun, of the Planets, of the Satellites, of Comets;
we may also consider separately the Secular Inequalities, which at
first sight appear to follow a different law from the other changes;
we may then speak of the results of the principle as they affect
this Earth, in its Figure, in the amount of Gravity at different
places, and in the phenomena of the Tides. Each of these subjects
has lent its aid to confirm the general law: but in each the
confirmation has had its peculiar difficulties, and has its separate
history. Our sketch of this history must be very rapid, for our aim
is only to show what is the kind and course of the confirmation
which such a theory demands and receives.

For the same reason we pass over many events of this period which
are highly important in the history of astronomy. They have lost
much of their interest for us, and even for common readers, because
they are of a class with which we are already familiar, truths
included in more general truths to which our eyes now most readily
turn. Thus, the discovery of new satellites and planets is but a
repetition of what was done by Galileo: the determination of their
nodes and apses, the reduction of their motions to the law of the
ellipse, is but a fresh exemplification of the discoveries of
Kepler. Otherwise, the formation of Tables of the satellites of
Jupiter and Saturn, the discovery of the eccentricities of the
orbits, and of the motions of the nodes and apses, by Cassini,
Halley, and others, would rank with the great achievements in
astronomy. Newton's peculiar advance in the _Tables_ of the
celestial motions is the introduction of Perturbations. To these
motions, so affected, we now proceed. {434}


_Sect._ 2.--_Application of the Newtonian Theory to the Moon._

THE Motions of the Moon may be first spoken of, as the most obvious
and the most important of the applications of the Newtonian Theory.
The verification of such a theory consists, as we have seen in
previous cases, in the construction of Tables derived from the
theory, and the comparison of these with observation. The
advancement of astronomy would alone have been a sufficient motive
for this labor; but there were other reasons which urged it on with
a stronger impulse. A perfect Lunar Theory, if the theory could be
perfected, promised to supply a method of finding the Longitude of
any place on the earth's surface; and thus the verification of a
theory which professed to be complete in its foundations, was
identified with an object of immediate practical use to navigators
and geographers, and of vast acknowledged value. A good method for
the near discovery of the longitude had been estimated by nations
and princes at large sums of money. The Dutch were willing to tempt
Galileo to this task by the offer of a chain of gold: Philip the
Third of Spain had promised a reward for this object still
earlier;[63\7] the parliament of England, in 1714, proposed a
recompense of 20,000_l._ sterling; the Regent Duke of Orléans, two
years afterwards, offered 100,000 francs for the same purpose. These
prizes, added to the love of truth and of fame, kept this object
constantly before the eyes of mathematicians, during the first half
of the last century.

[Note 63\7: Del. _A. M._ i. 39, 66.]

If the Tables could be so constructed as to represent the moon's
real place in the heavens with extreme precision, as it would be
seen from a _standard_ observatory, the observation of her apparent
place, as seen from any other point of the earth's surface, would
enable the observer to find his longitude from the standard point.
The motions of the moon had hitherto so ill agreed with the best
Tables, that this method failed altogether. Newton had discovered
the ground of this want of agreement. He had shown that the same
force which produces the Evection, Variation, and Annual Equation,
must produce also a long series of other Inequalities, of various
magnitudes and cycles, which perpetually drag the moon before or
behind the place where she would be sought by an astronomer who knew
only of those principal and notorious inequalities. But to calculate
and apply the new inequalities, was no slight undertaking. {435}

In the first edition of the _Principia_ in 1687, Newton had not
given any calculations of new inequalities affecting the longitude
of the moon. But in David Gregory's _Elements of Physical and
Geometrical Astronomy_, published in 1702, is inserted[64\7]
"Newton's Lunar Theory as applied by him to Practice;" in which the
great discoverer has given the results of his calculations of eight
of the lunar Equations, their quantities, epochs, and periods. These
calculations were for a long period the basis of new Tables of the
Moon, which were published by various persons;[65\7] as by Delisle
in 1715 or 1716, Grammatici at Ingoldstadt in 1726, Wright in 1732,
Angelo Capelli at Venice in 1733, Dunthorne at Cambridge in 1739.

[Note 64\7: P. 332.]

[Note 65\7: Lalande, 1457.]

Flamsteed had given Tables of the Moon upon Horrox's theory in 1681,
and wished to improve them; and though, as we have seen, he would
not, or could not, accept Newton's doctrines in their whole extent,
Newton communicated his theory to the observer in the shape in which
he could understand it and use it:[66\7] and Flamsteed employed
these directions in constructing new Lunar Tables, which he called
his _Theory_.[67\7] These Tables were not published till long after
his death, by Le Monnier at Paris in 1746. They are said, by
Lalande,[68\7] not to differ much from Halley's. Halley's Tables of
the Moon were printed in 1719 or 1720, but not published till after
his death in 1749. They had been founded on Flamsteed's observations
and his own; and when, in 1720, Halley succeeded Flamsteed in the
post of Astronomer Royal at Greenwich, and conceived that he had the
means of much improving what he had done before, he began by
printing what he had already executed.[69\7]

[Note 66\7: Baily. _Account of Flamsteed_, p. 72.]

[Note 67\7: P. 211.]

[Note 68\7: Lal. 1459.]

[Note 69\7: Mr. Baily* says that Mayer's _Nouvelles Tables de la
Lune_ in **1753, published upwards of fifty years after Gregory's
_Astronomy_, may be considered as the first lunar tables formed
_solely_ on Newton's principles. Though Wright in 1732 published
_New and Correct Tables of the Lunar Motions according to the
Newtonian Theory_, Newton's rules were in them only partially
adopted. In 1735 Leadbetter published his _Uranoscopia_, in which
those rules were more fully followed. But these _Newtonian Tables_
did not supersede Flamsteed's Horroxian Tables, till both were
supplanted by those of Mayer.

* _Supp._ p. 702.]

But Halley had long proposed a method, different from that of
Newton, but marked by great ingenuity, for amending the Lunar
Tables. He proposed to do this by the use of a cycle, which we have
mentioned as one of the earliest discoveries in astronomy;--the
Period of 223 lunations, or eighteen years and eleven days, the
Chaldean {436} Saros. This period was anciently used for predicting
the eclipses of the sun and moon; for those eclipses which happen
during this period, are repeated again in the same order, and with
nearly the same circumstances, after the expiration of one such
period and the commencement of a second. The reason of this is, that
at the end of such a cycle, the moon is in nearly the same position
with respect to the sun, her nodes, and her apogee, as she was at
first; and is only a few degrees distant from the same part of the
heavens. But on the strength of this consideration, Halley
conjectured that all the irregularities of the moon's motion,
however complex they may be, would recur after such an interval; and
that, therefore, if the requisite corrections were determined by
observation for one such period, we might by means of them give
accuracy to the Tables for all succeeding periods. This idea
occurred to him before he was acquainted with Newton's views.[70\7]
After the lunar theory of the _Principia_ had appeared, he could not
help seeing that the idea was confirmed; for the inequalities of the
moon's motion, which arise from the attraction of the sun, will
depend on her positions with regard to the sun, the apogee, and the
node; and therefore, however numerous, will recur when these
positions recur.

[Note 70\7: _Phil. Trans._ 1731, p. 188.]

Halley announced, in 1691,[71\7] his intention of following this
idea into practice; in a paper in which he corrected the text of
three passages in Pliny, in which this period is mentioned, and from
which it is sometimes called the Plinian period. In 1710, in the
preface to a new edition to Street's _Caroline Tables_, he stated
that he had already confirmed it to a considerable extent.[72\7] And
even after Newton's theory had been applied, he still resolved to
use his cycle as a means of obtaining further accuracy. On
succeeding to the Observatory at Greenwich in 1720, he was further
delayed by finding that the instruments had belonged to Flamsteed,
and were removed by his executors. "And this," he says,[73\7] "was
the more grievous to me, on account of my advanced age, being then
in my sixty-fourth year: which put me past all hopes of ever living
to see a complete period of eighteen years' observation. But, thanks
to God, he has been pleased hitherto (in 1731) to afford me
sufficient health and strength to execute my office, in all its
parts, with my own hands and eyes, without any assistance or
interruption, during one whole period of the moon's {437} apogee,
which period is performed in somewhat less than nine years." He
found the agreement very remarkable, and conceived hopes of
attaining the great object, of finding the Longitude with the
requisite degree of exactness; nor did he give up his labors on this
subject till he had completed his Plinian period in 1739.

[Note 71\7: Ib. p. 536.]

[Note 72\7: Ib. 1731, p. 187.]

[Note 73\7: Ib. p. 193.]

The accuracy with which Halley conceived himself able to predict the
moon's place[74\7] was within two minutes of space, or one fifteenth
of the breadth of the moon herself. The accuracy required for
obtaining the national reward was considerably greater. Le Monnier
pursued the idea of Halley.[75\7] But before Halley's method had
been completed, it was superseded by the more direct prosecution of
Newton's views.

[Note 74\7: _Phil. Trans._ 1731, p. 195.]

[Note 75\7: Bailly, _A. M._ c. 131.]

We have already remarked, in the history of analytical mechanics, that
in the Lunar Theory, considered as one of the cases of the Problem of
Three Bodies, no advance was made beyond what Newton had done, till
mathematicians threw aside the Newtonian artifices, and applied the
newly developed generalizations of the analytical method. The first
great apparent deficiency in the agreement of the law of universal
gravitation with astronomical observation, was removed by Clairaut's
improved approximation to the theoretical Motion of the Moon's Apogee,
in 1750; yet not till it had caused so much disquietude, that Clairaut
himself had suggested a modification of the law of attraction; and it
was only in tracing the consequences of this suggestion, that he found
the Newtonian law of the inverse square to be that which, when rightly
developed, agreed with the facts. Euler solved the problem by the aid
of his analysis in 1745,[76\7] and published Tables of the Moon in
1746. His tables were not very accurate at first;[77\7] but he,
D'Alembert, and Clairaut, continued to labor at this object, and the
two latter published Tables of the Moon in 1754.[78\7] Finally, Tobias
Mayer, an astronomer of Göttingen, having compared Euler's tables with
observations, corrected them so successfully, that in 1753 he
published Tables of the Moon, which really did possess the accuracy
which Halley only flattered himself that he had attained. Mayer's
success in his first Tables encouraged him to make them still more
perfect. He applied himself to the mechanical theory of the moon's
orbit; corrected all the coefficients of the series by a great number
of observations; and in 1755, sent his new Tables to London as worthy
to claim the prize offered for the discovery of longitude. He died
soon after {438} (in 1762), at the early age of thirty-nine, worn out
by his incessant labors; and his widow sent to London a copy of his
Tables with additional corrections. These Tables were committed to
Bradley, then Astronomer Royal, in order to be compared with
observation. Bradley labored at this task with unremitting zeal and
industry, having himself long entertained hopes that the Lunar Method
of finding the Longitude might be brought into general use. He and his
assistant, Gael Morris, introduced corrections into Mayer's Tables of
1755. In his report of 1756, he says,[79\7] that he did not find any
difference so great as a minute and a quarter; and in 1760, he adds,
that this deviation had been further diminished by his corrections. It
is not foreign to our purpose to observe the great labor which this
verification required. Not less than 1220 observations, and long
calculations founded upon each, were employed. The accuracy which
Mayer's Tables possessed was considered to entitle them to a part of
the parliamentary reward; they were printed in 1770, and his widow
received 3000_l._ from the English nation. At the same time, Euler,
whose Tables had been the origin and foundation of Mayer's, also had a
recompense of the same amount.

[Note 76\7: Lal. 1460.]

[Note 77\7: Bradley's Correspondence.]

[Note 78\7: Lal. 1460.]

[Note 79\7: Bradley's _Mem._ p. xcviii.]

This public national acknowledgment of the practical accuracy of
these Tables is, it will be observed, also a solemn recognition of
the truth of the Newtonian theory, as far as truth can be judged of
by men acting under the highest official responsibility, and aided
by the most complete command of the resources of the skill and
talents of others. The finding the Longitude is thus the seal of the
moon's gravitation to the sun and earth; and with this occurrence,
therefore, our main concern with the history of the Lunar Theory
ends. Various improvements have been since introduced into this
research; but on these we, with so many other subjects before us,
must forbear to enter.


_Sect._ 3.--_Application of the Newtonian Theory to the Planets,
Satellites, and Earth._

THE theories of the Planets and Satellites, as affected by the law
of universal gravitation, and therefore by perturbations, were
naturally subjects of interest, after the promulgation of that law.
Some of the effects of the mutual attraction of the planets had,
indeed, already attracted notice. The inequality produced by the
mutual attraction of Jupiter and Saturn cannot be overlooked by a
good observer. In the {439} preface to the second edition of the
_Principia_, Cotes remarks,[80\7] that the perturbation of Jupiter
and Saturn is not unknown to astronomers. In Halley's Tables it was
noticed[81\7] that there are very great deviations from regularity
in these two planets, and these deviations are ascribed to the
perturbing force of the planets on each other; but the correction of
these by a suitable equation is left to succeeding astronomers.

[Note 80\7: Preface to _Principia_, p. xxi.]

[Note 81\7: End of Planetary Tables.]

The motion of the planes and apsides of the planetary orbits was one
of the first results of their mutual perturbation which was
observed. In 1706, La Hire and Maraldi compared Jupiter with the
Rudolphine Tables, and those of Bullialdus: it appeared that his
aphelion had advanced, and that his nodes had regressed. In 1728, J.
Cassini found that Saturn's aphelion had in like manner travelled
forwards. In 1720, when Louville refused to allow in his solar
tables the motion of the aphelion of the earth, Fontenelle observed
that this was a misplaced scrupulousness, since the aphelion of
Mercury certainly advances. Yet this reluctance to admit change and
irregularity was not yet overcome. When astronomers had found an
approximate and apparent constancy and regularity, they were willing
to believe it absolute and exact. In the satellites of Jupiter, for
instance, they were unwilling to admit even the eccentricity of the
orbits; and still more, the variation of the nodes, inclinations,
and apsides. But all the fixedness of these was successively
disproved. Fontenelle in 1732, on the occasion of Maraldi's
discovery of the change of inclination of the fourth satellite,
expresses a suspicion that all the elements might prove liable to
change. "We see," says he, "the constancy of the inclination already
shaken in the three first satellites, and the eccentricity in the
fourth. The immobility of the nodes holds out so far, but there are
strong indications that it will share the same fate."

The motions of the nodes and apsides of the satellites are a
necessary part of the Newtonian theory; and even the Cartesian
astronomers now required only data, in order to introduce these
changes into their Tables.

The complete reformation of the Tables of the Sun, Planets, and
Satellites, which followed as a natural consequence from the
revolution which Newton had introduced, was rendered possible by the
labors of the great constellation of mathematicians of whom we have
spoken in the last book, Clairaut, Euler, D'Alembert, and their
successors; and {440} it was carried into effect in the course of
the last century. Thus Lalande applied Clairaut's theory to Mars, as
did Mayer; and the inequalities in this case, says Bailly[82\7] in
1785, may amount to two minutes, and therefore must not be
neglected. Lalande determined the inequalities of Venus, as did
Father Walmesley, an English mathematician; these were found to
reach only to thirty seconds.

[Note 82\7: _Ast. Mod._ iii. 170.]

The Planetary Tables[83\7] which were in highest repute, up to the
end of the last century, were those of Lalande. In these, the
perturbations of Jupiter and Saturn were introduced, their magnitude
being such that they cannot be dispensed with; but the Tables of
Mercury, Venus, and Mars, had no perturbations. Hence these latter
Tables might be considered as accurate enough to enable the observer
to find the object, but not to test the theory of perturbations. But
when the calculation of the mutual disturbances of the planets was
applied, it was always found that it enabled mathematicians to bring
the theoretical places to coincide more exactly with those observed.
In improving, as much as possible, this coincidence, it is necessary
to determine the mass of each planet; for upon that, according to
the law of universal gravitation, its disturbing power depends.
Thus, in 1813, Lindenau published Tables of Mercury, and concluded,
from them, that a considerable increase of the supposed mass of
Venus was necessary to reconcile theory with observation.[84\7] He
had published Tables of Venus in 1810, and of Mars in 1811. And, in
proving Bouvard's Tables of Jupiter and Saturn, values were obtained
of the masses of those planets. The form in which the question of
the truth of the doctrine of universal gravitation now offers itself
to the minds of astronomers, is this:--that it is taken for granted
that it will account for the motions of the heavenly bodies, and the
question is, with what supposed masses it will give the _best_
account.[85\7] The continually increasing accuracy of the table
shows the truth of the fundamental assumption.

[Note 83\7: Airy, _Report on Ast. to Brit. Ass._ 1832.]

[Note 84\7: Airy, _Report on Ast. to Brit. **Ass._ 1832.]

[Note 85\7: Among the most important corrections of the supposed
masses of the planets, we may notice that of Jupiter, by Professor
Airy.  This determination of Jupiter's mass was founded, not on the
effect as seen in perturbations, but on a much more direct datum,
the time of revolution of his fourth satellite. It appeared, from
this calculation, that Jupiter's mass required to be increased by
about 1⁄80th. This result agrees with that which has been derived by
German astronomers from the perturbations which the attractions of
Jupiter produce in the four new planets, and has been generally
adopted as an improvement of the elements of our system.]

The question of perturbation is exemplified in the satellites also.
{441} Thus the satellites of Jupiter are not only disturbed by the
sun, as the moon is, but also by each other, as the planets are.
This mutual action gives rise to some very curious relations among
their motions; which, like most of the other leading inequalities,
were forced upon the notice of astronomers by observation before
they were obtained by mathematical calculation. In Bradley's remarks
upon his own Tables of Jupiter's Satellites, published among
Halley's Tables, he observes that the places of the three interior
satellites are affected by errors which recur in a cycle of 437
days, answering to the time in which they return to the same
relative position with regard to each other, and to the axis of
Jupiter's shadow. Wargentin, who had noticed the same circumstance
without knowledge of what Bradley had done, applied it, with all
diligence, to the purpose of improving the tables of the satellites
in 1746. But, at a later period, Laplace established, by
mathematical reasoning, the very curious theorem on which this cycle
depends, which he calls the _libration of Jupiter's satellites_; and
Delambre was then able to publish Tables of Jupiter's Satellites
more accurate than those of Wargentin, which he did in 1789.[86\7]

[Note 86\7: Voiron, _Hist. Ast._ p. 322.]

The progress of physical astronomy from the time of Euler and
Clairaut, has consisted of a series of calculations and comparisons
of the most abstruse and recondite kind. The formation of Tables of
the Planets and Satellites from the theory, required the solution of
problems much more complex than the original case of the Problem of
Three Bodies. The real motions of the planets and their orbits are
rendered still further intricate by this, that all the lines and
points to which we can refer them, are themselves in motion. The
task of carrying order and law into this mass of apparent confusion,
has required a long series of men of transcendent intellectual
powers; and a perseverance and delicacy of observation, such as we
have not the smallest example of in any other subject. It is
impossible here to give any detailed account of these labors; but we
may mention one instance of the complex considerations which enter
into them. The nodes of Jupiter's fourth satellite do not go
backwards,[87\7] as the Newtonian theory seems to require; they
advance upon Jupiter's orbit. But then, it is to be recollected that
the theory requires the nodes to retrograde upon the orbit of the
perturbing body, which is here the third satellite; and Lalande
showed that, by the necessary relations of space, the latter motion
may be retrograde though the former is direct. {442}

[Note 87\7: Bailly, iii. 175.]

Attempts have been made, from the time of the solution of the
Problem of three bodies to the present, to give the greatest
possible accuracy to the Tables of the Sun, by considering the
effect of the various perturbations to which the earth is subject.
Thus, in 1756, Euler calculated the effect of the attractions of the
planets on the earth (the prize-question of the French Academy of
Sciences), and Clairaut soon after. Lacaille, making use of these
results, and of his own numerous observations, published Tables of
the Sun. In 1786, Delambre[88\7] undertook to verify and improve
these tables, by comparing them with 314 observations made by
Maskelyne, at Greenwich, in 1775 and 1784, and in some of the
intermediate years. He corrected most of the elements; but he could
not remove the uncertainty which occurred respecting the amount of
the inequality produced by the reaction of the moon. He admitted
also, in pursuance of Clairaut's theory, a second term of this
inequality depending on the moon's latitude; but irresolutely, and
half disposed to reject it on the authority of the observations.
Succeeding researches of mathematicians have shown, that this term
is not admissible as a result of mechanical principles. Delambre's
Tables, thus improved, were exact to seven or eight seconds;[89\7]
which was thought, and truly, a very close coincidence for the time.
But astronomers were far from resting content with this. In 1806,
the French Board of Longitude published Delambre's improved Solar
Tables; and in the _Connaissance des Tems_ for 1816, Burckhardt gave
the results of a comparison of Delambre's Tables with a great number
of Maskelyne's observations;--far greater than the number on which
they were founded.[90\7] It appeared that the epoch, the perigee,
and the eccentricity, required sensible alterations, and that the
mass of Venus ought to be reduced about one-ninth, and that of the
Moon to be sensibly diminished. In 1827, Professor Airy[91\7]
compared Delambre's tables with 2000 Greenwich observations, made
with the new transit-instrument at Cambridge, and deduced from this
comparison the correction of the elements. These in general agreed
closely with Burckhardt's, excepting that a diminution of Mars
appeared necessary. Some discordances, however, led Professor Airy
to suspect the existence of an inequality which had escaped the
sagacity of Laplace and Burckhardt. And, a few weeks after this
suspicion had been expressed, the same mathematician announced to
the Royal Society that he had {443} detected, in the planetary
theory such an inequality, hitherto unnoticed, arising from the
mutual attraction of Venus and the Earth. Its whole effect on the
earth's longitude, would be to increase or diminish it by nearly
three seconds of space, and its period is about 240 years. "This
term," he adds, "accounts completely for the difference of the
secular motions given by the comparison of the epochs of 1783 and
1821, and by that of the epochs of 1801 and 1821."

[Note 88\7: Voiron, _Hist._ p. 315.]

[Note 89\7: Montucla, iv. 42.]

[Note 90\7: Airy, _Report_, p. 150.]

[Note 91\7: _Phil. Trans._ 1828.]

Many excellent Tables of the motions of the sun, moon, and planets,
were published in the latter part of the last century; but the
Bureau des Longitudes which was established in France in 1795,
endeavored to give new or improved tables of most of these motions.
Thus were produced Delambre's Tables of the Sun, Burg's Tables of
the Moon, Bouvard's Tables of Jupiter, Saturn, and Uranus. The
agreement between these and observation is, in general, truly
marvellous.

We may notice here a difference in the mode of referring to
observation when a theory is first established, and when it is
afterwards to be confirmed and corrected. It was remarked as a merit
in the method of Hipparchus, and an evidence of the mathematical
coherence of his theory, that in order to determine the place of the
sun's apogee, and the eccentricity of his orbit, he required to know
nothing besides the lengths of winter and spring. But if the fewness
of the requisite data is a beauty in the first fixation of a theory,
the multitude of observations to which it applies is its excellence
when it is established; and in correcting Tables, mathematicians
take far more data than would be requisite to determine the
elements. For the theory ought to account for _all_ the facts: and
since it will not do this with mathematical rigor (for observation
is not perfect), the elements are determined, not so as to satisfy
any selected observations, but so as to make the whole mass of error
as small as possible. And thus, in the adaptation of theory to
observation, even in its most advanced state, there is room for
sagacity and skill, prudence and judgment.

In this manner, by selecting the best mean elements of the motions
of the heavenly bodies, the observed motions deviate from this mean
in the way the theory points out, and constantly return to it. To
this general rule, of the constant return to a mean, there are,
however, some apparent exceptions, of which we shall now speak. {444}


_Sect._ 4.--_Application of the Newtonian Theory to Secular
Inequalities._

SECULAR Inequalities in the motions of the heavenly bodies occur in
consequence of changes in the elements of the solar system, which go
on progressively from age to age. The example of such changes which
was first studied by astronomers, was the Acceleration of the Moon's
Mean Motion, discovered by Halley. The observed fact was, that the
moon now moves in a very small degree quicker than she did in the
earlier ages of the world. When this was ascertained, the various
hypotheses which appeared likely to account for the fact were
reduced to calculation. The resistance of the medium in which the
heavenly bodies move was the most obvious of these hypotheses.
Another, which was for some time dwelt upon by Laplace, was the
successive transmission of gravity, that is, the hypothesis that the
gravity of the earth takes a certain finite time to reach the moon.
But none of these suppositions gave satisfactory conclusions; and
the strength of Euler, D'Alembert, Lagrange, and Laplace, was for a
time foiled by this difficulty. At length, in 1787, Laplace
announced to the Academy that he had discovered the true cause of
this acceleration, and that it arose from the action of the sun upon
the moon, combined with the secular variation of the eccentricity of
the earth's orbit. It was found that the effects of this combination
would exactly account for the changes which had hitherto so
perplexed mathematicians. A very remarkable result of this
investigation was, that "this Secular Inequality of the motion of
the moon is periodical, but it requires millions of years to
re-establish itself;" so that after an almost inconceivable time,
the acceleration will become a retardation. Laplace some time after
(in 1797), announced other discoveries, relative to the secular
motions of the apogee and the nodes of the moon's orbit. Laplace
collected these researches in his "Theory of the Moon," which he
published in the third volume of the _Mécanique Céleste_ in 1802.

A similar case occurred with regard to an acceleration of Jupiter's
mean motion, and a retardation of Saturn's, which had been observed
by Cassini, Maraldi, and Horrox. After several imperfect attempts by
other mathematicians, Laplace, in 1787, found that there resulted
from the mutual attraction of these two planets a great Inequality,
of which the period is 929 years and a half, and which has
accelerated Jupiter and retarded Saturn ever since the restoration
of astronomy. {445}

Thus the secular inequalities of the celestial motions, like all the
others, confirm the law of universal gravitation. They are called
"secular," because ages are requisite to unfold their existence, and
because they are not obviously periodical. They might, in some
measure, be considered as extensions of the Newtonian theory, for
though Newton's law accounts for such facts, he did not, so far as
we know, foresee such a result of it. But on the other hand, they
are exactly of the same nature as those which he did foresee and
calculate. And when we call them _secular_ in opposition to
_periodical_, it is not that there is any real difference, for they,
too, have their cycle; but it is that we have assumed our _mean_
motion without allowing for these long inequalities. And thus, as
Laplace observes on this very occasion,[92\7] the lot of this great
discovery of gravitation is no less than this, that every apparent
exception becomes a proof, every difficulty a new occasion of a
triumph. And such, as he truly adds, is the character of a true
theory,--of a real representation of nature.

[Note 92\7: _Syst. du Monde_, 8vo, ii. 37.]

It is impossible for us here to enumerate even the principal objects
which have thus filled the triumphal march of the Newtonian theory
from its outset up to the present time. But among these secular
changes, we may mention the Diminution of the Obliquity of the
Ecliptic, which has been going on from the earliest times to the
present. This change has been explained by theory, and shown to
have, like all the other changes of the system, a limit, after which
the diminution will be converted into an increase.

We may mention here some subjects of a kind somewhat different from
those just spoken of. The true theoretical quantity of the
Precession of the Equinoxes, which had been erroneously calculated
by Newton, was shown by D'Alembert to agree with observation. The
constant coincidence of the Nodes of the Moon's Equator with those
of her Orbit, was proved to result from mechanical principles by
Lagrange. The curious circumstance that the Time of the Moon's
rotation on her axis is equal to the Time of her revolution about
the earth, was shown to be consistent with the results of the laws
of motion by Laplace. Laplace also, as we have seen, explained
certain remarkable relations which constantly connect the longitudes
of the three first satellites of Jupiter; Bailly and Lagrange
analyzed and explained the curious librations of the nodes and
inclinations of their orbits; and Laplace traced the effect of
Jupiter's oblate figure on their motions, {446} which masks the
other causes of inequality, by determining the direction of the
motions of the _perijove_ and node of each satellite.


_Sect._ 5.--_Application of the Newtonian Theory to the New
Planets._

WE are now so accustomed to consider the Newtonian theory as true,
that we can hardly imagine to ourselves the possibility that those
planets which were not discovered when the theory was founded,
should contradict its doctrines. We can scarcely conceive it
possible that Uranus or Ceres should have been found to violate
Kepler's laws, or to move without suffering perturbations from
Jupiter and Saturn. Yet if we can suppose men to have had any doubt
of the exact and universal truth of the doctrine of universal
gravitation, at the period of these discoveries, they must have
scrutinized the motions of these new bodies with an interest far
more lively than that with which we now look for the predicted
return of a comet. The solid establishment of the Newtonian theory
is thus shown by the manner in which we take it for granted not only
in our reasonings, but in our feelings. But though this is so, a
short notice of the process by which the new planets were brought
within the domain of the theory may properly find a place here.

William Herschel, a man of great energy and ingenuity, who had made
material improvements in reflecting telescopes, observing at Bath on
the 13th of March, 1781, discovered, in the constellation Gemini, a
star larger and less luminous than the fixed stars. On the
application of a more powerful telescope, it was seen magnified, and
two days afterwards he perceived that it had changed its place. The
attention of the astronomical world was directed to this new object,
and the best astronomers in every part of Europe employed themselves
in following it along the sky.[93\7]

[Note 93\7: Voiron, _Hist. Ast._ p. 12.]

The admission of an eighth planet into the long-established list, was
a notion so foreign to men's thoughts at that time, that other
suppositions were first tried. The orbit of the new body was at first
calculated as if it had been a comet running in a parabolic path. But
in a few days the star deviated from the course thus assigned it: and
it was in vain that in order to represent the observations, the
perihelion distance of the parabola was increased from fourteen to
eighteen times the earth's distance from the sun. Saron, of the
Academy of Sciences of Paris, is said[94\7] to have been the first
person who perceived that the {447} places were better represented by
a circle than by a parabola: and Lexell, a celebrated mathematician of
Petersburg, found that a motion in a circular orbit, with a radius
double of that of Saturn, would satisfy all the observations. This
made its period about eighty-two years.

[Note 94\7: Ibid.]

Lalande soon discovered that the circular motion was subject to a
sensible inequality: the orbit was, in fact, an ellipse, like those
of the other planets. To determine the equation of the centre of a
body which revolves so slowly, would, according to the ancient
methods, have required many years; but Laplace contrived methods by
which the elliptical elements were determined from four
observations, within little more than a year from its first
discovery by Herschel. These calculations were soon followed by
tables of the new planet, published by Nouet.

In order to obtain additional accuracy, it now became necessary to
take account of the perturbations. The French Academy of Sciences
proposed, in 1789, the construction of new Tables of this Planet as
its prize-question. It is a curious illustration of the constantly
accumulating evidence of the theory, that the calculation of the
perturbations of the planet enabled astronomers to discover that it
had been observed as a star in three different positions in former
times; namely, by Flamsteed in 1690, by Mayer in 1756, and by Le
Monnier in 1769. Delambre, aided by this discovery and by the theory
of Laplace, calculated Tables of the planet, which, being compared
with observation for three years, never deviated from it more than
seven seconds. The Academy awarded its prize to these Tables, they
were adopted by the astronomers of Europe, and the planet of Herschel
now conforms to the laws of attraction, along with those ancient
members of the known system from which the theory was inferred.

The history of the discovery of the other new planets, Ceres,
Pallas, Juno, and Vesta, is nearly similar to that just related,
except that their planetary character was more readily believed. The
first of these was discovered on the first day of this century by
Piazzi, the astronomer at Palermo; but he had only begun to suspect
its nature, and had not completed his third observation, when his
labors were suspended by a dangerous illness; and on his recovery
the star was invisible, being lost in the rays of the sun.

He declared it to be a planet with an elliptical orbit; but the path
which it followed, on emerging from the neighborhood of the sun, was
not that which Piazzi had traced out for it. Its extreme smallness
made it difficult to rediscover; and the whole of the year 1801 was
{448} employed in searching the sky for it in vain. At last, after
many trials, Von Zach and Olbers again found it, the one on the last
day of 1801, the other on the first day of 1802. Gauss and Burckhardt
immediately used the new observations in determining the elements of
the orbit; and the former invented a new method for the purpose. Ceres
now moves in a path of which the course and inequalities are known,
and can no more escape the scrutiny of astronomers.

The second year of the nineteenth century also produced its planet.
This was discovered by Dr. Olbers, a physician of Bremen, while he
was searching for Ceres among the stars of the constellation Virgo.
He found a star which had a perceptible motion even in the space of
two hours. It was soon announced as a new planet, and received from
its discoverer the name of Pallas. As in the case of Ceres,
Burckhardt and Gauss employed themselves in calculating its orbit.
But some peculiar difficulties here occurred. Its eccentricity is
greater than that of any of the old planets, and the inclination of
its orbit to the ecliptic is not less than thirty-five degrees.
These circumstances both made its perturbations large, and rendered
them difficult to calculate. Burckhardt employed the known processes
of analysis, but they were found insufficient: and the Imperial
Institute (as the French Academy was termed during the reign of
Napoleon) proposed the Perturbations of Pallas as a prize-question.

To these discoveries succeeded others of the same kind. The German
astronomers agreed to examine the whole of the zone in which Ceres
and Pallas move; in the hope of finding other planets, fragments, as
Olbers conceived they might possibly be, of one original mass. In
the course of this research, Mr. Harding of Lilienthal, on the first
of September, 1804, found a new star, which he soon was led to
consider as a planet. Gauss and Burckhardt also calculated the
elements of this orbit, and the planet was named Juno.

After this discovery, Olbers sought the sky for additional fragments
of his planet with extraordinary perseverance. He conceived that one
of two opposite constellations, the Virgin or the Whale, was the
place where its separation must have taken place; and where,
therefore, all the orbits of all the portions must pass. He resolved
to survey, three times a year, all the small stars in these two
regions. This undertaking, so curious in its nature, was successful.
The 29th of March, 1807, he discovered Vesta, which was soon found
to be a planet. And to show the manner in which Olbers pursued his
labors, we may state that he afterwards published a notification
that he had examined the {449} same parts of the heavens with such
regularity, that he was certain no new planet had passed that way
between 1808 and 1816. Gauss and Burckhardt computed the orbit of
Vesta; and when Gauss compared one of his orbits with twenty-two
observations of M. Bouvard, he found the errors below seventeen
seconds of space in right ascension, and still less in declination.

The elements of all these orbits have been successively improved,
and this has been done entirely by the German mathematicians.[95\7]
These perturbations are calculated, and the places for some time
before and after opposition are now given in the Berlin Ephemeris.
"I have lately observed," says Professor Airy, "and compared with
the Berlin Ephemeris, the right ascensions of Juno and Vesta, and I
find that they are rather more accurate than those of Venus:" so
complete is the confirmation of the theory by these new bodies; so
exact are the methods of tracing the theory to its consequences.

[Note 95\7: Airy, _Rep._ 157.]

We may observe that all these new-discovered bodies have received
names taken from the ancient mythology. In the case of the first of
these, astronomers were originally divided; the discoverer himself
named it the _Georgium Sidus_, in honor of his patron, George the
Third; Lalande and others called it _Herschel_. Nothing can be more
just than this mode of perpetuating the fame of the author of a
discovery; but it was felt to be ungraceful to violate the
homogeneity of the ancient system of names. Astronomers tried to
find for the hitherto neglected denizen of the skies, an appropriate
place among the deities to whose assembly he was at last admitted;
and _Uranus_, the father of Saturn, was fixed upon as best suiting
the order of the course.

The mythological nomenclature of planets appeared, from this time,
to be generally agreed to. Piazzi termed his _Ceres Ferdinandea_.
The first term, which contains a happy allusion to Sicily, the
country of the discovery in modern, and of the goddess in ancient,
times, has been accepted; the attempt to pay a compliment to royalty
out of the products of science, in this as in most other cases, has
been set aside. Pallas, Juno, and Vesta, were named, without any
peculiar propriety of selection, according to the choice of their
discoverers.


_Sect._ 6.--_Application of the Newtonian Theory to Comets._

A FEW words must be said upon another class of bodies, which at
first seemed as lawless as the clouds and winds; and which astronomy
{450} has reduced to a regularity as complete as that of the
sun;--upon _Comets_. No part of the Newtonian discoveries excited a
more intense interest than this. These anomalous visitants were
anciently gazed at with wonder and alarm; and might still, as in
former times, be accused of "perplexing nations," though with very
different fears and questionings. The conjecture that they, too,
obeyed the law of universal gravitation, was to be verified by
showing that they described a curve such as that force would
produce. Hevelius, who was a most diligent observer of these
objects, had, without reference to gravitation, satisfied himself
that they moved in parabolas.[96\7] To determine the elements of the
parabola from observations, even Newton called[97\7] "problema longe
difficillimum." Newton determined the orbit of the comet of 1680 by
certain graphical methods. His methods supposed the orbit to be a
parabola, and satisfactorily represented the motion in the visible
part of the comet's path. But this method did not apply to the
possible return of the wandering star. Halley has the glory of
having first detected a periodical comet, in the case of that which
has since borne his name. But this great discovery was not made
without labor. In 1705, Halley[98\7] explained how the parabolic
orbit of a planet may be determined from three observations; and,
joining example to precept, himself calculated the positions and
orbits of twenty-four comets. He found, as the reward of this
industry, that the comets of 1607 and of 1531 had the same orbit as
that of 1682. And here the intervals are also nearly the same,
namely, about seventy-five years. Are the three comets then
identical? In looking back into the history of such appearances, he
found comets recorded in 1456, in 1380, and in 1305; the intervals
are still the same, seventy-five or seventy-six years. It was
impossible now to doubt that they were the periods of a revolving
body; that the comet was a planet; its orbit a long ellipse, not a
parabola.[99\7]

[Note 96\7: Bailly, ii. 246.]

[Note 97\7: _Principia_, ed. 1. p. 494.]

[Note 98\7: Bailly, ii. 646.]

[Note 99\7: The importance of Halley's labors on Comets has always
been acknowledged. In speaking of Halley's _Synopsis Astronomicæ
Cometicæ_, Delambre says (_Ast._ xviii. _Siècle_, p. 130), "Voilà
bien, depuis Kepler, ce qu'on a fait de plus grand, de plus beau, de
plus neuf en astronomie." Halley, in predicting the comet of 1758,
says, if it returns, "Hoc primum ab homine Anglo iuventum fuisse non
inficiabitur æqua posteritas."]

But if this were so, the Comet must reappear in 1758 or 1759. Halley
predicted that it would do so; and the fulfilment of this prediction
was naturally looked forwards to, as an additional stamp of the
truths of the theory of gravitation. {451}

But in all this, the Comet had been supposed to be affected only by
the attraction of the sun. The planets must disturb its motion as
they disturb each other. How would this disturbance affect the time
and circumstances of its reappearance? Halley had proposed, but not
attempted to solve, this question.

The effect of perturbations upon a comet defeats all known methods
of approximation, and requires immense labor. "Clairaut," says
Bailly,[100\7] "undertook this: with courage enough to dare the
adventure, he had talent enough to obtain a memorable victory;" the
difficulties, the labors, grew upon him as he advanced, but he
fought his way through them, assisted by Lalande, and by a female
calculator, Madame Lepaute. He predicted that the comet would reach
its perihelion April 13, 1759, but claimed the license of a month
for the inevitable inaccuracy of a calculation which, in addition to
all other sources of error, was made in haste, that it might appear
as a prediction. The comet justified his calculations and his caution
together; for it arrived at its perihelion on the 13th of March.

[Note 100\7: Bailly, _A. M._ iii. 190.]

Two other Comets, of much shorter period, have been detected of late
years; Encke's, which revolves round the sun in three years and
one-third, and Biela's which describes an ellipse, not extremely
eccentric, in six years and three-quarters. These bodies, apparently
thin and vaporous masses, like other comets, have, since their
orbits were calculated, punctually conformed to the law of
gravitation. If it were still doubtful whether the more conspicuous
comets do so, these bodies would tend to prove the fact, by showing
it to be true in an intermediate case.

[2d Ed.] [A third Comet of short period was discovered by Faye, at the
Observatory of Paris, Nov. 22, 1843. It is included between the orbits
of Mars and Saturn, and its period is seven years and three-tenths.

This is commonly called _Faye's Comet_, as the two mentioned in the
text are called _Encke's_ and _Biela's_. In the former edition I had
expressed my assent to the rule proposed by M. Arago, that the latter
ought to be called _Gambart's Comet_, in honor of the astronomer who
first proved it to revolve round the Sun. But astronomers in general
have used the former name, considering that the discovery and
observation of the object are more distinct and conspicuous merits
than a calculation founded upon the observations of others. And in
reality {452} Biela had great merit in the discovery of his Comet's
periodicity, having set about his search of it from an anticipation of
its return founded upon former observations.

Also a Comet was discovered by De Vico at Rome on Aug. 22, 1844,
which was found to describe an elliptical orbit having its aphelion
near the orbit of Jupiter, which is consequently one of those of
short period. And on Feb. 26, 1846, M. Brorsen of Kiel discovered a
telescopic Comet whose orbit is found to be elliptical.]

We may add to the history of Comets, that of Lexell's, which, in
1770, appeared to be revolving in a period of about five years, and
whose motion was predicted accordingly. The prediction was
disappointed; but the failure was sufficiently explained by the
comet's having passed close to Jupiter, by which occurrence its
orbit was utterly deranged.

It results from the theory of universal gravitation, that Comets are
collections of extremely attenuated matter. Lexell's is supposed to
have passed twice (in 1767 and 1779) through the system of Jupiter's
Satellites, without disturbing their motions, though suffering
itself so great a disturbance as to have its orbit entirely altered.
The same result is still more decidedly proved by the last
appearance of Biela's Comet. It appeared double, but the two bodies
did not perceptibly affect each other's motions, as I am informed by
Professor Challis of Cambridge, who observed both of them from Jan.
23 to Mar. 25, 1846. This proves the quantity of matter in each body
to have been exceedingly small.

Thus, no verification of the Newtonian theory, which was possible in
the motions of the stars, has yet been wanting. The return of
Halley's Comet again in 1835, and the extreme exactitude with which
it conformed to its predicted course, is a testimony of truth, which
must appear striking even to the most incurious respecting such
matters.[101\7]

[Note 101\7: M. de Humboldt (_Kosmos_, p. 116) speaks of _nine_
returns of Halley's Comet, the comet observed in China in 1378 being
identified with this. But whether we take 1378 or 1380 for the
appearance in that century, if we begin with that, we have only
_seven_ appearances, namely, in 1378 or 1380, in 1456, in 1531, in
1607, in 1682, in 1759, and in 1835.]


_Sect._ 7.--_Application of the Newtonian Theory to the Figure of
the Earth._

THE Heavens had thus been consulted respecting the Newtonian
doctrine, and the answer given, over and over again, in a thousand
{453} different forms, had been, that it was true; nor had the most
persevering cross-examination been able to establish any thing of
contradiction or prevarication. The same question was also to be put
to the Earth and the Ocean, and we must briefly notice the result.

According to the Newtonian principles, the form of the earth must be
a globe somewhat flattened at the poles. This conclusion, or at
least the amount of the flattening, depends not only upon the
existence and law of attraction, but upon its belonging to each
particle of the mass separately; and thus the experimental
confirmation of the form asserted from calculation, would be a
verification of the theory in its widest sense. The application of
such a test was the more necessary to the interests of science,
inasmuch as the French astronomers had collected from their measures,
and had connected with their Cartesian system, the opinion that the
earth was not _oblate_ but _oblong_. Dominic Cassini had measured
seven degrees of latitude from Amiens to Perpignan, in 1701, and
found them to decrease in going from south to north. The prolongation
of this measure to Dunkirk confirmed the same result. But if the
Newtonian doctrine was true, the contrary ought to be the case, and
the degrees ought to increase in proceeding towards the pole.

The only answer which the Newtonians could at this time make to the
difficulty thus presented, was, that an arc so short as that thus
measured, was not to be depended upon for the determination of such
a question; inasmuch as the inevitable errors of observation might
exceed the differences which were the object of research. It would,
undoubtedly, have become the English to have given a more complete
answer, by executing measurements under circumstances not liable to
this uncertainty. The glory of doing this, however, they for a long
time abandoned to other nations. The French undertook the task with
great spirit.[102\7] In 1733, in one of the meetings of the French
Academy, when this question was discussed, De la Condamine, an
ardent and eager man, proposed to settle this question by sending
members of the Academy to measure a degree of the meridian near the
equator, in order to compare it with the French degrees, and offered
himself for the expedition. Maupertuis, in like manner, urged the
necessity of another expedition to measure a degree in the
neighborhood of the pole. The government received the applications
favorably, and these remarkable scientific missions were sent out at
the national expense. {454}

[Note 102\7: Bailly, iii. 11.]

As soon as the result of these measurements was known, there was no
longer any doubt as to the fact of the earth's oblateness, and the
question only turned upon its quantity. Even before the return of
the academicians, the Cassinis and Lacaille had measured the French
arc, and found errors which subverted the former result, making the
earth oblate to the amount of 1⁄168th of its diameter. The
expeditions to Peru and to Lapland had to struggle with difficulties
in the execution of their design, which make their narratives
resemble some romantic history of irregular warfare, rather than the
monotonous records of mere measurements. The equatorial degree
employed the observers not less than eight years. When they did
return, and the results were compared, their discrepancy, as to
quantity, was considerable. The comparison of the Peruvian and
French arcs gave an ellipticity of nearly 1⁄314th, that of the
Peruvian and Swedish arcs gave 1⁄213th for its value.

Newton had deduced from his theory, by reasonings of singular
ingenuity, an ellipticity of 1⁄230th; but this result had been
obtained by supposing the earth homogeneous. If the earth be, as we
should most readily conjecture it to be, more dense in its interior
than at its exterior, its ellipticity will be less than that of a
homogeneous spheroid revolving in the same time. It does not appear
that Newton was aware of this; but Clairaut, in 1743, in his _Figure
of the Earth_, proved this and many other important results of the
attraction of the particles. Especially he established that, in
proportion as the fraction expressing the Ellipticity becomes
smaller, that expressing the Excess of the polar over the equatorial
gravity becomes larger; and he thus connected the measures of the
ellipticity obtained by means of Degrees, with those obtained by
means of Pendulums in different latitudes.

The altered rate of a Pendulum when carried towards the equator, had
been long ago observed by Richer and Halley, and had been quoted by
Newton as confirmatory of his theory. Pendulums were swung by the
academicians who measured the degrees, and confirmed the general
character of the results.

But having reached this point of the verification of the Newtonian
theory, any additional step becomes more difficult. Many excellent
measures, both of Degrees and of Pendulums, have been made since
those just mentioned. The results of the Arcs[103\7] is an
Ellipticity of 1⁄298th;--of the Pendulums, an Ellipticity of about
1⁄285th. This difference {455} is considerable, if compared with the
quantities themselves; but does not throw a shadow of doubt on the
truth of the theory. Indeed, the observations of each kind exhibit
irregularities which we may easily account for, by ascribing them to
the unknown distribution of the denser portions of the earth; but
which preclude the extreme of accuracy and certainty in our result.

[Note 103\7: Airy, _Fig. Earth_, p. 230.]

But the near agreement of the determination, from Degrees and from
Pendulums, is not the only coincidence by which the doctrine is
confirmed. We can trace the effect of the earth's Oblateness in
certain minute apparent motions of the stars; for the attraction of
the sun and moon on the protuberant matter of the spheroid produces
the Precession of the equinoxes, and a Nutation of the earth's axis.
The Precession had been known from the time of Hipparchus, and the
existence of Nutation was foreseen by Newton; but the quantity is so
small, that it required consummate skill and great labor in Bradley
to detect it by astronomical observation. Being, however, so
detected, its amount, as well as that of the Precession, gives us
the means of determining the amount of Terrestrial Ellipticity, by
which the effect is produced. But it is found, upon calculation,
that we cannot obtain this determination without assuming some law
of density in the homogeneous strata of which we suppose the earth
to consist[104\7] The density will certainly increase in proceeding
towards the centre, and there is a simple and probable law of this
increase, which will give 1⁄300th for the Ellipticity, from the
amount of two lunar Inequalities (one in latitude and one in
longitude), which are produced by the earth's oblateness. Nearly the
same result follows from the quantity of Nutation. Thus every thing
tends to convince us that the ellipticity cannot deviate much from
this fraction.

[Note 104\7: Airy, _Fig. Earth_, p. 235.]

[2d Ed.] [I ought not to omit another class of phenomena in which
the effects of the Earth's Oblateness, acting according to the law
of universal gravitation, have manifested themselves;--I speak of
the Moon's Motion, as affected by the Earth's Ellipticity. In this
case, as in most others, observation anticipated theory. Mason had
inferred from lunar observations a certain Inequality in Longitude,
depending upon the distance of the Moon's Node from the Equinox.
Doubts were entertained by astronomers whether this inequality
really existed; but Laplace showed that such an inequality would
arise from the oblate form of the earth; and that its magnitude
might serve to {456} determine the amount of the oblateness. Laplace
showed, at the same time, that along with this Inequality in
Longitude there must be an Inequality in Latitude; and this
assertion Burg confirmed by the discussion of observations. The two
Inequalities, as shown in the observations, agree in assigning to
the earth's form an Ellipticity of 1⁄305th.]


_Sect._ 8.--_Confirmation of the Newtonian Theory by Experiments on
Attraction._

THE attraction of all the parts of the earth to one another was thus
proved by experiments, in which the whole mass of the earth is
concerned. But attempts have also been made to measure the
attraction of smaller portions; as mountains, or artificial masses.
This is an experiment of great difficulty; for the attraction of
such masses must be compared with that of the earth, of which it is
a scarcely perceptible fraction; and, moreover, in the case of
mountains, the effect of the mountain will be modified or disguised
by unknown or unappreciable circumstances. In many of the
measurements of degrees, indications of the attraction of mountains
had been perceived; but at the suggestion of Maskelyne, the
experiment was carefully made, in 1774, upon the mountain
Schehallien, in Scotland, the mountain being mineralogically
surveyed by Playfair. The result obtained was, that the attraction
of the mountain drew the plumb-line about six seconds from the
vertical; and it was deduced from this, by Hutton's calculations,
that the density of the earth was about once and four-fifths that of
Schehallien, or four and a half times that of water.

Cavendish, who had suggested many of the artifices in this
calculation, himself made the experiment in the other form, by using
leaden balls, about nine inches diameter. This observation was
conducted with an extreme degree of ingenuity and delicacy, which
could alone make it valuable; and the result agreed very nearly with
that of the Schehallien experiment, giving for the density of the
earth about five and one-third times that of water. Nearly the same
result was obtained by Carlini, in 1824, from observations of the
pendulum, made at a point of the Alps (the Hospice, on Mount Cenis) at
a considerable elevation above the average surface of the earth. {457}


_Sect._ 9.--_Application of the Newtonian Theory to the Tides._

WE come, finally, to that result, in which most remains to be done
for the verification of the general law of attraction--the subject
of the Tides. Yet, even here, the verification is striking, as far
as observations have been carried. Newton's theory explained, with
singular felicity, all the prominent circumstances of the tides then
known;--the difference of spring and neap tides; the effect of the
moon's and sun's declination and parallax; even the difference of
morning and evening tides, and the anomalous tides of particular
places. About, and after, this time, attempts were made both by the
Royal Society of England, and by the French Academy, to collect
numerous observations  but these were not followed up with
sufficient perseverance. Perhaps, indeed, the theory had not been at
that time sufficiently developed  but the admirable prize-essays of
Euler, Bernoulli, and D'Alembert, in 1740, removed, in a great
measure, this deficiency. These dissertations supplied the means of
bringing this subject to the same test to which all the other
consequences of gravitation had been subjected;--namely, the
calculation of tables, and the continued and orderly comparison of
these with observation. Laplace has attempted this verification in
another way, by calculating the results of the theory (which he has
done with an extraordinary command of analysis), and then by
comparing these, in supposed critical cases, with the Brest
observations. This method has confirmed the theory as far as it
could do so; but such a process cannot supersede the necessity of
applying the proper criterion of truth in such cases, the
construction and verification of Tables. Bernoulli's theory, on the
other hand, has been used for the construction of Tide-tables; but
these have not been properly compared with experiment; and when the
comparison has been made, having been executed for purposes of gain
rather than of science, it has not been published, and cannot be
quoted as a verification of the theory.

Thus we have, as yet, no sufficient comparison of fact with theory,
for Laplace's is far from a complete comparison. In this, as in
other parts of physical astronomy, our theory ought not only to
agree with observations selected and grouped in a particular manner,
but with the whole course of observation, and with every part of the
phenomena. In this, as in other cases, the true theory should be
verified by its giving us the best Tables; but Tide-tables were
never, I believe, {458} calculated upon Laplace's theory, and thus
it was never fairly brought to the test.

It is, perhaps, remarkable, considering all the experience which
astronomy had furnished, that men should have expected to reach the
completion of this branch of science by improving the mathematical
theory, without, at the same time, ascertaining the laws of the
facts. In all other departments of astronomy, as, for instance, in
the cases of the moon and the planets, the leading features of the
phenomena had been made out empirically, before the theory explained
them. The course which analogy would have recommended for the
cultivation of our knowledge of the tides, would have been, to
ascertain, by an analysis of long series of observations, the effect
of changes in the time of transit, parallax, and declination of the
moon, and thus to obtain the laws of phenomena  and then proceed to
investigate the laws of causation.

Though this was not the course followed by mathematical theorists,
it was really pursued by those who practically calculated
Tide-tables; and the application of knowledge to the useful purposes
of life being thus separated from the promotion of the theory, was
naturally treated as a gainful property, and preserved by secrecy.
Art, in this instance, having cast off her legitimate subordination
to Science, or rather, being deprived of the guidance which it was
the duty of Science to afford, resumed her ancient practices of
exclusiveness and mystery. Liverpool, London, and other places, had
their Tide-tables, constructed by undivulged methods, which methods,
in some instances at least, were handed down from father to son for
several generations as a family possession; and the publication of
new Tables, accompanied by a statement of the mode of calculation,
was resented as an infringement of the rights of property.

The mode in which these secret methods were invented, was that which
we have pointed out;--the analysis of a considerable series of
observations. Probably the best example of this was afforded by the
Liverpool Tide-tables. These were deduced by a clergyman named
Holden, from observations made at that port by a harbor-master of
the name of Hutchinson; who was led, by a love of such pursuits, to
observe the tides carefully for above twenty years, day and night.
Holden's Tables, founded on four years of these observations, were
remarkably accurate.

At length men of science began to perceive that such calculations
were part of their business; and that they were called upon, as the
{459} guardians of the established theory of the universe, to
compare it in the greatest possible detail with the facts. Mr.
Lubbock was the first mathematician who undertook the extensive
labors which such a conviction suggested. Finding that regular
tide-observations had been made at the London Docks from 1795, he
took nineteen years of these (purposely selecting the length of a
cycle of the motions of the lunar orbit), and caused them (in 1831)
to be analyzed by Mr. Dessiou, an expert calculator. He thus
obtained[105\7] Tables for the effect of the Moon's Declination,
Parallax, and hour of Transit, on the tides; and was enabled to
produce Tide-tables founded upon the data thus obtained. Some
mistakes in these as first published (mistakes unimportant as to the
theoretical value of the work), served to show the jealousy of the
practical tide-table calculators, by the acrimony with which the
oversights were dwelt upon; but in a very few years, the tables thus
produced by an open and scientific process were more exact than
those which resulted from any of the secrets; and thus practice was
brought into its proper subordination to theory.

[Note 105\7: _Phil. Trans._ 1831. _British Almanac_, 1832.]

The theory with which Mr. Lubbock was led to compare his results, was
the Equilibrium-theory of Daniel Bernoulli; and it was found that this
theory, with certain modifications of its elements, represented the
facts to a remarkable degree of precision. Mr. Lubbock pointed out
this agreement especially in the semi-mensual inequality of the times
of high water. The like agreement was afterwards (in 1833) shown by
Mr. Whewell[106\7] to obtain still more accurately at Liverpool, both
for the Times and Heights; for by this time, nineteen years of
Hutchinson's Liverpool Observations had also been discussed by Mr.
Lubbock. The other inequalities of the Times and Heights (depending
upon the Declination and Parallax of the Moon and Sun,) were variously
compared with the Equilibrium-theory by Mr. Lubbock and Mr. Whewell;
and the general result was, that the facts agreed with the condition
of equilibrium at a certain anterior time, but that this anterior time
was different for different phenomena. In like manner it appeared to
follow from these researches, that in order to explain the facts, the
mass of the moon must be supposed different in the calculation at
different places. A result in effect the same was obtained by M.
Daussy,[107\7] an active French Hydrographer; for he found that
observations at various stations could not be reconciled with the
formulæ of Laplace's _Mécanique_ {460} _Céleste_ (in which the ratio
of the heights of spring-tides and neap-tides was computed on an
assumed mass of the moon) without an alteration of level which was, in
fact, equivalent to an alteration of the moon's mass. Thus all things
appeared to tend to show that the Equilibrium-theory would give the
_formulæ_ for the inequalities of the tides, but that the _magnitudes_
which enter into these formulæ must be sought from observation.

[Note 106\7: _Phil. Trans._ 1834.]

[Note 107\7: _Connaissance des Tems_, 1838.]

Whether this result is consistent with theory, is a question not so
much of Physical Astronomy as of Hydrodynamics, and has not yet been
solved. A Theory of the Tides which should include in its conditions
the phenomena of Derivative Tides, and of their combinations, will
probably require all the resources of the mathematical mechanician.

As a contribution of empirical materials to the treatment of this
hydrodynamical problem, it may be allowable to mention here Mr.
Whewell's attempts to trace the progress of the tide into all the
seas of the globe, by drawing on maps of the ocean what he calls
_Cotidal Lines_;--lines marking the contemporaneous position of the
various points of the great wave which carries high water from shore
to shore.[108\7] This is necessarily a task of labor and difficulty,
since it requires us to know the time of high water on the same day
in every part of the world; but in proportion as it is completed, it
supplies steps between our general view of the movements of the
ocean and the phenomena of particular ports.

[Note 108\7: Essay towards a First Approximation to a Map of Cotidal
Lines. _Phil. Trans._ 1833, 1836.]

Looking at this subject by the light which the example of the
history of astronomy affords, we may venture to repeat, that it will
never have justice done it till it is treated as other parts of
astronomy are treated; that is, till Tables of all the phenomena
which can be observed, are calculated by means of the best knowledge
which we at present possess, and till these tables are constantly
improved by a comparison of the predicted with the observed fact. A
set of Tide-observations and Tide-ephemerides of this kind, would
soon give to this subject that precision which marks the other parts
of astronomy; and would leave an assemblage of unexplained _residual
phenomena_, in which a careful research might find the materials of
other truths as yet unsuspected.

[2d Ed.] [That there would be, in the tidal movements of the ocean,
inequalities of the heights and times of high and low water {461}
_corresponding_ to those which the equilibrium theory gives, could
be considered only as a conjecture, till the comparison with
observation was made. It was, however, a natural conjecture; since
the waters of the ocean are at every moment _tending_ to acquire the
form assumed in the equilibrium theory: and it may be considered
likely that the causes which prevent their assuming this form
produce an effect nearly constant for each place. Whatever be
thought of this reasoning, the conjecture is confirmed by
observation with curious exactness. The laws of a great number of
the tidal phenomena--namely, of the Semi-mensual Inequality of the
Heights, of the Semi-mensual Inequality of the Times, of the Diurnal
Inequality, of the effect of the Moon's Declination, of the effect
of the Moon's Parallax--are represented very closely by formulæ
derived from the equilibrium theory. The hydrodynamical mode of
treating the subject has not added any thing to the knowledge of the
laws of the phenomena to which the other view had conducted us.

We may add, that Laplace's assumption, that in the moving fluid the
motions must have a _periodicity_ corresponding to that of the
forces, is also a conjecture. And though this conjecture may, in
some cases of the problem, be verified, by substituting the
resulting expressions in the equations of motion, this cannot be
done in the actual case, where the revolving motion of the ocean is
prevented by the intrusion of tracts of land running nearly from
pole to pole.

Yet in Mr. Airy's Treatise _On Tides and Waves_ (in the
_Encyclopædia Metropolitana_) much has been done to bring the
hydrodynamical theory of oceanic tides into agreement with
observation. In this admirable work, Mr. Airy has, by peculiar
artifices, solved problems which come so near the actual cases that
they may represent them. He has, in this way, deduced the laws of
the semi-diurnal and the diurnal tide, and the other features of the
tides which the equilibrium theory in some degree imitates; but he
has also, taking into account the effect of friction, shown that the
actual tide may be represented as the tide of an earlier
epoch;--that the relative mass of the moon and sun, as inferred from
the tides, would depend upon the depth of the ocean (Art.
455);--with many other results remarkably explaining the observed
phenomena. He has also shown that the relation of the cotidal lines
to the tide waves really propagated is, in complex cases, very
obscure, because different waves of different magnitudes, travelling
in different directions, may coexist, and the cotidal line is the
compound result of all these. {462}

With reference to the _Maps of Cotidal Lines_, mentioned in the
text, I may add, that we are as yet destitute of observations which
should supply the means of drawing such lines on a large scale in
the Pacific Ocean. Admiral Lütke has however supplied us with some
valuable materials and remarks on this subject in his _Notice sur
les Marées Périodiques dans le grand Océan Boréal et dans la Mer
Glaciale_; and has drawn them, apparently on sufficient data, in the
White Sea.]




CHAPTER V.

DISCOVERIES ADDED TO THE NEWTONIAN THEORY.


_Sect._ 1.--_Tables of Astronomical Refraction._

WE have travelled over an immense field of astronomical and
mathematical labor in the last few pages, and have yet, at the end
of every step, still found ourselves under the jurisdiction of the
Newtonian laws. We are reminded of the universal monarchies, where a
man could not escape from the empire without quitting the world. We
have now to notice some other discoveries, in which this reference
to the law of universal gravitation is less immediate and obvious; I
mean the astronomical discoveries respecting Light.

The general truths to which the establishment of the true laws of
Atmospheric Refraction led astronomers, were the law of Deflection
of the rays of light, which applies to all refractions, and the real
structure and size of the Atmosphere, so far as it became known. The
great discoveries of Römer and Bradley, namely, the Velocity of
Light, the Aberration of Light, and the Nutation of the earth's
axis, gave a new distinctness to the conceptions of the propagation
of light in the minds of philosophers, and confirmed the doctrines
of Copernicus, Kepler, and Newton, respecting the motions which
belong to the earth.

The true laws of Atmospheric Refraction were slowly discovered.
Tycho attributed the apparent displacement of the heavenly bodies to
the low and gross part of the atmosphere only, and hence made it
cease at a point half-way to the zenith; but Kepler rightly extended
it to the zenith itself. Dominic Cassini endeavored to discover the
law of this correction by observation, and gave his result in the
form {463} which, as we have said, sound science prescribes, a Table
to be habitually used for all observations. But great difficulties
at this time embarrassed this investigation, for the parallaxes of
the sun and of the planets were unknown, and very diverse values had
been assigned them by different astronomers. To remove some of these
difficulties, Richer, in 1762, went to observe at the equator; and
on his return, Cassini was able to confirm and amend his former
estimations of parallax and refraction. But there were still
difficulties. According to La Hire, though the phenomena of twilight
give an altitude of 34,000 toises to the atmosphere,[109\7] those of
refraction make it only 2000. John Cassini undertook to support and
improve the calculations of his father Dominic, and took the true
supposition, that the light follows a curvilinear path through the
air. The Royal Society of London had already ascertained
experimentally the refractive power of air.[110\7] Newton calculated
a Table of Refractions, which was published under Halley's name in
the _**Philosophical Transactions_ for 1721, without any indication
of the method by which it was constructed. But M. Biot has recently
shown,[111\7] by means of the published correspondence of Flamsteed,
that Newton had solved the problem in a manner nearly corresponding
to the most improved methods of modern analysis.

[Note 109\7: Bailly, ii. 612.]

[Note 110\7: Ibid. ii. 607.]

[Note 111\7: Biot, _Acad. Sc. Compte Rendu_, Sept. 5, 1836.]

Dominic Cassini and Picard proved,[112\7] Le Monnier in 1738
confirmed more fully, the fact that the variations of the
Thermometer affect the Refraction. Mayer, taking into account both
these changes, and the changes indicated by the Barometer, formed a
theory, which Lacaille, with immense labor, applied to the
construction of a Table of Refractions from observation. But
Bradley's Table (published in 1763 by Maskelyne) was more commonly
adopted in England; and his formula, originally obtained
empirically, has been shown by Young to result from the most
probable suppositions we can make respecting the atmosphere.
Bessel's Refraction Tables are now considered the best of those
which have appeared.

[Note 112\7: Bailly, iii. 92.]


_Sect._ 2.--_Discovery of the Velocity of Light.--Römer._

THE astronomical history of Refraction is not marked by any great
discoveries, and was, for the most part, a work of labor only. The
progress of the other portions of our knowledge respecting light is
{464} more striking. In 1676, a great number of observations of
eclipses of Jupiter's satellites were accumulated, and could be
compared with Cassini's Tables. Römer, a Danish astronomer, whom
Picard had brought to Paris, perceived that these eclipses happened
constantly later than the calculated time at one season of the year,
and earlier at another season;--a difference for which astronomy
could offer no account. The error was the same for all the
satellites; if it had depended on a defect in the Tables of Jupiter,
it might have affected all, but the effect would have had a
reference to the velocities of the satellites. The cause, then, was
something extraneous to Jupiter. Römer had the happy thought of
comparing the error with the earth's distance from Jupiter, and it
was found that the eclipses happened later in proportion as Jupiter
was further off.[113\7] Thus we see the eclipse later, as it is more
remote; and thus light, the messenger which brings us intelligence
of the occurrence, travels over its course in a measurable time. By
this evidence, light appeared to take about eleven minutes in
describing the diameter of the earth's orbit.

[Note 113\7: Bailly, ii. 17.]

This discovery, like so many others, once made, appears easy and
inevitable; yet Dominic Cassini had entertained the idea for a
moment,[114\7] and had rejected it; and Fontenelle had congratulated
himself publicly on having narrowly escaped this seductive error.
The objections to the admission of the truth arose principally from
the inaccuracy of observation, and from the persuasion that the
motions of the satellites were circular and uniform. Their
irregularities disguised the fact in question. As these irregularities
became clearly known, Römer's discovery was finally established, and
the "Equation of Light" took its place in the Tables.

[Note 114\7: Ib. ii. 419.]


_Sect._ 3.--_Discovery of Aberration.--Bradley._

IMPROVEMENTS in instruments, and in the art of observing, were
requisite for making the next great step in tracing the effect of
the laws of light. It appears clear, on consideration, that since
light and the spectator on the earth are both in motion, the
apparent direction of an object will be determined by the
composition of these motions. But yet the effect of this composition
of motions was (as is usual in such cases) traced as a fact in
observation, before it was clearly seen as a consequence of
reasoning. This fact, the Aberration of Light, the greatest
astronomical discovery of the eighteenth century, belongs to
Bradley, {465} who was then Professor of Astronomy at Oxford, and
afterwards Astronomer Royal at Greenwich. Molyneux and Bradley, in
1725, began a series of observations for the purpose of
ascertaining, by observations near the zenith, the existence of an
annual parallax of the fixed stars, which Hooke had hoped to detect,
and Flamsteed thought he had discovered. Bradley[115\7] soon found
that the star observed by him had a minute apparent motion different
from that which the annual parallax would produce. He thought of a
nutation of the earth's axis as a mode of accounting for this; but
found, by comparison of a star on the other side of the pole, that
this explanation would not apply. Bradley and Molyneux then
considered for a moment an annual alteration of figure in the
earth's atmosphere, such as might affect the refractions, but this
hypothesis was soon rejected.[116\7] In 1727, Bradley resumed his
observations, with a new instrument, at Wanstead, and obtained
empirical rules for the changes of declination of different stars.
At last, accident turned his thoughts to the direction in which he
was to find the cause of the variations which he had discovered.
Being in a boat on the Thames, he observed that the vane on the top
of the mast gave a different apparent direction to the wind, as the
boat sailed one way or the other. Here was an image of his case: the
boat represented the earth moving in different directions at
different seasons, and the wind represented the light of a star. He
had now to trace the consequences of this idea; he found that it led
to the empirical rules, which he had already discovered, and, in
1729, he gave his discovery to the Royal Society. His paper is a
very happy narrative of his labors and his thoughts. His theory was
so sound that no astronomer ever contested it; and his observations
were so accurate, that the quantity which he assigned as the
greatest amount of the change (one nineteenth of a degree) has
hardly been corrected by more recent astronomers. It must be
noticed, however, that he considered the effects in declination
only; the effects in right ascension required a different mode of
observation, and a consummate goodness in the machinery of clocks,
which at that time was hardly attained.

[Note 115\7: Rigaud's Bradley.]

[Note 116\7: Rigaud, p. xxiii.]


_Sect._ 4.--_Discovery of Nutation._

WHEN Bradley went to Greenwich as Astronomer Royal, he continued
with perseverance observations of the same kind as those by which he
had detected Aberration. The result of these was another {466}
discovery; namely, that very Nutation which he had formerly
rejected. This may appear strange, but it is easily explained. The
aberration is an annual change, and is detected by observing a star
at different seasons of the year: the Nutation is a change of which
the cycle is eighteen years; and which, therefore, though it does
not much change the place of a star in one year, is discoverable in
the alterations of several successive years. A very few years'
observations showed Bradley the effect of this change;[117\7] and
long before the half cycle of nine years had elapsed, he had
connected it in his mind with the true cause, the motion of the
moon's nodes. Machin was then Secretary to the Royal Society,[118\7]
and was "employed in considering the theory of gravity, and its
consequences with regard to the celestial motions:" to him Bradley
communicated his conjectures; from him he soon received a Table
containing the results of his calculations; and the law was found to
be the same in the Table and in observation, though the quantities
were somewhat different. It appeared by both, that the earth's pole,
besides the motion which the precession of the equinoxes gives it,
moves, in eighteen years, through a small circle;--or rather, as was
afterwards found by Bradley, an ellipse, of which the axes are
nineteen and fourteen seconds.[119\7]

[Note 117\7: Rigaud, lxiv.]

[Note 118\7: Ib. 25.]

[Note 119\7: Ib. lxvi.]

For the rigorous establishment of the mechanical theory of that
effect of the moon's attraction from which the phenomena of Nutation
flow, Bradley rightly and prudently invited the assistance of the
great mathematicians of his time. D'Alembert, Thomas Simpson, Euler,
and others, answered this call, and the result was, as we have
already said in the last chapter (Sect. 7), that this investigation
added another to the recondite and profound evidences of the
doctrine of universal gravitation.

It has been said[120\7] that Bradley's discoveries "assure him the
most distinguished place among astronomers after Hipparchus and
Kepler." If his discoveries had been made before Newton's, there
could have been no hesitation as to placing him on a level with
those great men. The existence of such suggestions as the Newtonian
theory offered on all astronomical subjects, may perhaps dim, in our
eyes, the brilliance of Bradley's achievements; but this
circumstance cannot place any other person above the author of such
discoveries, and therefore we may consider Delambre's adjudication
of precedence as well warranted, and deserving to be permanent. {467}

[Note 120\7: Delambre, _Ast. du_ 18 _Sièc._ p. 420. Rigaud, xxxvii.]


_Sect._ 5.--_Discovery of the Laws of Double Stars.--The two
Herschels._

NO truth, then, can be more certainly established, than that the law
of gravitation prevails to the very boundaries of the solar system.
But does it hold good further? Do the fixed stars also obey this
universal sway? The idea, the question, is an obvious one--but where
are we to find the means of submitting it to the test of observation?

If the Stars were each insulated from the rest, as our Sun appears
to be from them, we should have been quite unable to answer this
inquiry. But among the stars, there are some which are called
_Double Stars_, and which consist of two stars, so near to each
other that the telescope alone can separate them. The elder Herschel
diligently observed and measured the relative positions of the two
stars in such pairs; and as has so often happened in astronomical
history, pursuing one object he fell in with another. Supposing such
pairs to be really unconnected, he wished to learn, from their
phenomena, something respecting the annual parallax of the earth's
orbit. But in the course of twenty years' observations he made the
discovery (in 1803) that some of these couples were turning round
each other with various angular velocities. These revolutions were
for the most part so slow that he was obliged to leave their
complete determination as an inheritance to the next generation. His
son was not careless of the bequest, and after having added an
enormous mass of observations to those of his father, he applied
himself to determine the laws of these revolutions. A problem so
obvious and so tempting was attacked also by others, as Savary and
Encke, in 1830 and 1832, with the resources of analysis. But a
problem in which the data are so minute and inevitably imperfect,
required the mathematician to employ much judgment, as well as skill
in using and combining these data; and Sir John Herschel, by
employing positions only of the line joining the pair of stars
(which can be observed with comparative exactness), to the exclusion
of their distances (which cannot be measured with much correctness),
and by inventing a method which depended upon the whole body of
observations, and not upon selected ones only, for the determination
of the motion, has made his investigations by far the most
satisfactory of those which have appeared. The result is, that it
has been rendered very probable, that in several of the double stars
the two stars describe ellipses about each other; and therefore that
here also, at an {468} immeasurable distance from our system, the
law of attraction according to the inverse square of the distance,
prevails. And, according to the practice of astronomers when a law
has been established, Tables have been calculated for the future
motions; and we have Ephemerides of the revolutions of suns round
each other, in a region so remote, that the whole circle of our
earth's orbit, if placed there, would be imperceptible by our
strongest telescopes. The permanent comparison of the observed with
the predicted motions, continued for more than one revolution, is
the severe and decisive test of the truth of the theory; and the
result of this test astronomers are now awaiting.

[2d Ed.] [In calculating the orbits of revolving systems of double
stars, there is a peculiar difficulty, arising from the plane of the
orbit being in a position unknown, but probably oblique, to the
visual ray. Hence it comes to pass that even if the orbit be an
ellipse described about the focus by the laws of planetary motion,
it will appear otherwise; and the true orbit will have to be deduced
from the apparent one.

With regard to a difficulty which has been mentioned, that the two
stars, if they are governed by gravity, will not revolve the one
about the other, but both about their common centre of
gravity;--this circumstance adds little difficulty to the problem.
Newton has shown (_Princip._ lib. i. Prop. 61) in the _problem of
two bodies_, the relation between the relative orbits and the orbit
about the common centre of gravity.

_How many of the apparently double stars have orbitual motions?_ Sir
John Herschel in 1833 gave, in his _Astronomy_ (Art. 606), a list of
nine stars, with periods extending from 43 years (η Coronæ) to 1200
years (γ Leonis), which he presented as the chief results then
obtained in this department. In his work on Double Stars, the fruit
of his labors in both hemispheres, which the astronomical world are
looking for with eager expectation, he will, I believe, have a few
more to add to these.

_Is it well established that such double stars attract each other
according to the law of the inverse square of the distance?_ The
answer to this question must be determined by ascertaining whether the
above cases are regulated by the laws of elliptical motion. This is a
matter which it must require a long course of careful observation to
determine in such a number of cases as to prove the universality of
the rule. Perhaps the minds of astronomers are still in suspense upon
the subject. When Sir John Herschel's work shall appear, it will
probably {469} be found that with regard to some of these stars, and γ
Virginis in particular, the conformity of the observations with the
laws of elliptical motion amounts to a degree of exactness which must
give astronomers a strong conviction of the truth of the law. For
since Sir W. Herschel's first measures in 1781, the arc described by
one star about the other is above 305 degrees; and during this period
the angular annual motion has been very various, passing through all
gradations from about 20 minutes to 80 degrees. Yet in the whole of
this change, the two curves constructed, the one from the
observations, the other from the elliptical elements, for the purpose
of comparison, having a total ordinate of 305 parts, do not, in any
part of their course, deviate from each other so much as _two_ such
parts.]

The verification of Newton's discoveries was sufficient employment
for the last century; the first step in the extension of them
belongs to this century. We cannot at present foresee the magnitude
of this task, but every one must feel that the law of gravitation,
before verified in all the particles of our own system, and now
probably extended to the all but infinite distance of the fixed
stars, presses upon our minds with a strong claim to be accepted as
a universal law of the whole material creation.

Thus, in this and the preceding chapter, I have given a brief sketch
of the history of the verification and extension of Newton's great
discovery. By the mass of labor and of skill which this head of our
subject includes, we may judge of the magnitude of the advance in
our knowledge which that discovery made. A wonderful amount of
talent and industry have been requisite for this purpose; but with
these, external means have co-operated. Wealth, authority,
mechanical skill, the division of labor, the power of associations
and of governments, have been largely and worthily applied in
bringing astronomy to its present high and flourishing condition. We
must consider briefly what has thus been done. {470}




CHAPTER VI.

THE INSTRUMENTS AND AIDS OF ASTRONOMY DURING THE NEWTONIAN PERIOD.


_Sect._ 1.--_Instruments._

SOME instruments or other were employed at all periods of
astronomical observation. But it was only when observation had
attained a considerable degree of delicacy, that the exact
construction of instruments became an object of serious care.
Gradually, as the possibility and the value of increased exactness
became manifest, it was seen that every thing which could improve
the astronomer's instruments was of high importance to him. And
hence in some cases a vast increase of size and of expense was
introduced; in other cases new combinations, or the result of
improvements in other sciences, were brought into play. Extensive
knowledge, intense thought, and great ingenuity, were requisite in
the astronomical instrument maker. Instead of ranking with artisans,
he became a man of science, sharing the honor and dignity of the
astronomer himself.

1. _Measure of Angles._--Tycho Brahe was the first astronomer who
acted upon a due appreciation of the importance of good instruments.
The collection of such at Uraniburg was by far the finest which had
ever existed. He endeavored to give steadiness to the frame, and
accuracy to the divisions of his instruments. His Mural Quadrant was
well adapted for this purpose; its radius was five cubits: it is
clear, that as we enlarge the instrument we are enabled to measure
smaller arcs. On this principle many large _gnomons_ were erected.
Cassini's celebrated one in the church of St. Petronius at Bologna,
was eighty-three feet (French) high. But this mode of obtaining
accuracy was soon abandoned for better methods. Three great
improvements were introduced about the same time. The application of
the Micrometer to the telescope, by Huyghens, Malvasia, and Auzout;
the application of the Telescope to the astronomical quadrant; and
the fixation of the centre of its field by a Cross of fine wires
placed in the focus by Gascoigne, and afterwards by Picard. We may
judge how great was the improvement which these contrivances
introduced into the art of {471} observing, by finding that Hevelius
refused to adopt them because they would make all the old
observations of no value. He had spent a laborious and active life
in the exercise of the old methods, and could not bear to think that
all the treasures which he had accumulated had lost their worth by
the discovery of a new mine of richer ore.

[2d Ed.] [Littrow, in his _Die Wunder des Himmels_, Ed. 2, pp. 684,
685, says that Gascoigne invented and used the telescope with wires
in the common focus of the lenses in 1640. He refers to _Phil.
Trans._ xxx. 603. Picard reinvented this arrangement in 1667. I have
already spoken of Gascoigne as the inventor of the micrometer.

Römer (already mentioned, p. 464) brought into use the Transit
Instrument, and the employment of complete Circles, instead of the
Quadrants used till then; and by these means gave to practical
astronomy a new form, of which the full value was not discovered
till long afterwards.**]

The apparent place of the object in the instrument being so
precisely determined by the new methods, the exact Division of the
arc into degrees and their subdivisions became a matter of great
consequence. A series of artists, principally English, have acquired
distinguished places in the lists of scientific fame by their
performances in this way; and from that period, particular
instruments have possessed historical interest and individual
reputation. Graham was one of the first of these artists. He
executed a great Mural Arc for Halley at Greenwich; for Bradley he
constructed the Sector which detected aberration. He also made the
Sector which the French academicians carried to Lapland; and
probably the goodness of this instrument, compared with the
imperfection of those which were sent to Peru, was one main cause of
the great difference of duration in the two series of observations.
Bird, somewhat later[121\7] (about 1750), divided several Quadrants
for public observatories. His method of dividing was considered so
perfect, that the knowledge of it was purchased by the English
government, and published in 1767. Ramsden was equally celebrated.
The error of one of his best Quadrants (that at Padua) is said to be
never greater than two seconds. But at a later period, Ramsden
constructed Mural Circles only, holding this to be a kind of
instrument far superior to the quadrant. He made one of five feet
diameter, in 1788, for M. Piazzi at Palermo; and one of eight feet
for the observatory of Dublin. Troughton, a worthy successor of the
{472} artists we have mentioned, has invented a method of dividing
the circle still superior to the former ones; indeed, one which is
theoretically perfect, and practically capable of consummate
accuracy. In this way, circles have been constructed for Greenwich,
Armagh, Cambridge, and many other places; and probably this method,
carefully applied, offers to the astronomer as much exactness as his
other implements allow him to receive; but the slightest casualty
happening to such an instrument, after it has been constructed, or
any doubt whether the method of graduation has been rightly applied,
makes it unfit for the jealous scrupulosity of modern astronomy.

[Note 121\7: Mont. iv. 337.]

The English artists sought to attain accurate measurements by
continued bisection and other aliquot subdivision of the limb of
their circle; but Mayer proposed to obtain this end otherwise, by
_repeating_ the measure on different parts of the circumference till
the error of the division becomes unimportant, instead of attempting
to divide an instrument without error. This invention of the
Repeating Circle was zealously adopted by the French, and the
relative superiority of the rival methods is still a matter of
difference of opinion.

[2d Ed.] [In the series of these great astronomical mechanists, we
must also reckon George Reichenbach. He was born Aug. 24, 1772, at
Durlach; became Lieutenant of Artillery in the Bavarian service in
1794; (Salinenrath) Commissioner of Salt-works in 1811; and in 1820,
First Commissioner of Water-works and Roads. He became, with
Fraunhofer, the ornament of the mechanical and optical Institute
erected in 1805 at Benedictbeuern by Utzschneider; and his
astronomical instruments, meridian circles, transit instruments,
equatorials, heliometers, make an epoch in Observing Astronomy. His
contrivances in the Salt-works at Berchtesgaden and Reichenhall, in
the Arms Manufactory at Amberg, and in the works for boring cannon
at Vienna, are enduring monuments of his rare mechanical talent. He
died May 21, 1826, at Munich.]

2. _Clocks._--The improvements in the measures of space require
corresponding improvements in the measure of time. The beginning of
any thing which we can call accuracy, in this subject, was the
application of the Pendulum to clocks, by Huyghens, in 1656. That
the successive oscillations of a pendulum occupy equal times, had
been noticed by Galileo; but in order to take advantage of this
property, the pendulum must be connected with machinery by which its
motion is kept from languishing, and by which the number of its
swings is recorded. By inventing such machinery, Huyghens at once
obtained {473} a measure of time more accurate than the sun itself.
Hence astronomers were soon led to obtain the right ascension of a
star, not directly, by measuring a Distance in the heavens, but
indirectly, by observing the Moment of its Transit. This observation
is now made with a degree of accuracy which might, at first sight,
appear beyond the limits of human sense, being noted to a _tenth of
a second of time_: but we may explain this, by remarking that though
the number of the second at which the transit happens is given by
the clock, and is reckoned according to the course of time, the
subdivision of the second of time into smaller fractions is
performed by the eye,--by seeing the space described by the heavenly
body in a whole second, and hence estimating a smaller time,
according to the space which its description occupies.

But in order to make clocks so accurate as to justify this degree of
precision, their construction was improved by various persons in
succession. Picard soon found that Huyghens' clocks were affected in
their going by temperature, for heat caused expansion of the
metallic pendulum. This cause of error was remedied by combining
different metals, as iron and copper, which expand in a different
degree, in such a way that their effects compensate each other.
Graham afterwards used quicksilver for the same purpose. The
_Escapement_ too (which connects the force which impels the clock
with the pendulum which regulates it), and other parts of the
machinery, had the most refined mechanical skill and ingenuity of
the best artists constantly bestowed upon then. The astronomer of
the present day, constantly testing the going of such a clock by the
motions of the fixed stars, has a scale of time as stable and as
minutely exact as the scales on which he measures distance.

The construction of good Watches, that is, portable or marine
clocks, was important on another account, namely, because they might
be used in determining the longitude of places. Hence the
improvement of this little machine became an object of national
interest, and was included in the reward of 20,000_l._, which we
have already noticed as offered by the English parliament for the
discovery of the longitude. Harrison,[122\7] originally a carpenter,
turned his mind to this subject with success. After thirty years of
labor, in which he was encouraged by many eminent persons, he
produced, in 1758, a time-keeper, which was sent on a voyage to
Jamaica for trial. After 161 days, the error {474} of the watch was
only one minute five seconds, and the artist received from the
nation 5000_l._ At a later period,[123\7] at the age of seventy-five
years, after a life devoted to this object, having still further
satisfied the commissioners, he received, in 1765, 10,000_l._, at
the same time that Euler and the heirs of Mayer received each
3000_l._ for the lunar tables which they had constructed.

[Note 122\7: Mont. iv. 554.]

[Note 123\7: Mont. iv. 560.]

The two methods of finding the longitude, by Chronometers and by
Lunar Observations, have solved the problem for all practical
purposes; but the latter could not have been employed at sea without
the aid of that invaluable instrument, the Sextant, in which the
distance of two objects is observed, by bringing one to coincide
apparently with the reflected image of the other. This instrument
was invented by Hadley, in 1731. Though the problem of finding the
longitude be, in fact, one of geography rather than astronomy, it is
an application of astronomical science which has so materially
affected the progress of our knowledge, that it deserves the notice
we have bestowed upon it.

3. _Telescopes._--We have spoken of the application of the telescope
to astronomical measurements, but not of the improvement of the
telescope itself. If we endeavor to augment the optical power of
this instrument, we run, according to the path we take, into various
inconveniences;--distortion, confusion, want of light, or colored
images. Distortion and confusion are produced, if we increase the
magnifying power, retaining the length and the aperture of the
object-glass. If we diminish the aperture we suffer from loss of
light. What remains then is to increase the focal length. This was
done to an extraordinary extent, in telescopes constructed in the
beginning of the last century. Huyghens, in his first attempts, made
them 22 feet long;[124\7] afterwards, Campani, by order of Louis the
Fourteenth, made them of 86, 100, and 136 feet. Huyghens, by new
exertions, made a telescope 210 feet long. Auzout and Hartsoecker
are said to have gone much further, and to have succeeded in making
an object-glass of 600 feet focus. But even such telescopes as those
of Campani are almost unmanageable: in that of Huyghens, the
object-glass was placed on a pole, and the observer was placed at
the focus with an eye-glass.

[Note 124\7: Bailly, ii. 253.]

The most serious objection to the increase of the aperture of
object-glasses, was the coloration of the image produced, in
consequence of the unequal refrangibility of differently colored
rays. Newton, who discovered the principle of this defect in lenses,
had maintained that {475} the evil was irremediable, and that a
compound lens could no more refract without producing color, than a
single lens could. Euler and Klingenstierna doubted the exactness of
Newton's proposition; and, in 1755, Dollond disproved it by
experiment. This discovery pointed out a method of making
object-glasses which should give no color;--which should be
_achromatic_. For this purpose Dollond fabricated various kinds of
glass (flint and crown glass); and Clairaut and D'Alembert
calculated formulæ. Dollond and his son[125\7] succeeded in
constructing telescopes of three feet long (with a triple
object-glass) which produced an effect as great as those of
forty-five feet on the ancient principles. At first it was conceived
that these discoveries opened the way to a vast extension of the
astronomer's power of vision; but it was found that the most
material improvement was the compendious size of the new
instruments; for, in increasing the dimensions, the optician was
stopped by the impossibility of obtaining lenses of flint-glass of
very large dimensions. And this branch of art remained long
stationary; but, after a time, its epoch of advance again arrived.
In the present century, Fraunhofer, at Munich, with the help of
Guinand and the pecuniary support of Utzschneider, succeeded in
forming lenses of flint-glass of a magnitude till then unheard of.
Achromatic object-glasses, of a foot in diameter, and twenty feet
focal length, are now no longer impossible; although in such
attempts the artist cannot reckon on certain success.

[Note 125\7: Bailly, iii. 118.]

[2d Ed.] [Joseph Fraunhofer was born March 6, 1787, at Straubing in
Bavaria, the son of a poor glazier. He was in his earlier years
employed in his father's trade, so that he was not able to attend
school, and remained ignorant of writing and arithmetic till his
fourteenth year. At a later period he was assisted by Utzschneider,
and tried rapidly to recover his lost ground. In the year 1806 he
entered the establishment of Utzschneider as an optician. In this
establishment (transferred from Benedictbeuern to Munich in 1819) he
soon came to be the greatest Optician of Germany. His excellent
telescopes and microscopes are known throughout Europe. His greatest
telescope, that in the Observatory at Dorpat, has an object-glass of
9 inches diameter, and a focal length of 13⅓ feet. His written
productions are to be found in the _Memoirs_ of the Bavarian
Academy, in Gilbert's _Annalen der Physik_, and in Schumacher's
_Astronomische Nachrichten_. He died the 7th of June, 1826.] {476}

Such telescopes might be expected to add something to our knowledge
of the heavens, if they had not been anticipated by reflectors of an
equal or greater scale. James Gregory had invented, and Newton had
more efficaciously introduced, reflecting telescopes. But these were
not used with any peculiar effect, till the elder Herschel made them
his especial study. His skill and perseverance in grinding specula,
and in contriving the best apparatus for their use, were rewarded by
a number of curious and striking discoveries, among which, as we
have already related, was the discovery of a new planet beyond
Saturn. In 1789, Herschel surpassed all his former attempts, by
bringing into action a reflecting telescope of forty feet length,
with a speculum of four feet in diameter. The first application of
this magnificent instrument showed a new satellite (the sixth) of
Saturn. He and his son have, with reflectors of twenty feet, made a
complete survey of the heavens, so far as they are visible in this
country; and the latter is now in a distant region completing this
survey, by adding to it the other hemisphere.

In speaking of the improvements of telescopes we ought to notice,
that they have been pursued in the eye-glasses as well as in the
object-glasses. Instead of the single lens, Huyghens substituted an
eye-piece of two lenses, which, though introduced for another
purpose, attained the object of destroying color.[126\7] Ramsden's
eye-piece is one fit to be used with a micrometer, and others of
more complex construction have been used for various purposes.

[Note 126\7: Coddington's _Optics_, ii. 21.]


_Sect._ 2.--_Observatories._

ASTRONOMY, which is thus benefited by the erection of large and
stable instruments, requires also the establishment of permanent
Observatories, supplied with funds for their support, and for that
of the observers. Such observatories have existed at all periods of
the history of the science; but from the commencement of the period
which we are now reviewing, they multiplied to such an extent that
we cannot even enumerate them. Yet we must undoubtedly look upon
such establishments, and the labors of which they have been the
scene, as important and essential parts of the history of the
progress of astronomy. Some of the most distinguished of the
observatories of modern times we may mention. The first of these
were that of Tycho Brahe {477} at Uraniburg, and that of the
Landgrave of Hesse Cassel, at Cassel, where Rothman and Byrgius
observed. But by far the most important observations, at least since
those of Tycho, which were the basis of the discoveries of Kepler
and Newton, have been made at Paris and Greenwich. The Observatory
of Paris was built in 1667. It was there that the first Cassini made
many of his discoveries; three of his descendants have since labored
in the same place, and two others of his family, the
Maraldis;[127\7] besides many other eminent astronomers, as Picard,
La Hire, Lefêvre, Fouchy, Legentil, Chappe, Méchain, Bouvard.
Greenwich Observatory was built a few years later (1675); and ever
since its erection, the observations there made have been the
foundation of the greatest improvements which astronomy, for the
time, received. Flamsteed, Halley, Bradley, Bliss, Maskelyne, Pond,
have occupied the place in succession: on the retirement of the
last-named astronomer in 1835, Professor Airy was removed thither
from the Cambridge Observatory. In every state, and in almost every
principality in Europe, Observatories have been established; but
these have often fallen speedily into inaction, or have contributed
little to the progress of astronomy, because their observations have
not been published. From the same causes, the numerous private
observatories which exist throughout Europe have added little to our
knowledge, except where the attention of the astronomer has been
directed to some definite points; as, for instance, the magnificent
labors of the Herschels, or the skilful observations made by Mr.
Pond with the Westbury circle, which first pointed out the error of
graduation of the Greenwich quadrants. The Observations, now
regularly published,[128\7] are those of Greenwich, begun by
Maskelyne, and continued quarterly by Mr. Pond; those of Königsberg,
published by Bessel since 1814; of Vienna, by Littrow since 1820; of
Speier, by Schwerd since 1826; those of Cambridge, commenced by Airy
in 1828; of Armagh, by Robinson in 1829. Besides these, a number of
useful observations have been published in journals and occasional
forms; as, for instance, those of Zach, made by Seeberg, near Gotha,
since 1788; and others have been employed in forming catalogues, of
which we shall speak shortly.

[Note 127\7: Mont. iv. 346.]

[Note 128\7: Airy, _Rep._ p. 128.]

[2d Ed.] [I have left the statement of published Observations in the
text as it stood originally. I believe that at present (1847) the
twelve places contained in the following list publish their
Observations quite regularly, or nearly so;--Greenwich, Oxford,
Cambridge, Vienna, {478} Berlin, Dorpat, Munich, Geneva, Paris,
Königsberg, Madras, the Cape of Good Hope.

Littrow, in his translation, adds to the publications noticed in the
text as containing astronomical Observations, Zach's _Monatliche
Correspondenz_, Lindenau and Bohnenberger's _Zeitschrift für
Astronomie_, Bode's _Astronomisches Jahrbuch_, Schumacher's
_Astronomische Nachrichten_.]

Nor has the establishment of observatories been confined to Europe.
In 1786, M. de Beauchamp, at the expense of Louis the Sixteenth,
erected an observatory at Bagdad, "built to restore the Chaldean and
Arabian observations," as the inscription stated; but, probably, the
restoration once effected, the main intention had been fulfilled,
and little perseverance in observing was thought necessary. In 1828,
the British government completed the building of an observatory at
the Cape of Good Hope, which Lacaille had already made an
astronomical station by his observations there at an earlier period
(1750); and an observatory formed in New South Wales by Sir T. M.
Brisbane in 1822, and presented by him to the government, is also in
activity. The East India Company has founded observatories at
Madras, Bombay, and St. Helena; and observations made at the former
of these places, and at St. Helena, have been published.

The bearing of the work done at such observatories upon the past
progress of astronomy, has already been seen in the preceding
narrative. Their bearing upon the present condition of the science
will be the subject of a few remarks hereafter.


_Sect._ 3.--_Scientific Societies._

THE influence of Scientific Societies, or Academical Bodies, has
also been very powerful in the subject before us. In all branches of
knowledge, the use of such associations of studious and inquiring
men is great; the clearness and coherence of a speculator's ideas,
and their agreement with facts (the two main conditions of
scientific truth), are severally but beneficially tested by
collision with other minds. In astronomy, moreover, the vast extent
of the subject makes requisite the division of labor and the support
of sympathy. The Royal Societies of London and of Paris were founded
nearly at the same time as the metropolitan Observatories of the two
countries. We have seen what constellations of philosophers, and
what activity of research, existed at those periods; these
philosophers appear in the lists, their discoveries {479} in the
publications, of the above-mentioned eminent Societies. As the
progress of physical science, and principally of astronomy,
attracted more and more admiration, Academies were created in other
countries. That of Berlin was founded by Leibnitz in 1710; that of
St Petersburg was established by Peter the Great in 1725; and both
these have produced highly valuable Memoirs. In more modern times
these associations have multiplied almost beyond the power of
estimation. They have been formed according to divisions, both of
locality and of subject, conformable to the present extent of
science, and the vast population of its cultivators. It would be
useless to attempt to give a view either of their number or of the
enormous mass of scientific literature which their Transactions
present. But we may notice, as especially connected with our present
subject, the Astronomical Society of London, founded in 1820, which
gave a strong impulse to the pursuit of the science in England.


_Sect._ 4.--_Patrons of Astronomy._

The advantages which letters and philosophy derive from the
patronage of the great have sometimes been questioned; that love of
knowledge, it has been thought, cannot be genuine which requires
such stimulation, nor those speculations free and true which are
thus forced into being. In the sciences of observation and
calculation, however, in which disputed questions can be
experimentally decided, and in which opinions are not disturbed by
men's practical principles and interests, there is nothing
necessarily operating to poison or neutralize the resources which
wealth and power supply to the investigation of truth.

Astronomy has, in all ages, flourished under the favor of the rich and
powerful; in the period of which we speak, this was eminently the
case. Louis the Fourteenth gave to the astronomy of France a
distinction which, without him, it could not have attained. No step
perhaps tended more to this than his bringing the celebrated Dominic
Cassini to Paris. This Italian astronomer (for he was born at
Permaldo, in the county of Nice, and was professor at Bologna), was
already in possession of a brilliant reputation, when the French
ambassador, in the name of his sovereign, applied to Pope Clement the
Ninth, and to the senate of Bologna, that he should be allowed to
remove to Paris. The request was granted only so far as an absence of
six years; but at the end of that time, the benefits and honors which
{480} the king had conferred upon him, fixed him in France. The
impulse which his arrival (in 1669) and his residence gave to
astronomy, showed the wisdom of the measure. In the same spirit, the
French government drew to Paris Römer from Denmark, Huyghens from
Holland, and gave a pension to Hevelius, and a large sum when his
observatory at Dantzic had been destroyed by fire in 1679.

When the sovereigns of Prussia and Russia were exerting themselves to
encourage the sciences in their countries, they followed the same
course which had been so successful in France. Thus, as we have said,
the Czar Peter took Delisle to Petersburg in 1725; the celebrated
Frederick the Great drew to Berlin, Voltaire and Maupertuis, Euler and
Lagrange; and the Empress Catharine obtained in the same way Euler,
two of the Bernoulli's, and other mathematicians. In none of these
instances, however, did it happen that "the generous plant did still
its stock renew," as we have seen was the case at Paris, with the
Cassinis, and their kinsmen the Maraldis.

[2d Ed.] [I may notice among instances of the patronage of
Astronomy, the reward at present offered by the King of Denmark for
the discovery of a Comet.]

It is not necessary to mention here the more recent cases in which
sovereigns or statesmen have attempted to patronize individual
astronomers.


_Sect._ 5.--_Astronomical Expeditions._

BESIDES the pensions thus bestowed upon resident mathematicians and
astronomers, the governments of Europe have wisely and usefully
employed considerable sums upon expeditions and travels undertaken
by men of science for some appropriate object. Thus Picard, in 1671,
was sent to Uraniburg, the scene of Tycho's observations, to
determine its latitude and its longitude. He found that "the City of
the Skies" had utterly disappeared from the earth; and even its
foundations were retraced with difficulty. With the same object,
that of accurately connecting the labors of the places which had
been at different periods the metropolis of astronomy, Chazelles was
sent, in 1693, to Alexandria. We have already mentioned Richer's
astronomical expedition to Cayenne in 1672. Varin and
Deshayes[129\7] were sent a few years later into the same regions
for similar purposes. Halley's expedition to St. {481} Helena in
1677, with the view of observing the southern stars, was at his own
expense; but at a later period (in 1698), he was appointed to the
command of a small vessel by King William the Third, in order that
he might make his magnetical observations in all parts of the world.
Lacaille was maintained by the French government four years at the
Cape of Good Hope (1750-4), for the purpose of observing the stars
of the southern hemisphere. The two transits of Venus in 1761 and
1769, occasioned expeditions to be sent to Kamtschatka and Tobolsk
by the Russians; to the Isle of France, and to Coromandel, by the
French;[130\7] to the isles of St. Helena and Otaheite by the
English; to Lapland and to Drontheim, by the Swedes and Danes. I
shall not here refer to the measures of degrees executed by various
nations, still less the innumerable surveys by land and sea; but I
may just notice the successive English expeditions of Captains Basil
Hall, Sabine, and Foster, for the purpose of determining the length
of the seconds' pendulum in different latitudes; and the voyages of
M. Biot and others, sent by the French government for the same
purpose. Much has been done in this way, but not more than the
progress of astronomy absolutely required; and only a small portion
of that which the completion of the subject calls for.

[Note 129\7: Bailly, ii. 374.]

[Note 130\7: Bailly, iii. 107.]


_Sect._ 6.--_Present State of Astronomy._

ASTRONOMY, in its present condition, is not only much the most
advanced of the sciences, but is also in far more favorable
circumstances than any other science for making any future advance, as
soon as this is possible. The general methods and conditions by which
such an advantage is to be obtained for the various sciences, we shall
endeavor hereafter to throw some light upon; but in the mean time, we
may notice here some of the circumstances in which this peculiar
felicity of the present state of astronomy may be traced.

The science is cultivated by a number of votaries, with an assiduity
and labor, and with an expenditure of private and public resources,
to which no other subject approaches; and the mode of its
cultivation in all public and most private observatories, has this
character--that it forms, at the same time, a constant process of
verification of existing discoveries, and a strict search for any
new discoverable laws. The observations made are immediately
referred to the best tables, and {482} corrected by the best formulæ
which are known; and if the result of such a reduction leaves any
thing unaccounted for, the astronomer is forthwith curious and
anxious to trace this deviation from the expected numbers to its
rule and its origin; and till the first, at least, of these things
is performed, he is dissatisfied and unquiet. The reference of
observations to the state of the heavens as known by previous
researches, implies a great amount of calculation. The exact places
of the stars at some standard period are recorded in _Catalogues_;
their movements, according to the laws hitherto detected, are
arranged in _Tables_; and if these tables are applied to predict the
numbers which observation on each day ought to give, they form
_Ephemerides_. Thus the catalogues of fixed stars of Flamsteed, of
Piazzi, of Maskelyne, of the Astronomical Society, are the basis of
all observation. To these are applied the Corrections for Refraction
of Bradley or Bessel, and those for Aberration, for Nutation, for
Precession, of the best modern astronomers. The observations so
corrected enable the observer to satisfy himself of the delicacy and
fidelity of his measures of time and space; his Clocks and his Arcs.
But this being done, different stars so observed can be compared
with each other, and the astronomer can then endeavor further to
correct his fundamental Elements;--his Catalogue, or his Tables of
Corrections. In these Tables, though previous discovery has
ascertained the law, yet the exact quantity, the _constant_ or
_coefficient_ of the formula, can be exactly fixed only by numerous
observations and comparisons. This is a labor which is still going
on, and in which there are differences of opinion on almost every
point; but the amount of these differences is the strongest evidence
of the certainty and exactness of those doctrines in which all
agree. Thus Lindenau makes the coefficient of Nutation rather less
than nine seconds, which other astronomers give as about nine
seconds and three-tenths. The Tables of Refraction are still the
subject of much discussion, and of many attempts at improvement. And
after or amid these discussions, arise questions whether there be
not other corrections of which the law has not yet been assigned.
The most remarkable example of such questions is the controversy
concerning the existence of an Annual Parallax of the fixed stars,
which Brinkley asserted, and which Pond denied. Such a dispute
between two of the best modern observers, only proves that the
quantity in question, if it really exist, is of the same order as
the hitherto unsurmounted errors of instruments and corrections.

[2d Ed.] [The belief in an appreciable parallax of some of the fixed
{483} stars appears to gain ground among astronomers. The parallax
of 61 _Cygni_, as determined by Bessel, is 0"·34; about one-third of
a second, or 1⁄10000 of a degree. That of _α Centauri_, as
determined by Maclear, is 0"·9, or 1⁄4000 of a degree.]

But besides the fixed stars and their corrections, the astronomer
has the motions of the planets for his field of action. The
established theories have given us tables of these, from which their
daily places are calculated and given in our Ephemerides, as the
_Berliner Jahrbuch_ of Encke, or the _Nautical Almanac_, published
by the government of this country, the _Connaissance des Tems_ which
appears at Paris, or the _Effemeridi di Milano_. The comparison of
the observed with the tabular place, gives us the means of
correcting the coefficients of the tables; and thus of obtaining
greater exactness in the constants of the solar system. But these
constants depend upon the mass and form of the bodies of which the
system is composed; and in this province, as well as in sidereal
astronomy, different determinations, obtained by different paths,
may be compared; and doubts may be raised and may be solved. In this
way, the perturbations produced by Jupiter on different planets gave
rise to a doubt whether his attraction be really proportional to his
mass, as the law of universal gravitation asserts. The doubt has
been solved by Nicolai and Encke in Germany, and by Airy in England.
The mass of Jupiter, as shown by the perturbations of Juno, of
Vesta, and of Encke's Comet, and by the motion of his outermost
Satellite, is found to agree, though different from the mass
previously received on the authority of Laplace. Thus also
Burckhardt, Littrow, and Airy, have corrected the elements of the
Solar Tables. In other cases, the astronomer finds that no change of
the coefficients will bring the Tables and the observations to a
coincidence;--that a new term in the formula is wanting. He obtains,
as far as he can, the law of this unknown term; if possible, he
traces it to some known or probable cause. Thus Mr. Airy, in his
examination of the Solar Tables, not only found that a diminution of
the received mass of Mars was necessary, but perceived discordances
which led him to suspect the existence of a new inequality. Such an
inequality was at length found to result theoretically from the
attraction of Venus. Encke, in his examination of his comet, found a
diminution of the periodic time in the successive revolutions; from
which he inferred the existence of a resisting medium. Uranus still
deviates from his tabular place, and the cause remains yet to be
discovered. (But see the _Additions_ to this volume.) {484}

Thus it is impossible that an assertion, false to any amount which
the existing state of observation can easily detect, should have any
abiding prevalence in astronomy. Such errors may long keep their
ground in any science which is contained mainly in didactic works,
and studied in the closet, but not acted upon elsewhere;--which is
reasoned upon much, but brought to the test of experiment rarely or
never. Here, on the contrary, an error, if it arise, makes its way
into the Tables, into the Ephemeris, into the observer's nightly
List, or his sheet of Reductions; the evidence of sense flies in its
face in a thousand observatories; the discrepancy is traced to its
source, and soon disappears forever.

In this favored branch of knowledge, the most recondite and delicate
discoveries can no more suffer doubt or contradiction, than the most
palpable facts of sense which the face of nature offers to our
notice. The last great discovery in astronomy--the motion of the
stars arising from Aberration--is as obvious to the vast population
of astronomical observers in all parts of the world, as the motion
of the stars about the pole is to the casual night wanderer. And
this immunity from the danger of any large error in the received
doctrines, is a firm platform on which the astronomer can stand and
exert himself to reach perpetually further and further into the
region of the unknown.

The same scrupulous care and diligence in recording all that has
hitherto been ascertained, has been extended to those departments of
astronomy in which we have as yet no general principles which serve
to bind together our acquired treasures. These records may be
considered as constituting a _Descriptive Astronomy_; such are, for
instance, Catalogues of Stars, and Maps of the Heavens, Maps of the
Moon, representations of the appearance of the Sun and Planets as
seen through powerful telescopes, pictures of Nebulæ, of Comets, and
the like. Thus, besides the Catalogue of Fundamental Stars which may
be considered as standard points of reference for all observations
of the Sun, Moon, and Planets, there exist many large catalogues of
smaller stars. Flamsteed's _Historia Celestis_, which much surpassed
any previous catalogue, contained above 3000 stars. But in 1801, the
French _Histoire Céleste_ appeared, comprising observations of
50,000 stars. Catalogues or charts of other special portions of the
sky have been published more recently; and in 1825, the Berlin
Academy proposed to the astronomers of Europe to carry on this work
by portioning out the heavens among them.

[2d Ed.] [Before Flamsteed, the best Catalogue of the Stars was
{485} Tycho Brahe's, containing the places of about 1000 stars,
determined very roughly with the naked eye. On the occasion of a
project of finding the longitude, which was offered to Charles II.,
in 1674, Flamsteed represented that the method was quite useless, in
consequence, among other things, of the inaccuracy of Tycho's places
of the stars. Flamsteed's letters being shown King Charles, he was
startled at the assertion of the fixed stars' places being false in
the Catalogue, and said, with some vehemence, "He must have them
anew observed, examined, and corrected for the use of his seamen."
This was the immediate occasion of building Greenwich Observatory,
and placing Flamsteed there as an observer. Flamsteed's _Historia
Celestis_ contained above 3000 stars, observed with telescopic
sights. It has recently been republished with important improvements
by Mr. Baily. See Baily's _Flamsteed_, p. 38.

The French _Histoire Céleste_ was published in 1801 by Lalande,
containing 50,000 stars, simply as observed by himself and other
French astronomers. The reduction of the observations contained in
this Catalogue to the mean places at the beginning of the year 1800
may be effected by means of Tables published by Schumacher for that
purpose in 1825.

In 1807, Piazzi's Catalogue of 6748 stars, founded on Maskelyne's
Catalogue of 1700, was published; afterwards extended to 7646 stars
in 1814. This is considered as the greatest work undertaken by any
modern astronomer; the observations being well made, reduced, and
compared with those of former astronomers. Piazzi's Catalogue is the
standard and accurate Catalogue, as the _Histoire Céleste_ is the
standard approximate Catalogue for small stars. But the new planets
were discovered mostly by a comparison of the heavens with Bode's
(Berlin) Catalogue.

I may mention other Catalogues of Stars which have recently been
published. Pond's Catalogue contains 1112 Northern stars; Johnson's,
606; Wrottesley's, 1318 (in Right Ascension only); Airy's First
Cambridge Catalogue, 726; his Greenwich Catalogue, 1439. Pearson's
has 520 zodiacal stars; Groombridge's, 4243 circumpolar stars as far
as 50 degrees of North Polar distance; Santini's, a zone 18 degrees
North of the equator. Besides these, Mr. Taylor has published, by
order of the Madras government, a Catalogue of 11,000 stars observed
by him at Madras; and Rumker, who observed in the Observatory
established by Sir Thomas Brisbane at Paramatta (in Australia), has
commenced a Catalogue which is to contain 12,000. Mr. Baily {486}
published two Standard Catalogues; that of the Royal Astronomical
Society, containing 2881 stars; and that of the British Association,
containing 8377 stars. I omit other Catalogues, as those of
Argelander, &c., and Catalogues of Southern Stars.

Of the Berlin Maps, fourteen hours in Right Ascension have been
published; and their value may be judged of by this circumstance, that
it was in a great measure by comparing the heavens with these Maps
that the new planet Astræa was discovered. The Zone observations made
at Königsberg, by the late illustrious astronomer Bessel, deserve to
be mentioned, as embracing a vast number of stars.

The common mode of _designating the Stars_ is founded upon the
ancient constellations as given by Ptolemy; to which Bayer, of
Augsburg, in his _Uranometria_, added the artifice of designating
the brightest stars in each constellation by the Greek letters, α,
β, γ, &c., applied in order of brightness, and when these were
exhausted, the Latin letters. Flamsteed used numbers. As the number
of observed stars increased, various methods were employed for
designating them; and the confusion which has been thus introduced,
both with regard to the boundaries of the constellations and the
nomenclature of the stars in each, has been much complained of
lately. Some attempts have been made to remedy this variety and
disorder. Mr. Argelander has recently recorded stars, according to
their magnitudes as seen by the naked eye, in a _Neue Uranometrie_.

Among representations of the Moon I may mention Hevelius's
_Selenographia_, a work of former times, and Beer and Madler's Map
of the Moon, recently published.]

I have already said something of the observations of the two
Herschels on _Double Stars_, which have led to a knowledge of the
law of the revolution of such systems. But besides these, the same
illustrious astronomers have accumulated enormous treasures of
observations of _Nebulæ_; the materials, it may be, hereafter, of
some vast new generalization with respect to the history of the
system of the universe.

[2d Ed.] [A few measures of Double Stars are to be found in previous
astronomical records. But the epoch of the creation of this part of
the science of astronomy must be placed at the beginning of the
present century, when Sir William Herschel (in 1802) published in
the _Phil. Trans._ a Catalogue of 500 new Nebulæ of various classes,
and in the _Phil. Trans._ 1803, a paper "On the changes in the
relative situation of the Double Stars in 25 years." In succeeding
papers he pursued the subject. In one in 1814 he noticed the
breaking up of the {487} Milky Way in different places, apparently
from some principle of Attraction; and in this, and in one in 1817,
he published those remarkable views on the distribution of the stars
in our own cluster as forming a large stratum, and on the connection
of stars and nebulæ (the stars appearing sometimes to be accompanied
by nebulæ, sometimes to have absorbed a part of the nebula, and
sometimes to have been formed from nebulæ), which have been accepted
and propounded by others as the _Nebular Theory_. Sir William
Herschel's last paper was a Catalogue of 145 new Double Stars
communicated to the Astronomical Society in 1822. In 1827 M. Struve,
of Dorpat (in Russia), published his _Catalogus Novus_, containing
the places of 3112 double stars. While this was going on, Sir John
Herschel and Sir James South published (in the _Phil. Trans._ 1824)
accurate measures of 380 Double and Triple Stars, to which Sir J.
South afterwards added 458. Mr. Dunlop published measures of 253
Southern Double Stars. Other Observations have been published by
Capt. Smyth, Mr. Dawes, &c. The great work of Struve, _Mensuræ
Micrometricæ_, &c., contains 3134 such objects, including most of
Sir W. Herschel's Double Stars. Sir J. Herschel in 1826, 7, and 8
presented to the Astronomical Society about 1000 measures of Double
Stars; and in 1830, good measures of 1236, made with his 20-feet
reflector. His paper in vol. v. of the _Ast. Soc. Mem._, besides
measures of 364 such stars, exhibits all the most striking results,
as to the motion of Double Stars, which have yet been obtained. In
1835 he carried his 20-feet reflector to the Cape of Good Hope for
the purpose of completing the survey of Double Stars and Nebulæ in
the southern hemisphere with the same instruments which had explored
the northern skies. He returned from the Cape in 1838, and is now
(1846) about to give the world the results of his labors. Besides
the stars just mentioned, his work will contain from 1500 to 2000
additional double stars; making a gross number of above 8000; in
which of course are included a number of objects of no great
scientific interest, but in which also are contained the materials
of the most important discoveries which remain to be made by
astronomers. The publication of Sir John Herschel's great work upon
Double Stars and Nebulæ is looked for with eager interest by
astronomers.

Of the observations of Nebulæ we may say what has just been said of
the observations of Double Stars;--that they probably contain the
materials of important future discoveries. It is impossible not to
regard these phenomena with reference to the _Nebular Hypothesis_,
which has been propounded by Laplace, and much more strongly {488}
insisted upon by other persons;--namely, the hypothesis that systems
of revolving planets, of which the Solar System is an example, arise
from the gradual contraction and separation of vast masses of
nebulous matter. Yet it does not appear that any changes have been
observed in nebulæ which tend to confirm this hypothesis; and the
most powerful telescope in the world, recently erected by the Earl
of Rosse, has given results which militate against the hypothesis;
inasmuch as it has shown that what appeared a diffused nebulous mass
is, by a greater power of vision, resolved, in all cases yet
examined, into separate stars.

When astronomical phenomena are viewed with reference to the Nebular
Hypothesis, they do not belong so properly to Astronomy, in the view
here taken of it, as to Cosmogony. If such speculations should
acquire any scientific value, we shall have to arrange them among
those which I have called _Palætiological_ Sciences; namely, those
Sciences which contemplate the universe, the earth, and its
inhabitants, with reference to their historical changes and the
causes of those changes.]



{{489}}
ADDITIONS TO THE THIRD EDITION.




INTRODUCTION.


THERE is a difficulty in writing for popular readers a History of the
Inductive Sciences, arising from this;--that the sympathy of such
readers goes most readily and naturally along the course which leads
to false science and to failure. Men, in the outset of their attempts
at knowledge, are prone to rush from a few hasty observations of facts
to some wide and comprehensive principles; and then, to frame a system
on these principles. This is the opposite of the method by which the
Sciences have really and historically been conducted; namely, the
method of a gradual and cautious ascent from observation to principles
of limited generality, and from them to others more general. This
latter, the true Scientific Method, is _Induction_, and has led to the
_Inductive Sciences_. The other, the spontaneous and delusive course,
has been termed by Francis Bacon, who first clearly pointed out the
distinction, and warned men of the error, _Anticipation_. The
hopelessness of this course is the great lesson of his philosophy; but
by this course proceeded all the earlier attempts of the Greek
philosophers to obtain a knowledge of the Universe.

Laborious observation, narrow and modest inference, caution, slow and
gradual advance, limited knowledge, are all unwelcome efforts and
restraints to the mind of man, when his speculative spirit is once
roused: yet these are the necessary conditions of all advance in the
Inductive Sciences. Hence, as I have said, it is difficult to win the
sympathy of popular readers to the true history of these sciences. The
career of bold systems and fanciful pretences of knowledge is more
entertaining and striking. Not only so, but the bold guesses and
fanciful reasonings of men unchecked by doubt or fear of failure are
often presented as the dictates of _Common Sense_;--as the plain,
unsophisticated, unforced reason of man, acting according to no
artificial rules, but following its own natural course. Such Common
Sense, while it {490} complacently plumes itself on its
clear-sightedness in rejecting arbitrary systems of others, is no less
arbitrary in its own arguments, and often no less fanciful in its
inventions, than those whom it condemns.

We cannot take a better representative of the Common Sense of the
ancient Greeks than Socrates: and we find that his Common Sense,
judging with such admirable sagacity and acuteness respecting moral
and practical matters, offered, when he applied it to physical
questions, examples of the unconscious assumptions and fanciful
reasonings which, as we have said, Common Sense on such subjects
commonly involves.

Socrates, Xenophon tells us (_Memorabilia_, iv. 7), recommended his
friends not to study astronomy, so as to pursue it into scientific
details. This was practical advice: but he proceeded further to
speak of the palpable mistakes made by those who had carried such
studies farthest. Anaxagoras, for instance, he said, held that the
Sun was a Fire:--he did not consider that men can look at a fire,
but they cannot look at the Sun; they become dark by the Sun shining
upon them, but not so by the fire. He did not consider that no
plants can grow well except they have sunshine, but if they are
exposed to the fire they are spoiled. Again, when he said that the
Sun was a stone red-hot, he did not consider that a stone heated by
the fire is not luminous, and soon cools, but the Sun is always
luminous and always hot.

We may easily conceive how a disciple of Anaxagoras would reply to
these arguments. He would say, for example, as we should probably
say at present, that if there were a mass of matter so large and so
hot as Anaxagoras supposed the Sun to be, its light might be as
great and its heat as permanent as the heat and light of the Sun
are, as yet, known to be. In this case the arguments of Socrates are
at any rate no better than the doctrine of Anaxagoras.



{{491}}
BOOK I.

THE GREEK SCHOOL PHILOSOPHY.

CHAPTER II.

THE GREEK SCHOOLS.


_The Platonic Doctrine of Ideas._

IN speaking of the Foundation of the Greek School Philosophy, I have
referred to the dialogue entitled _Parmenides_, commonly ascribed to
Plato. And the doctrines ascribed to Parmenides, in that and in
other works of ancient authors, are certainly remarkable examples of
the tendency which prevailed among the Greeks to rush at once to the
highest generalizations of which the human mind is capable. The
distinctive dogma of the Eleatic School, of which Parmenides was one
of the most illustrious teachers, was that _All Things are One_.
This indeed was rather a doctrine of metaphysical theology than of
physical science. It tended to, or agreed with, the doctrine that
All things are God:--the doctrine commonly called _Pantheism_. But
the tenet of the Platonists which was commonly put in opposition to
this, that we must seek _The One in the Many_, had a bearing upon
physical science; at least, if we interpret it, as it is generally
interpreted, that we must seek the one Law which pervades a
multiplicity of Phenomena. We may however take the liberty of
remarking, that to speak of a Rule which is exemplified in many
cases, as being "the One in the Many" (a way of speaking by which we
put out of sight the consideration what very different kinds of
things _the One_ and _the Many_ are), is a mode of expression which
makes a very simple matter look very mysterious; and is another
example of the tendency which urges speculative men to aim at
metaphysical generality rather than scientific truth.

The Dialogue _Parmenides_ is, as I have said, commonly referred to
Plato. Yet it is entirely different in substance, manner, and
tendency {492} from the most characteristic of the Platonic
Dialogues. In these, Socrates is represented as finally successful
in refuting or routing his adversaries, however confident their tone
and however popular their assertions. They are angered or humbled;
he retains his good temper and his air of superiority, and when they
are exhausted, he sums up in his own way.

In the _Parmenides_, on the contrary, everything is the reverse of
this. Parmenides and Zeno exchange good-humoured smiles at
Socrates's criticism, when the bystanders expect them to grow angry.
They listen to Socrates while he propounds Plato's doctrine of
Ideas; and reply to him with solid arguments which he does not
answer, and which have never yet been answered. Parmenides, in a
patronising way, lets him off; and having done this, being much
entreated, he pronounces a discourse concerning the One and the
Many; which, obscure as it may seem to us, was obviously intended to
be irrefutable: and during the whole of this part of the Dialogue,
the friend of Socrates appears only as a passive respondent, saying
_Yes_ or _No_ as the assertions of Parmenides require him to do;
just in the same way in which the opponents of Socrates are
represented in other Dialogues.

These circumstances, to which other historical difficulties might be
added, seem to show plainly that the _Parmenides_ must be regarded
as an Eleatic, not as a Platonic Dialogue;--as composed to confute,
not to assert, the Platonic doctrine of Ideas.

The Platonic doctrine of Ideas has an important bearing upon the
philosophy of Science, and was suggested in a great measure by the
progress which the Greeks had really made in Geometry, Astronomy,
and other Sciences, as I shall elsewhere endeavor to show. This
doctrine has been recommended in our own time,[1\A] as containing "a
mighty substance of imperishable truth." It cannot fail to be
interesting to see in what manner the doctrine is presented by those
who thus judge of it. The following is the statement of its leading
features which they give us.

[Note 1\A: A. Butler's _Lectures_, Second Series, Lect. viii. p. 132.]

Man's soul is made to contain not merely a consistent scheme of its
own notions, but a direct apprehension of _real and eternal laws
beyond it_. These real and eternal laws are things _intelligible_,
and not things sensible. The laws, impressed upon creation by its
Creator, and apprehended by man, are something equally distinct from
the Creator {493} and from man; and the whole mass of them may be
termed the World of Things purely Intelligible.

Further; there are qualities in the Supreme and Ultimate Cause of
all, which are manifested in his creation; and not merely
manifested, but in a manner--after being brought out of his
super-essential nature into the stage of being which is below him,
but next to him--are then, by the causative act of creation,
deposited in things, differencing them one from the other, so that
the things participate of them (μετέχουσι), communicate with them
(κοινωνοῦσι).

The Intelligence of man, excited to reflection by the impressions of
these objects, thus (though themselves transitory) participant of a
divine quality, may rise to higher conceptions of the perfections
thus faintly exhibited; and inasmuch as the perfections are
unquestionably _real_ existences, and known to be such in the very
act of contemplation, this may be regarded as a distinct
intellectual apprehension of them;--a union of the Reason with the
Ideas in that sphere of being which is common to both.

Finally, the Reason, in proportion as it learns to contemplate the
Perfect and Eternal, desires the enjoyment of such contemplations in
a more consummate degree, and cannot be fully satisfied except in
the actual fruition of the Perfect itself.

These propositions taken together constitute the THEORY OF IDEAS.
When we have to treat of the Philosophy of Science, it may be worth
our while to resume the consideration of this subject.


In this part of the History, the _Timæus_ of Plato is referred to as
an example of the loose notions of the Greek philosophers in their
physical reasonings. And undoubtedly this Dialogue does remarkably
exemplify the boldness of the early Greek attempts at generalization
on such subjects. Yet in this and in other parts the writings of
Plato contain speculations which may be regarded as containing germs
of true physical science; inasmuch as they assume that the phenomena
of the world are governed by mathematical laws;--by relations of
space and number;--and endeavor, too boldly, no doubt, but not
vaguely or loosely, to assign those laws. The Platonic writings
offer, in this way, so much that forms a Prelude to the Astronomy
and other Physical Sciences of the Greeks, that they will deserve
our notice, as supplying materials for the next two Books of the
History, in which these subjects are treated of. {494}




CHAPTER III.

FAILURE OF THE GREEK PHYSICAL PHILOSOPHY.


_Francis Bacon's Remarks._

THOUGH we do not accept, as authority, even the judgments of Francis
Bacon, and shall have to estimate the strong and the weak parts of
his, no less than of other philosophies, we shall find his remarks
on the Greek philosophers very instructive. Thus he says of
Aristotle, (_Nov. Org._ 1. Aph. lxiii.):

"He is an example of the kind of philosophy in which much is made
out of little; so that the basis of experience is too narrow. He
corrupted Natural Philosophy by his Logic, and made the world out of
his Categories. He disposed of the distinction of _dense_ and
_rare_, by which bodies occupy more or less dimensions or space, by
the frigid distinction of _act_ and _power_. He assigned to each
kind of body a single proper motion, so that if they have any other
motion they must receive it from some extraneous source; and imposed
many other arbitrary rules upon Nature; being everywhere more
careful how one may give a ready answer, and make a positive
assertion, than how he may apprehend the variety of nature.

"And this appears most evidently by the comparison of his philosophy
with the other philosophies which had any vogue in Greece. For the
_Homoiomeria_[2\A] of Anaxagoras, the _Atoms_ of Leucippus and
Democritus, the Heaven and Earth of Parmenides, the Love and Hate of
Empedocles, the Fire of Heraclitus, had some trace of the thoughts
of a natural philosopher; some savor of experience, and nature, and
bodily things; while the Physics of Aristotle, in general, sound
only of Logical Terms.

[Note 2\A: For these technical forms of the Greeks, see Sec. 3 of
this chapter.]

"Nor let any one be moved by this--that in his books _Of Animals_,
and in his _Problems_, and in others of his tracts, there is often a
quoting of experiments. For he had made up his mind beforehand; and
did not consult experience in order to make right propositions and
axioms, but when he had settled his system to his will, he twisted
experience {495} round, and made her bend to his system: so that in
this way he is even more wrong than his modern followers, the
Schoolmen, who have deserted experience altogether."

We may note also what Bacon says of the term _Sophist_. (Aph. lxxi.)
"The wisdom of the Greeks was professorial, and prone to run into
disputations: which kind is very adverse to the discovery of Truth.
And the name of _Sophists_, which was cast in the way of contempt,
by those who wished to be reckoned philosophers, upon the old
professors of rhetoric, Gorgias, Protagoras, Hippias, Polus, does,
in fact, fit the whole race of them, Plato,[3\A] Aristotle, Zeno,
Epicurus, Theophrastus; and their successors, Chrysippus, Carneades,
and the rest."

[Note 3\A: It is curious that the attempt to show that Plato's
opponents were not commonly illusive and immoral reasoners, has been
represented as an attempt to obliterate the distinction of "Sophist"
and "Philosopher."--See A. Butler's _Lectures_, i. 357. Note.]

That these two classes of teachers, as moralists, were not different
in their kind, has been urged by Mr. Grote in a very striking and
amusing manner. But Bacon speaks of them here as physical
philosophers; in which character he holds that all of them were
_sophists_, that is, illusory reasoners.


_Aristotle's Account of the Rainbow._

To exemplify the state of physical knowledge among the Greeks, we may
notice briefly Aristotle's account of the _Rainbow_; a phenomenon so
striking and definite, and so completely explained by the optical
science of later times. We shall see that not only the explanations
there offered were of no value, but that even the observation of
facts, so common and so palpable, was inexact. In his _Meteorologica_
(lib. iii. c. 2) he says, "The Rainbow is never more than a
semicircle. And at sunset and sunrise, the circle is least, but the
arch is greatest; when the sun is high, the circle is larger, but the
arch is less." This is erroneous, for the diameter of the circle of
which the arch of the rainbow forms a part, is always the same, namely
82°. "After the autumnal equinox," he adds, "it appears at every hour
of the day; but in the summer season, it does not appear about noon."
It is curious that he did not see the reason of this. The centre of
the circle of which the rainbow is part, is always opposite to the
sun. And therefore if the sun be more than 41° above the horizon, the
centre of the rainbow will be so much below the horizon, that the
place of the rainbow will {496} be entirely below the horizon. In the
latitude of Athens, which is 38°, the equator is 52° above the
horizon, and the rainbow can be visible only when the sun is 11° lower
than it is at the equinoctial noon. These remarks, however, show a
certain amount of careful observation; and so do those which Aristotle
makes respecting the colors. "Two rainbows at most appear: and of
these, each has three colors; but those in the outer bow are duller;
and their order opposite to those in the inner. For in the inner bow
the first and largest arch is red; but in the outer bow the smallest
arch is red, the nearest to the inner; and the others in order. The
colors are red, green, and purple, such as painters cannot imitate."
It is curious to observe how often modern painters disregard even the
order of the colors, which they could imitate, if they attended to it.

It may serve to show the loose speculation which we oppose to
science, if we give Aristotle's attempt to explain the phenomenon of
the Rainbow. It is produced, he says (c. iv.), by Reflexion
(ἀνάκλασις) from a cloud opposite to the sun, when the cloud forms
into drops. And as a reason for the red color, he says that a
bright object seen through darkness appears red, as the flame
through the smoke of a fire of green wood. This notion hardly
deserves notice; and yet it was taken up again by Göthe in our own
time, in his speculations concerning colors.



{{497}}
BOOK II.

THE PHYSICAL SCIENCES IN ANCIENT GREECE.


_Plato's Timæus and Republic._

ALTHOUGH a great portion of the physical speculations of the Greek
philosophers was fanciful, and consisted of doctrines which were
rejected in the subsequent progress of the Inductive Sciences; still
many of these speculations must be considered as forming a Prelude
to more exact knowledge afterwards attained; and thus, as really
belonging to the Progress of knowledge. These speculations express,
as we have already said, the conviction that the phenomena of nature
are governed by laws of space and number; and commonly, the
mathematical laws which are thus asserted have some foundation in
the facts of nature. This is more especially the case in the
speculations of Plato. It has been justly stated by Professor
Thompson (A. Butler's _Lectures_, Third Series, Lect. i. Note 11),
that it is Plato's merit to have discovered that the laws of the
physical universe are resolvable into numerical relations, and
therefore capable of being represented by mathematical formulæ. Of
this truth, it is there said, Aristotle does not betray the
slightest consciousness.

The _Timæus_ of Plato contains a scheme of mathematical and physical
doctrines concerning the universe, which make it far more analogous
than any work of Aristotle to Treatises which, in modern times, have
borne the titles of _Principia_, _System of the World_, and the like.
And fortunately the work has recently been well and carefully studied,
with attention, not only to the language, but to the doctrines and
their bearing upon our real knowledge. Stallbaum has published an
edition of the Dialogue, and has compared the opinions of Plato with
those of Aristotle on the like subjects. Professor Archer Butler of
Dublin has devoted to it several of his striking and eloquent
Lectures; and these have been furnished with valuable annotations by
Professor Thompson of Cambridge; and M. The. Henri Martin, then
Professor at Rennes, published in 1841 two volumes of _Etudes sur le
Timée de Platon_, in {498} which the bearings of the work on Science
are very fully discussed. The Dialogue treats not only concerning the
numerical laws of harmonical sounds, of visual appearances, and of the
motions of planets and stars, but also concerning heat, as well as
light; and concerning water, ice, gold, gems, iron, rust, and other
natural objects;--concerning odors, tastes, hearing, sight, light,
colors, and the powers of sense in general:--concerning the parts and
organs of the body, as the bones, the marrow, the brain, the flesh,
muscles, tendons, ligaments, nerves; the skin, the hair, the nails;
the veins and arteries; respiration; generation; and in short every
obvious point of physiology.

But the opinions delivered in the _Timæus_ upon these latter
subjects have little to do with the progress of real knowledge. The
doctrines, on the other hand, which depend upon geometrical and
arithmetical relations, are portions or preludes of the sciences
which, in the fulness of time, assumed a mathematical form for the
expression of truth.

Among these may be mentioned the arithmetical relations of
harmonical sounds, to which I have referred in the History. These
occur in various parts of Plato's writings. In the _Timæus_, in
which the numbers are most fully given, the meaning of the numbers
is, at first sight, least obvious. The numbers are given as
representing the proportion of the parts of the Soul (_Tim._ pp. 35,
36), which does not immediately refer us to the relations of Sounds.
But in a subsequent part of the Dialogue (47, D), we are told that
music is a privilege of the hearing given on account of Harmony; and
that Harmony has Cycles corresponding to the movements of the Soul;
(referring plainly to those already asserted.) And the numbers which
are thus given by Plato as elements of harmony, are in a great
measure the same as those which express the musical relations of the
tones of the musical scale at this day in use, as M. Henri Martin
shows (_Et. sur le Timée_, note xxiii.) The intervals C to D, C to
F, C to G, C to C, are expressed by the fractions 9/8, 4/3, 3/2,
2/1, and are now called a Tone, a Fourth, a Fifth, an Octave. They
were expressed by the same fractions among the Greeks, and were
called _Tone_, _Diatessaron_, _Diapente_, _Diapason_. The Major and
Minor Third, and the Major and Minor Sixth, were however wanting, it
is conceived, in the musical scale of Plato.

The _Timæus_ contains also a kind of theory of vision by reflexion
from a plane, and in a concave mirror; although the theory is in
this case less mathematical and less precise than that of Euclid,
referred to in chap. ii. of this Book.

One of the most remarkable speculations in the _Timæus_ is that in
{499} which the Regular Solids are assigned as the forms of the
Elements of which the Universe is composed. This curious branch of
mathematics, Solid Geometry, had been pursued with great zeal by
Plato and his friends, and with remarkable success. The five Regular
Solids, the Tetrahedron or regular Triangular Pyramid, the Cube, the
Octahedron, the Dodecahedron, and the Icosahedron, had been
discovered; and the remarkable theorem, that of regular solids there
can be just so many, these and no others, was known. And in the
_Timæus_ it is asserted that the particles of the various elements
have the forms of these solids. Fire has the Pyramid; Earth has the
Cube; Water the Octahedron; Air the Icosahedron; and the
Dodecahedron is the plan of the Universe itself. It was natural that
when Plato had learnt that other mathematical properties had a
bearing upon the constitution of the Universe, he should suppose
that the singular property of space, which the existence of this
limited and varied class of solids implied, should have some
corresponding property in the Universe, which exists in space.

We find afterwards, in Kepler and others, a recurrence to this
assumption; and we may say perhaps that Crystallography shows us that
there are properties of bodies, of the most intimate kind, which
involve such spatial relations as are exhibited in the Regular Solids.
If the distinctions of Crystalline System in bodies were hereafter to
be found to depend upon the chemical elements which predominate in
their composition, the admirers of Plato might point to his doctrine,
of the different form of the particles of the different elements of
the Universe, as a remote Prelude to such a discovery.

But the mathematical doctrines concerning the parts and elements of
the Universe are put forwards by Plato, not so much as assertions
concerning physical facts, of which the truth or falsehood is to be
determined by a reference to nature herself. They are rather
propounded as examples of a truth of a higher kind than any
reference to observation can give or can test, and as revelations of
principles such as must have prevailed in the mind of the Creator of
the Universe; or else as contemplations by which the mind of man is
to be raised above the region of sense, and brought nearer to the
Divine Mind. In the _Timæus_ these doctrines appear rather in the
former of the two lights; as an exposition of the necessary scheme
of creation, so far as its leading features are concerned. In the
seventh Book of the _Polity_, the same doctrines are regarded more
as a mental discipline; as the necessary study of the true
philosopher. But in both places these mathematical {500}
propositions are represented as Realities more real than the
Phenomena;--as a Natural Philosophy of a higher kind than the study
of Nature itself can teach. This is no doubt an erroneous
assumption: yet even in this there is a germ of truth; namely, that
the mathematical laws, which prevail in the universe, involve
mathematical truths  which being demonstrative, are of a higher and
more cogent kind than mere experimental truths.

Notions, such as these of Plato, respecting a truth at which science
is to aim, which is of an exact and demonstrative kind, and is
imperfectly manifested in the phenomena of nature, may help or may
mislead inquirers; they may be the impulse and the occasion to great
discoveries; or they may lead to the assertion of false and the loss
of true doctrines. Plato considers the phenomena which nature offers
to the senses as mere suggestions and rude sketches of the objects
which the philosophic mind is to contemplate. The heavenly bodies
and all the splendors of the sky, though the most beautiful of
visible objects, being only visible objects, are far inferior to the
true objects of which they are the representatives. They are merely
diagrams which may assist in the study of the higher truth  as we
might study geometry by the aid of diagrams constructed by some
consummate artist. Even then, the true object about which we reason
is the conception which we have in the mind.

We have, I conceive, an instance of the error as well as of the
truth, to which such views may lead, in the speculations of Plato
concerning Harmony, contained in that part of his writings (the
seventh Book of the _Republic_), in which these views are especially
urged. He there, by way of illustrating the superiority of
philosophical truth over such exactness as the senses can attest,
speaks slightingly of those who take immense pains in measuring
musical notes and intervals by the ear, as the astronomers measure the
heavenly motions by the eye. "They screw their pegs and pinch their
strings, and dispute whether two notes are the same or not." Now, in
truth, the ear is the final and supreme judge whether two notes are
the same or not. But there is a case in which notes which are
nominally the same, are different really and to the ear; and it is
probably to disputes on this subject, which we know did prevail among
the Greek musicians, that Plato here refers. We may ascend from a note
A_{1} to a note C_{3} by two octaves and a third. We may also ascend
from the same note A_{1} to C_{3} by fifths four times repeated. But
the two notes C_{3} thus arrived at are not the same: they differ by a
small interval, which the Greeks called a {501} Comma, of which the
notes are in the ratio of 80 to 81. That the ear really detects this
defect of the musical coincidence of the two notes under the proper
conditions, is a proof of the coincidence of our musical perceptions
with the mathematical relations of the notes; and is therefore an
experimental confirmation of the mathematical principles of harmony.
But it seems to be represented by Plato, that to look out for such
confirmation of mathematical principles, implies a disposition to lean
on the senses, which he regards as very unphilosophical.


_Hero of Alexandria._

THE other branches of mathematical science which I have spoken of in
the History as cultivated by the Greeks, namely Mechanics and
Hydrostatics, are not treated expressly by Plato; though we know
from Aristotle and others that some of the propositions of those
sciences were known about his time. Machines moved not only by
weights and springs, but by water and air, were constructed at an
early period. Ctesibius, who lived probably about B. C. 250, under
the Ptolemies, is said to have invented a clepsydra or water-clock,
and an hydraulic organ; and to have been the first to discover the
elastic power of air, and to apply it as a moving power. Of his
pupil Hero, the name is to this day familiar, through the little
pneumatic instrument called _Hero's Fountain_. He also described
pumps and hydraulic machines of various kinds; and an instrument
which has been spoken of by some modern writers as a _steam-engine_,
but which was merely a toy made to whirl round by the steam emitted
from holes in its arms. Concerning mechanism, besides descriptions
of _Automatons_, Hero composed two works: the one entitled
_Mechanics_, or _Mechanical Introductions_; the other _Barulcos_,
the _Weight-lifter_. In these works the elementary contrivances by
which weights may be lifted or drawn were spoken of as the _Five
Mechanical Powers_, the same enumeration of such machines as
prevails to this day; namely, the Lever, the Wheel and Axle, the
Pulley, the Wedge, and the Screw. In his Mechanics, it appears that
Hero reduced all these machines to one single machine, namely to the
lever. In the _Barulcos_, Hero proposed and solved the problem which
it was the glory of Archimedes to have solved: To move any object
(however large) by any power (however small). This, as may easily be
conceived by any one acquainted with the elements of Mechanics, is
done by means of a combination of the mechanical powers, and
especially by means of a train of toothed-wheels and axles. {502}

The remaining writings of Hero of Alexandria have been the subject
of a special, careful, and learned examination by M. Th. H. Martin
(Paris, 1854), in which the works of this writer, Hero the Ancient,
as he is sometimes called, are distinguished from those of another
writer of the same name of later date.

Hero of Alexandria wrote also, as it appears, a treatise on
_Pneumatics_, in which he described machines, either useful or
amusing, moved by the force of air and vapor.

He also wrote a work called _Catoptrics_, which contained proofs of
properties of the rays of reflected light.

And a treatise _On the Dioptra_; which subject however must be
carefully distinguished from the subject entitled _Dioptrics_ by the
moderns. This latter subject treats of the properties of refracted
light; a subject on which the ancients had little exact knowledge
till a later period; as I have shown in the History. The _Dioptra_,
as understood by Hero, was an instrument for taking angles so as to
measure the position and hence to determine the distance of
inaccessible objects; as is done by the _Theodolite_ in our times.

M. Martin is of opinion that Hero of Alexandria lived at a later
period than is generally supposed; namely, after B. C. 81.



{{503}}
BOOK III.

THE GREEK ASTRONOMY.

INTRODUCTION.


THE mathematical opinions of Plato respecting the philosophy of
nature, and especially respecting what we commonly call "the
heavenly bodies," the Sun, Moon, and Planets, were founded upon the
view which I have already described: namely, that it is the business
of philosophy to aim at a truth higher than observation can teach;
and to solve problems which the phenomena of the universe only
suggest. And though the students of nature in more recent times have
learnt that this is too presumptuous a notion of human knowledge,
yet the very boldness and hopefulness which it involved impelled men
in the pursuit of truth, with more vigor than a more timorous temper
could have done; and the belief that there must be, in nature,
mathematical laws more exact than experience could discover,
stimulated men often to discover true laws, though often also to
invent false laws. Plato's writings, supplying examples of both
these processes, belong to the Prelude of true Astronomy, as well as
to the errors of false philosophy. We may find specimens of both
kinds in those parts of his Dialogues to which we have referred in
the preceding Book of our History.

To Plato's merits in preparing the way for the Theory of Epicycles,
I have already referred in Chapter ii. of this Book. I conceive that
he had a great share in that which is an important step in every
discovery, the proposing distinctly the problem to be solved; which
was, in this case, as he states it, To account for the apparent
movements of the planets by a combination of two circular motions
for each:--the motion of identity, and the motion of difference.
(_Tim._ 39, A.) In the tenth Book of the _Republic_, quoted in our
text, the spindle which Destiny or Necessity holds between her
knees, and on which are rings, by means of which the planets revolve
round it as an axis, is a step towards the conception of the
problem, as the construction of a machine.

It will not be thought surprising that Plato expected that {504}
Astronomy, when further advanced, would be able to render an account
of many things for which she has not accounted even to this day.
Thus, in the passage in the seventh Book of the _Republic_, he says
that the philosopher requires a reason for the proportion of the day
to the month, and the month to the year, deeper and more substantial
than mere observation can give. Yet Astronomy has not yet shown us
any reason why the proportion of the times of the earth's rotation
on its axis, the moon's revolution round the earth, and the earth's
revolution round the sun, might not have been made by the Creator
quite different from what they are. But in thus asking Mathematical
Astronomy for reasons which she cannot give, Plato was only doing
what a great astronomical discoverer, Kepler, did at a later period.
One of the questions which Kepler especially wished to have answered
was, why there are five planets, and why at such particular
distances from the sun? And it is still more curious that he thought
he had found the reason of these things, in the relations of those
Five Regular Solids which, as we have seen, Plato was desirous of
introducing into the philosophy of the universe. We have Kepler's
account of this, his imaginary discovery, in the _Mysterium
Cosmographicum_, published in 1596, as stated in our History, Book
v. Chap. iv. Sect. 2.

Kepler regards the law which thus determines the number and magnitude
of the planetary orbits by means of the five regular solids as a
discovery no less remarkable and certain than the Three Laws which
give his name its imperishable place in the history of astronomy.

We are not on this account to think that there is no steady
criterion of the difference between imaginary and real discoveries
in science. As discovery becomes possible by the liberty of
guessing, it becomes real by allowing observation constantly and
authoritatively to determine the value of guesses. Kepler added to
Plato's boldness of fancy his own patient and candid habit of
testing his fancies by a rigorous and laborious comparison with the
phenomena; and thus his discoveries led to those of Newton. {505}




CHAPTER I.

EARLIEST STAGES OF ASTRONOMY.


_The Globular Form of the Earth._

THERE are parts of Plato's writings which have been adduced as bearing
upon the subsequent progress of science; and especially upon the
globular form of the earth, and the other views which led to the
discovery of America. In the _Timæus_ we read of a great continent
lying in the Ocean west of the Pillars of Hercules, which Plato calls
_Atlantis_. He makes the personage in his Dialogue who speaks of this
put it forward as an Egyptian tradition. M. H. Martin, who has
discussed what has been written respecting the Atlantis of Plato, and
has given therein a dissertation rich in erudition and of the most
lively interest, conceives that Plato's notions on this subject arose
from his combining his conviction of the spherical form of the earth,
with interpretations of Homer, and perhaps with traditions which were
current in Egypt (_Etudes sur le Timée_, Note xiii. § ix.). He does
not consider that the belief in Plato's Atlantis had any share in the
discoveries of Columbus.

It may perhaps surprise modern readers who have a difficulty in
getting rid of the persuasion that there is a natural direction
_upwards_ and a natural direction _downwards_, to learn that both
Plato and Aristotle, and of course other philosophers also, had
completely overcome this difficulty. They were quite ready to allow
and to conceive that _down_ meant nothing but towards some centre,
and _up_, the opposite direction. (Aristotle has, besides, an
ingenious notion that while heavy bodies, as earth and water, tend
to the centre, and light bodies, as fire, tend from the centre, the
fifth element, of which the heavenly bodies are composed, tends to
move _round_ the centre.)

Plato explains this in the most decided manner in the _Timæus_ (62,
C). "It is quite erroneous to suppose that there are two opposite
regions in the universe, one above and the other below; and that
heavy things naturally tend to the latter place. The heavens are
spherical, and every thing tends to the centre; and thus _above_ and
_below_ have no real meaning. If there be a solid globe in the
middle, {506} and if a person walk round it, he will become the
antipodes to himself, and the direction which is _up_ at one time
will be _down_ at another."

The notion of _antipodes_, the inhabitants of the part of the globe
of the earth opposite to ourselves, was very familiar. Thus in
Cicero's _Academic Questions_ (ii. 39) one of the speakers says,
"Etiam dicitis esse e regione nobis, e contraria parte terræ, qui
adversis vestigiis stant contra nostra vestigia, quos Antipodas
vocatis." See also _Tusc. Disp._ i. 28 and v. 24.


_The Heliocentric System among the Ancients._

As the more clear-sighted of the ancients had overcome the natural
prejudice of believing that there is an absolute _up_ and _down_, so
had they also overcome the natural prejudice of believing that the
earth is at rest. Cicero says (_Acad. Quest._ ii. 39), "Hicetas of
Syracuse, as Theophrastus tells us, thinks that the heavens, the
sun, the moon, the stars, do not move; and that nothing does move
but the earth. The earth revolves about her axis with immense
velocity; and thus the same effect is produced as if the earth were
at rest and the heavens moved; and this, he says, Plato teaches in
the _Timæus_, though somewhat obscurely." Of course the assertion
that the moon and planets do not move, was meant of the diurnal
motion only. The passage referred to in the _Timæus_ seems to be
this (40, C)--"As to the Earth, which is our nurse, and which
_clings to_ the axis which stretches through the universe, God made
her the producer and preserver of day and night." The word
εἱλλομένην, which I have translated _clings to_, some translate
_revolves_; and an extensive controversy has prevailed, both in
ancient and modern times (beginning with Aristotle), whether Plato
did or did not believe in the rotation of the earth on her axis.
(See M. Cousin's Note on the _Timæus_, and M. Henri Martin's
Dissertation, Note xxxvii., in his _Etudes sur le Timée_.) The
result of this discussion seems to be that, in the _Timæus_, the
Earth is supposed to be at rest. It is however related by Plutarch
(_Platonic Questions_, viii. 1), that Plato in his old age repented
of having given to the Earth the place in the centre of the universe
which did not belong to it.

In describing the Prelude to the Epoch of Copernicus (Book v. Chap.
i.), I have spoken of Philolaus, one of the followers of Pythagoras,
who lived at the time of Socrates, as having held the doctrine that
the earth revolves about the sun. This has been a current {507}
opinion;--so current, indeed, that the Abbé Bouillaud, or
Bullialdus, as we more commonly call him, gave the title of
_Philolaus_ to the defence of Copernicus which he published in 1639;
and Chiaramonti, an Aristotelian, published his answer under the
title of _Antiphilolaus_. In 1645 Bullialdus published his
_Astronomia Philolaica_, which was another exposition of the
heliocentric doctrine.

Yet notwithstanding this general belief, it appears to be tolerably
certain that Philolaus did not hold the doctrine of the earth's
motion round the sun. (M. H. Martin, _Etudes sur le Timée_, 1841,
Note xxxvii. Sect. i.; and Bœckh, _De vera Indole Astronomiæ
Philolaicæ_, 1810.) In the system of Philolaus, the earth revolved
about _the central fire_; but this central fire was not the sun. The
Sun, along with the moon and planets, revolved in circles external
to the earth. The Earth had the _Antichthon_ or _Counter-Earth_
between it and the centre; and revolving round this centre in one
day, the Antichthon, being always between it and the centre, was,
during a portion of the revolution, interposed between the Earth and
the Sun, and thus made night; while the Sun, by his proper motion,
produced the changes of the year.

When men were willing to suppose the earth to be in motion, in order
to account for the recurrence of day and night, it is curious that
they did not see that the revolution of a spherical earth about an
axis passing through its centre was a scheme both simple and quite
satisfactory. Yet the illumination of a globular earth by a distant
sun, and the circumstances and phenomena thence resulting, appear to
have been conceived in a very confused manner by many persons. Thus
Tacitus (_Agric._ xii.), after stating that he has heard that in the
northern part of the island of Britain, the night disappears in the
height of summer, says, as his account of this phenomenon, that "the
extreme parts of the earth are low and level, and do not throw their
shadow upwards; so that the shade of night falls below the sky and
the stars." But, as a little consideration will show, it is the
globular form of the earth, and not the level character of the
country, which produces this effect.

It is not in any degree probable that Pythagoras taught that the Earth
revolves round the Sun, or that it rotates on its own axis. Nor did
Plato hold either of these motions of the Earth. They got so far as to
believe in the Spherical Form of the Earth; and this was apparently
such an effort that the human mind made a pause before going any
further. "It required," says M. H. Martin, "a great struggle for {508}
men to free themselves from the prejudices of the senses, and to
interpret their testimony in such a manner as to conceive the
sphericity of the earth. It is natural that they should have stopped
at this point, before putting the earth in motion in space."

Some of the expressions which have been understood, as describing a
system in which the Sun is the _centre of motion_, do really imply
merely the Sun is the _middle term_ of the series of heavenly bodies
which revolve round the earth: the series being Moon, Mercury,
Venus, Sun, Mars, Jupiter, Saturn. This is the case, for instance,
in a passage of Cicero's _Vision of Scipio_, which has been supposed
to imply, (as I have stated in the History,) that Mercury and Venus
revolve about the Sun.

But though the doctrine of the diurnal rotation and annual
revolution of the earth is not the doctrine of Pythagoras, or of
Philolaus, or of Plato, it was nevertheless held by some of the
philosophers of antiquity. The testimony of Archimedes that this
doctrine was held by his contemporary Aristarchus of Samos, is
unquestionable  and there is no reason to doubt Plutarch's assertion
that Seleucus further enforced it.

It is curious that Copernicus appears not to have known anything of
the opinions of Aristarchus and Seleucus, which were really
anticipations of his doctrine; and to have derived his notion from
passages which, as I have been showing, contain no such doctrine. He
says, in his Dedication to Pope Paul III., "I found in Cicero that
Nicetas [or Hicetas] held that the earth was in motion: and in
Plutarch I found that some others had been of that opinion: and his
words I will transcribe that any one may read them: 'Philosophers in
general hold that the earth is at rest. But Philolaus the
Pythagorean teaches that it moves round the central fire in an
oblique circle, in the same direction as the Sun and the Moon.
Heraclides of Pontus and Ecphantus the Pythagorean give the earth a
motion, but not a motion of translation; they make it revolve like a
wheel about its own centre from west to east.'" This last opinion was
a correct assertion of the diurnal motion.


_The Eclipse of Thales._

"THE Eclipse of Thales" is so remarkable a point in the history of
astronomy, and has been the subject of so much discussion among
astronomers, that it ought to be more especially noticed. The
original {509} record is in the first Book of Herodotus's History
(chap. lxxiv.) He says that there was a war between the Lydians and
the Medes; and after various turns of fortune, "in the sixth year a
conflict took place; and on the battle being joined, it happened
that the day suddenly became night. And this change, Thales of
Miletus had predicted to them, definitely naming this year, in which
the event really took place. The Lydians and the Medes, when they
saw day turned into night, ceased from fighting; and both sides were
desirous of peace." Probably this prediction was founded upon the
Chaldean period of eighteen years, of which I have spoken in Section
11. It is probable, as I have already said, that this period was
discovered by noticing the recurrence of eclipses. It is to be
observed that Thales predicted only the year of the eclipse, not the
day or the month. In fact, the exact prediction of the circumstances
of an eclipse of the sun is a very difficult problem; much more
difficult, it may be remarked, than the prediction of the
circumstance of an eclipse of the moon.

Now that the Theory of the Moon is brought so far towards
completeness, astronomers are able to calculate backwards the
eclipses of the sun which have taken place in former times; and the
question has been much discussed in what year this Eclipse of Thales
really occurred. The Memoir of Mr. Airy, the Astronomer Royal, on
this subject, in the _Phil. Trans._ for 1853, gives an account of
the modern examinations of this subject. Mr. Airy starts from the
assumption that the eclipse must have been one decidedly total; the
difference between such a one and an eclipse only _nearly_ total
being very marked. A total eclipse alone was likely to produce so
strong an effect on the minds of the combatants. Mr. Airy concludes
from his calculations that the eclipse predicted by Thales took
place B. C. 585.

Ancient eclipses of the Moon and Sun, if they can be identified, are
of great value for modern astronomy; for in the long interval of
between two and three thousand years which separates them from our
time, those of the _inequalities_, that is, accelerations or
retardations of the Moon's motion, which go on increasing
constantly,[4\A] accumulate to a large amount; so that the actual
time and circumstances of the eclipse give astronomers the means of
determining what the rate of these accelerations or retardations has
been. Accordingly Mr. Airy has discussed, as even more important
than the eclipse of Thales, an eclipse which Diodorus relates to
have happened during an expedition of {510} Agathocles, the ruler of
Sicily, and which is hence known as the Eclipse of Agathocles. He
determines it to have occurred B. C. 310.

[Note 4\A: Or at least for very long periods.]

M. H. Martin, in Note xxxvii. to his _Etudes sur le Timée_,
discusses among other astronomical matters, the Eclipse of Thales.
He does not appear to render a very cordial belief to the historical
fact of Thales having delivered the prediction before the event. He
says that even if Thales did make such a prediction of an eclipse of
the sun, as he might do, by means of the Chaldean period of 18
years, or 223 lunations, he would have to take the chance of its
being visible in Greece, about which he could only guess:--that no
author asserts that Thales, or his successors Anaximander and
Anaxagoras, ever tried their luck in the same way again:--that "en
revanche" we are told that Anaximander predicted an earthquake, and
Anaxagoras the fall of aërolites, which are plainly fabulous
stories, though as well attested as the Eclipse of Thales. He adds
that according to Aristotle, Thales and Anaximenes were so far from
having sound notions of cosmography, that they did not even believe
in the roundness of the earth.



{{511}}
BOOK IV.

PHYSICAL SCIENCE IN THE MIDDLE AGES.

GENERAL REMARKS.


IN the twelfth Book of the _Philosophy_, in which I have given a
Review of Opinions on the Nature of Knowledge and the method of
seeking it, I have given some account of several of the most important
persons belonging to the ages now under consideration. I have there
(vol. ii. b. xii. p. 146) spoken of the manner in which remarks made
by Aristotle came to be accepted as fundamental maxims in the schools
of the middle ages, and of the manner in which they were discussed by
the greatest of the schoolmen, as Thomas Aquinas, Albertus Magnus, and
the like. I have spoken also (p. 149) of a certain kind of recognition
of the derivation of our knowledge from experience; as shown in
Richard of St. Victor, in the twelfth century. I have considered (p.
152) the plea of the admirers of those ages, that religious authority
was not claimed for physical science.

I have noticed that the rise of Experimental Philosophy exhibited
two features (chap. vii. p. 155), the Insurrection against
Authority, and the Appeal to Experience: and as exemplifying these
features, I have spoken of Raymond Lully and of Roger Bacon. I have
further noticed the opposition to the prevailing Aristotelian
dogmatism manifested (chap. viii.) by Nicolas of Cus, Marsilius
Ficinus, Francis Patricius, Picus of Mirandula, Cornelius Agrippa,
Theophrastus Paracelsus, Robert Fludd. I have gone on to notice the
Theoretical Reformers of Science (chap. ix.), Bernardinus Telesius,
Thomas Campanella, Andreas Cæsalpinus, Peter Ramus; and the
Protestant Reformers, as Melancthon. After these come the Practical
Reformers of Science, who have their place in the subsequent history
of Inductive Philosophy; Leonardo da Vinci, and the Heralds of the
dawning light of real science, whom Francis Bacon welcomes, as
Heralds are accosted in Homer:
  Χαίρετε Κήρυκες Διὸς ἄγγελοι ἠδὲ καὶ ἀνδρῶν.
  Hail, Heralds, messengers of Gods and men! {512}

I have, in the part of the _Philosophy_ referred to, discussed the
merits and defects of Francis Bacon's _Method_, and I shall have
occasion, in the next Book, to speak of his mode of dealing with the
positive science of his time. There is room for much more reflexion on
these subjects, but the references now made may suffice at present.




CHAPTER V.

PROGRESS IN THE MIDDLE AGES.


_Thomas Aquinas._

AQUINAS wrote (besides the _Summa_ mentioned in the text) a
Commentary on the Physics of Aristotle: _Commentaria in Aristotelis
Libros Physicorum_, Venice, 1492. This work is of course of no
scientific value; and the commentary consists of empty permutations
of abstract terms, similar to those which constitute the main
substance of the text in Aristotle's physical speculations. There
is, however, an attempt to give a more technical form to the
propositions and their demonstrations. As specimens of these, I may
mention that in Book vi. c. 2, we have a demonstration that when
bodies move, the time and the magnitude (that is, the space
described), are divided similarly; with many like propositions. And
in Book viii. we have such propositions as this (c. 10):
"Demonstration that a finite mover (_movens_) cannot move anything
in an infinite time." This is illustrated by a diagram in which two
hands are represented as engaged in moving a whole sphere, and one
hand in moving a hemisphere.

This mode of representing force, in diagrams illustrative of
mechanical reasonings, by human hands pushing, pulling, and the
like, is still employed in elementary books. Probably this is the
first example of such a mode of representation.


_Roger Bacon._

THIS writer, a contemporary of Thomas Aquinas, exhibits to us a kind
of knowledge, speculation, and opinion, so different from that of any
known person near his time, that he deserves especial notice here;
{513} and I shall transfer to this place the account which I have
given of him in the _Philosophy_. I do this the more willingly because
I regard the existence of such a work as the _Opus Majus_ at that
period as a problem which has never yet been solved. Also I may add,
that the scheme of the Contents of this work which I have given,
deserves, as I conceive, more notice than it has yet received.

"Roger Bacon was born in 1214, near Ilchester, in Somersetshire, of
an old family. In his youth he was a student at Oxford, and made
extraordinary progress in all branches of learning. He then went to
the University of Paris, as was at that time the custom of learned
Englishmen, and there received the degree of Doctor of Theology. At
the persuasion of Robert Grostête, bishop of Lincoln, he entered the
brotherhood of Franciscans in Oxford, and gave himself up to study
with extraordinary fervor. He was termed by his brother monks
_Doctor Mirabilis_. We know from his own works, as well as from the
traditions concerning him, that he possessed an intimate
acquaintance with all the science of his time which could be
acquired from books; and that he had made many remarkable advances
by means of his own experimental labors. He was acquainted with
Arabic, as well as with the other languages common in his time. In
the title of his works, we find the whole range of science and
philosophy, Mathematics and Mechanics, Optics, Astronomy, Geography,
Chronology, Chemistry, Magic, Music, Medicine, Grammar, Logics,
Metaphysics, Ethics, and Theology; and judging from those which are
published, these works are full of sound and exact knowledge. He is,
with good reason, supposed to have discovered, or to have had some
knowledge of, several of the most remarkable inventions which were
made generally known soon afterwards; as gunpowder, lenses, burning
specula, telescopes, clocks, the correction of the calendar, and the
explanation of the rainbow.

"Thus possessing, in the acquirements and habits of his own mind,
abundant examples of the nature of knowledge and of the process of
invention, Roger Bacon felt also a deep interest in the growth and
progress of science, a spirit of inquiry respecting the causes which
produced or prevented its advance, and a fervent hope and trust in
its future destinies; and these feelings impelled him to speculate
worthily and wisely respecting a Reform of the Method of
Philosophizing. The manuscripts of his works have existed for nearly
six hundred years in many of the libraries of Europe, and especially
in those of England; and for a long period the very imperfect
portions of them which were {514} generally known, left the
character and attainments of the author shrouded in a kind of
mysterious obscurity. About a century ago, however, his _Opus Majus_
was published[5\A] by Dr. S. Jebb, principally from a manuscript in
the library of Trinity College, Dublin; and this contained most or
all of the separate works which were previously known to the public,
along with others still more peculiar and characteristic. We are
thus able to judge of Roger Bacon's knowledge and of his views, and
they are in every way well worthy our attention.

[Note 5\A: _Fratris Rogeri Bacon Ordinis Minorum_ Opus Majus _ad
Clementem Quartum, Pontificem Romanum, ex MS. Codice Dubliniensi cum
aliis quibusdam collato nunc primum edidit_ S. Jebb, M.D. Londini,
1733.]

"The _Opus Majus_ is addressed to Pope Clement the Fourth, whom
Bacon had known when he was legate in England as Cardinal-bishop of
Sabina, and who admired the talents of the monk, and pitied him for
the persecutions to which he was exposed. On his elevation to the
papal chair, this account of Bacon's labours and views was sent, at
the earnest request of the pontiff. Besides the _Opus Majus_, he
wrote two others, the _Opus Minus_ and _Opus Tertium_; which were
also sent to the pope, as the author says,[6\A] 'on account of the
danger of roads, and the possible loss of the work.' These works
still exist unpublished, in the Cottonian and other libraries.

[Note 6\A: _Opus Majus_, Præf.]

"The _Opus Majus_ is a work equally wonderful with regard to its
general scheme, and to the special treatises with which the outlines
of the plan are filled up. The professed object of the work is to
urge the necessity of a reform in the mode of philosophizing, to set
forth the reasons why knowledge had not made a greater progress, to
draw back attention to the sources of knowledge which had been
unwisely neglected, to discover other sources which were yet almost
untouched, and to animate men in the undertaking, by a prospect of
the vast advantages which it offered. In the developement of this
plan, all the leading portions of science are expounded in the most
complete shape which they had at that time assumed; and improvements
of a very wide and striking kind are proposed in some of the
principal of these departments. Even if the work had had no leading
purpose, it would have been highly valuable as a treasure of the
most solid knowledge and soundest speculations of the time; even if
it had contained no such details, it would have been a work most
remarkable for its general views and scope. It may be considered as,
at the same time, the _Encyclopedia_ and the _Novum Organon_ of the
thirteenth century. {515}

"Since this work is thus so important in the history of Inductive
Philosophy I shall give, in a Note, a view[7\A] of its divisions and
contents. But I must now endeavor to point out more especially the
way in which the various principles, which the reform of scientific
method involved, are here brought into view.

[Note 7\A: Contents of Roger Bacon's _Opus Majus_:
Part I.   On the four causes of human ignorance:--Authority, Custom,
           Popular Opinion, and the Pride of supposed Knowledge.
Part II.  On the source of perfect wisdom in the Sacred Scripture.
Part III. On the Usefulness of Grammar.
Part IV.  On the Usefulness of Mathematics.
           (1.) The Necessity of Mathematics in Human Things
            (published separately as the _Specula Mathematica_).
           (2.) The Necessity of Mathematics in Divine Things.--1°.
            This study has occupied holy men: 2°. Geography: 3°.
            Chronology: 4°. Cycles; the Golden Number, &c.: 5°.
            Natural Phenomena, as the Rainbow: 6°. Arithmetic:
            7°. Music.
           (3.) The Necessity of Mathematics in Ecclesiastical
            Things. 1°. The Certification of Faith: 2°. The
            Correction of the Calendar.
           (4.) The Necessity of Mathematics in the State.--1°. Of
            Climates: 2°. Hydrography: 3°. Geography: 4°. Astrology.
Part V.   On Perspective (published separately as _Perspectiva_).
           (1.) The organs of vision.
           (2.) Vision in straight lines.
           (3.) Vision reflected and refracted.
           (4.) De multiplicatione specierum (on the propagation of
            the impressions of light, heat, &c.)
Part VI.  On Experimental Science.]

"One of the first points to be noticed for this purpose, is the
resistance to authority; and at the stage of philosophical history
with which we here have to do, this means resistance to the
authority of Aristotle, as adopted and interpreted by the Doctors of
the Schools. Bacon's work[8\A] is divided into Six Parts; and of
these Parts, the First is, Of the four universal Causes of all Human
Ignorance. The causes thus enumerated[9\A] are:--the force of
unworthy authority;--traditionary habit;--the imperfection of the
undisciplined senses;--and the disposition to conceal our ignorance
and to make an ostentatious show of our knowledge. These influences
involve every man, occupy every condition. They prevent our
obtaining the most useful and large and fair doctrines of wisdom,
the secrets of all sciences and arts. He then proceeds to argue,
from the testimony of philosophers themselves, that the authority of
antiquity, and especially of Aristotle, is not infallible. 'We
find[10\A] their books full of doubts, obscurities, and
perplexities. They {516} scarce agree with each other in one empty
question or one worthless sophism, or one operation of science, as
one man agrees with another in the practical operations of medicine,
surgery, and the like arts of secular men. Indeed,' he adds,[11\A]
'not only the philosophers, but the saints have fallen into errors
which they have afterwards retracted,' and this he instances in
Augustin, Jerome, and others. He gives an admirable sketch of the
progress of philosophy from the Ionic School to Aristotle; of whom
he speaks with great applause. 'Yet,' he adds, 'those who came after
him corrected him in some things, and added many things to his
works, and shall go on adding to the end of the world.' Aristotle,
he adds, is now called peculiarly[12\A] the Philosopher, 'yet there
was a time when his philosophy was silent and unregarded, either on
account of the rarity of copies of his works, or their difficulty,
or from envy; till after the time of Mahomet, when Avicenna and
Averroes, and others, recalled this philosophy into the full light
of exposition. And although the Logic and some other works were
translated by Boethius from the Greek, yet the philosophy of
Aristotle first received a quick increase among the Latins at the
time of Michael Scot; who, in the year of our Lord 1230, appeared,
bringing with him portions of the books of Aristotle on Natural
Philosophy and Mathematics. And yet a small part only of the works
of this author is translated, and a still smaller part is in the
hands of common students.' He adds further[13\A] (in the Third Part
of the _Opus Majus_, which is a Dissertation on Language) that the
translations which are current of these writings, are very bad and
imperfect. With these views, he is moved to express himself somewhat
impatiently[14\A] respecting these works: 'If I had,' he says,
'power over the works of Aristotle, I would have them all burnt; for
it is only a loss of time to study in them, and a course of error,
and a multiplication of ignorance beyond expression.' 'The common
herd of students,' he says, 'with their heads, have no principle by
which they can be excited to any worthy employment; and hence they
mope and make asses of themselves over their bad translations, and
lose their time, and trouble, and money.' {517}

[Note 8\A: _Op. Maj._ p. 1.]

[Note 9\A: Ib. p. 2.]

[Note 10\A: Ib. p. 10.]

[Note 11\A: _Op. Maj._ p. 36.]

[Note 12\A: _Autonomaticè_.]

[Note 13\A: _Op. Maj._ p. 46.]

[Note 14\A: See _Pref._ to Jebb's edition. The passages there quoted,
however, are not extracts from the _Opus Majus_, but (apparently) from
the _Opus Minus_ (_MS. Cott._ Tib. c . 5). "Si haberem potestatem
supra libros Aristotelis, ego facerem omnes cremari; quia non est nisi
temporis amissio studere in illis, et causa erroris, et multiplicatio
ignorantiæ ultra id quod valeat explicari. . . . Vulgus studentum cum
capitibus suis non habet unde excitetur ad aliquid dignum, et ideo
languet et _asininat_ circa male translata, et tempus et studium
amittit in omnibus et expensas."]

"The remedies which he recommends for these evils, are, in the first
place, the study of that only perfect wisdom which is to be found in
the Sacred Scripture;[15\A] in the next place, the study of
mathematics and the use of experiment.[16\A] By the aid of these
methods, Bacon anticipates the most splendid progress for human
knowledge. He takes up the strain of hope and confidence which we
have noticed as so peculiar in the Roman writers; and quotes some of
the passages of Seneca which we adduced in illustration of
this:--that the attempts in science were at first rude and
imperfect, and were afterwards improved;--that the day will come,
when what is still unknown shall be brought to light by the progress
of time and the labors of a longer period;--that one age does not
suffice for inquiries so wide and various;--that the people of
future times shall know many things unknown to us;--and that the
time shall arrive when posterity will wonder that we overlooked what
was so obvious. Bacon himself adds anticipations more peculiarly in
the spirit of his own time. 'We have seen,' he says, at the end of
the work, 'how Aristotle, by the ways which wisdom teaches, could
give to Alexander the empire of the world. And this the Church ought
to take into consideration against the infidels and rebels, that
there may be a sparing of Christian blood, and especially on account
of the troubles that shall come to pass in the days of Antichrist;
which by the grace of God it would be easy to obviate, if prelates
and princes would encourage study, and join in searching out the
secrets of nature and art.'

[Note 15\A: Part ii.]

[Note 16\A: Parts iv. v. and vi.]

"It may not be improper to observe here that this belief in the
appointed progress of knowledge, is not combined with any
overweening belief in the unbounded and independent power of the
human intellect. On the contrary, one of the lessons which Bacon
draws from the state and prospects of knowledge, is the duty of
faith and humility. 'To him,' he says,[17\A] 'who denies the truth
of the faith because he is unable to understand it, I will propose
in reply the course of nature, and as we have seen it in examples.'
And after giving some instances, he adds, 'These, and the like,
ought to move men and to excite them to the reception of divine
truths. For if, in the vilest objects of creation, truths are found,
before which the inward pride of man must bow, and believe though it
cannot understand, how much more should man humble his mind before
the glorious truths of God!' He had before said:[18\A] 'Man is
incapable of perfect wisdom in this life; it is hard for {518} him
to ascend towards perfection, easy to glide downwards to falsehoods
and vanities: let him then not boast of his wisdom, or extol his
knowledge. What he knows is little and worthless, in respect of that
which he believes without knowing; and still less, in respect of
that which he is ignorant of. He is mad who thinks highly of his
wisdom; he most mad, who exhibits it as something to be wondered
at.' He adds, as another reason for humility, that he has proved by
trial, he could teach in one year, to a poor boy, the marrow of all
that the most diligent person could acquire in forty years'
laborious and expensive study.

[Note 17\A: _Op. Maj._ p. 476.]

[Note 18\A: Ib. p. 15.]

"To proceed somewhat more in detail with regard to Roger Bacon's views
of a Reform in Scientific Inquiry, we may observe that by making
Mathematics and Experiment the two great points of his recommendation,
he directed his improvement to the two essential parts of all
knowledge, Ideas and Facts, and thus took the course which the most
enlightened philosophy would have suggested. He did not urge the
prosecution of experiment, to the comparative neglect of the existing
mathematical sciences and conceptions; a fault which there is some
ground for ascribing to his great namesake and successor Francis
Bacon: still less did he content himself with a mere protest against
the authority of the schools, and a vague demand for change, which was
almost all that was done by those who put themselves forward as
reformers in the intermediate time. Roger Bacon holds his way steadily
between the two poles of human knowledge; which, as we have seen, it
is far from easy to do. 'There are two modes of knowing,' says
he;[19\A] 'by argument, and by experiment. Argument concludes a
question; but it does not make us feel certain, or acquiesce in the
contemplation of truth, except the truth be also found to be so by
experience.' It is not easy to express more decidedly the clearly-seen
union of exact conceptions with certain facts, which, as we have
explained, constitutes real knowledge.

[Note 19\A: _Op. Maj._ p. 445; see also p. 448. "Scientiæ aliæ
sciunt sua principia invenire per experimenta, sed conclusiones per
argumenta facta ex principiis inventis. Si vero debeant habere
experientiam conclusionum suarum particularem et completam, tunc
oportet quod habeant per adjutorium istius scientiæ nobilis
(experimentalis)."]

"One large division of the _Opus Majus_ is 'On the Usefulness of
Mathematics,' which is shown by a copious enumeration of existing
branches of knowledge, as Chronology, Geography, the Calendar and
(in a separate Part) Optics. There is a chapter,[20\A] in which it
is proved {519} by reason, that all science requires mathematics.
And the arguments which are used to establish this doctrine, show a
most just appreciation of the office of mathematics in science. They
are such as follows:--That other sciences use examples taken from
mathematics as the most evident:--That mathematical knowledge is, as
it were, innate to us, on which point he refers to the well-known
dialogue of Plato, as quoted by Cicero:--That this science, being
the easiest, offers the best introduction to the more
difficult:--That in mathematics, things as known to us are identical
with things as known to nature:--That we can here entirely avoid
doubt and error, and obtain certainty and truth:--That mathematics
is prior to other sciences in nature, because it takes cognizance of
quantity, which is apprehended by intuition (_intuitu intellectus_).
'Moreover,' he adds,[21\A] 'there have been found famous men, as
Robert, bishop of Lincoln, and Brother Adam Marshman (de Marisco),
and many others, who by the power of mathematics have been able to
explain the causes of things; as may be seen in the writings of
these men, for instance, concerning the Rainbow and Comets, and the
generation of heat, and climates, and the celestial bodies.'

[Note 20\A: Ib. p. 60.]

[Note 21\A: _Op. Maj._ p. 64.]

"But undoubtedly the most remarkable portion of the _Opus Majus_ is
the Sixth and last Part, which is entitled 'De Scientia
experimentali.' It is indeed an extraordinary circumstance to find a
writer of the thirteenth century, not only recognizing experiment as
one source of knowledge, but urging its claims as something far more
important than men had yet been aware of, exemplifying its value by
striking and just examples, and speaking of its authority with a
dignity of diction which sounds like a foremurmur of the Baconian
sentences uttered nearly four hundred years later. Yet this is the
character of what we here find.[22\A] 'Experimental science, the
sole mistress of speculative sciences, has three great Prerogatives
among other parts of knowledge: First she tests by experiment the
noblest conclusions of all other sciences: Next she discovers
respecting the notions which other sciences deal with, magnificent
truths to which these sciences of themselves can by no means attain:
her Third dignity is, that she by her own power and without respect
of other sciences, investigates the secrets of nature.' {520}

[Note 22\A: "Veritates magnificas in terminis aliarum scientiarum in
quas per nullam viam possunt illæ scientiæ, hæc sola scientiarum
domina speculativarum, potest dare."--_Op. Maj._ p. 465.]

"The examples which Bacon gives of these 'Prerogatives' are very
curious, exhibiting, among some error and credulity, sound and clear
views. His leading example of the First Prerogative is the Rainbow, of
which the cause, as given by Aristotle, is tested by reference to
experiment with a skill which is, even to us now, truly admirable. The
examples of the Second Prerogative are three--_first_, the art of
making an artificial sphere which shall move with the heavens by
natural influences, which Bacon trusts may be done, though astronomy
herself cannot do it--'et tunc,' he says, 'thesaurum unius regis
valeret hoc instrumentum;'--_secondly_, the art of prolonging life,
which experiment may teach, though medicine has no means of securing
it except by regimen;[23\A]--_thirdly_, the art of making gold finer
than fine gold, which goes beyond the power of alchemy. The Third
Prerogative of experimental science, arts independent of the received
sciences, is exemplified in many curious examples, many of them
whimsical traditions. Thus it is said that the character of a people
may be altered by altering the air.[24\A] Alexander, it seems, applied
to Aristotle to know whether he should exterminate certain nations
which he had discovered, as being irreclaimably barbarous; to which
the philosopher replied, 'If you can alter their air, permit them to
live; if not, put them to death.' In this part, we find the suggestion
that the fire-works made by children, of saltpetre, might lead to the
invention of a formidable military weapon.

[Note 23\A: One of the ingredients of a preparation here mentioned,
is the flesh of a dragon, which, it appears, is used as food by the
Ethiopians. The mode of preparing this food cannot fail to amuse the
reader. "Where there are good flying dragons, by the art which they
possess, they draw them out of their dens, and have bridles and
saddles in readiness, and they ride upon them, and make them bound
about in the air in a violent manner, that the hardness and
toughness of the flesh may be reduced, as boars are hunted and bulls
are baited before they are killed for eating."--_Op. Maj._ p. 470.]

[Note 24\A: _Op. Maj._ p. 472.]

"It could not be expected that Roger Bacon, at a time when
experimental science hardly existed, could give any _precepts_ for
the discovery of truth by experiment. But nothing can be a better
_example_ of the method of such investigation, than his inquiry
concerning the cause of the Rainbow. Neither Aristotle, nor
Avicenna, nor Seneca, he says, have given us any clear knowledge of
this matter, but experimental science can do so. Let the
experimenter (_experimentator_) consider the cases in which he finds
the same colors, as the hexagonal crystals from Ireland and India;
by looking into these he will see colors like those of the rainbow.
Many think that this arises from some {521} special virtue of these
stones and their hexagonal figure; let therefore the experimenter go
on, and he will find the same in other transparent stones, in dark
ones as well as in light-colored. He will find the same effect also
in other forms than the hexagon, if they be furrowed in the surface,
as the Irish crystals are. Let him consider too, that he sees the
same colors in the drops which are dashed from oars in the
sunshine;--and in the spray thrown by a mill wheel;--and in the dew
drops which lie on the grass in a meadow on a summer morning;--and
if a man takes water in his mouth and projects it on one side into a
sunbeam;--and if in an oil lamp hanging in the air, the rays fall in
certain positions upon the surface of the oil;--and in many other
ways, are colors produced. We have here a collection of instances,
which are almost all examples of the same kind as the phenomenon
under consideration; and by the help of a principle collected by
induction from these facts, the colors of the rainbow were
afterwards really explained.

"With regard to the form and other circumstances of the bow he is
still more precise. He bids us measure the height of the bow and of
the sun, to show that the centre of the bow is exactly opposite to
the sun. He explains the circular form of the bow,--its being
independent of the form of the cloud, its moving when we move, its
flying when we follow,--by its consisting of the reflections from a
vast number of minute drops. He does not, indeed, trace the course
of the rays through the drop, or account for the precise magnitude
which the bow assumes; but he approaches to the verge of this part
of the explanation; and must be considered as having given a most
happy example of experimental inquiry into nature, at a time when
such examples were exceedingly scanty. In this respect, he was more
fortunate than Francis Bacon, as we shall hereafter see.

"We know but little of the biography of Roger Bacon, but we have
every reason to believe that his influence upon his age was not
great. He was suspected of magic, and is said to have been put into
close confinement in consequence of this charge. In his work he
speaks of Astrology, as a science well worth cultivating. 'But,'
says he, 'Theologians and Decretists, not being learned in such
matters, and seeing that evil as well as good may be done, neglect
and abhor such things, and reckon them among Magic Arts.' We have
already seen, that at the very time when Bacon was thus raising his
voice against the habit of blindly following authority, and seeking
for all science in Aristotle, Thomas Aquinas was employed in
fashioning Aristotle's tenets into that fixed form in which they
became the great impediment to the {522} progress of knowledge. It
would seem, indeed, that something of a struggle between the
progressive and stationary powers of the human mind was going on at
this time. Bacon himself says,[25\A] 'Never was there so great an
appearance of wisdom, nor so much exercise of study in so many
Faculties, in so many regions, as for this last forty years. Doctors
are dispersed everywhere, in every castle, in every burgh, and
especially by the students of two Orders, (he means the Franciscans
and Dominicans, who were almost the only religious orders that
distinguished themselves by an application to study,[26\A]) which
has not happened except for about forty years. And yet there was
never so much ignorance, so much error.' And in the part of his work
which refers to Mathematics, he says of that study,[27\A] that it is
the door and the key of the sciences; and that the neglect of it for
thirty or forty years has entirely ruined the studies of the Latins.
According to these statements, some change, disastrous to the
fortunes of science, must have taken place about 1230, soon after
the foundation of the Dominican and Franciscan Orders.[28\A] Nor can
we doubt that the adoption of the Aristotelian philosophy by these
two Orders, in the form in which the Angelical Doctor had
systematized it, was one of the events which most tended to defer,
for three centuries, the reform which Roger Bacon urged as a matter
of crying necessity in his own time."

[Note 25\A: Quoted by Jebb, Pref. to _Op. Maj._]

[Note 26\A: Mosheim, _Hist._ iii. 161.]

[Note 27\A: _Op. Maj._ p. 57.]

[Note 28\A: Mosheim, iii. 161.]

It is worthy of remark that in the _Opus Majus_ of Roger Bacon, as
afterwards in the _Novum Organon_ of Francis Bacon, we have certain
features of experimental research pointed out conspicuously as
_Prærogativæ_: although in the former, this term is employed to
designate the superiority of experimental science in general to the
science of the schools; in the latter work, the term is applied to
certain classes of experiments as superior to others.



{{523}}
BOOK V.

FORMAL ASTRONOMY.



CHAPTER I.

PRELUDE TO COPERNICUS.


_Nicolas of Cus._

I WILL quote the passage, in the writings of this author, which
bears upon the subject in question. I translate it from the edition
of his book _De Docta Ignorantia_, from his works published at Basil
in 1565. He praises _Learned Ignorance_--that is, Acknowledged
Ignorance--as the source of knowledge. His ground for asserting the
motions of the earth is, that there is no such thing as perfect
rest, or an exact centre, or a perfect circle, nor perfect
uniformity of motion. "Neque verus circulus dabilis est, quinetiam
verior dari possit, neque unquam uno tempore sicut alio æqualiter
præcisè, aut movetur, aut circulum veri similem, æqualem describit,
etiamsi nobis hoc non appareat. Et ubicumque quis fuerit, se in
centro esse credit." (Lib. i. cap. xi. p. 39.) He adds, "The
Ancients did not attain to this knowledge, because they were wanting
in Learned Ignorance. Now it is manifest to us that the Earth is
truly in motion, although this do not appear to us; since we do not
apprehend motion except by comparison with something fixed. For if
any one were in a boat in the middle of a river, ignorant that the
water was flowing, and not seeing the banks, how could he apprehend
that the boat was moving? And thus since every one, whether he be in
the Earth, or in the Sun, or in any other star, thinks that he is in
an immovable centre, and that everything else is moving; he would
assign different poles for himself, others as being in the Sun,
others in the Earth, and others in the Moon, and so of the rest.
Whence the machine of the world is as if it had its centre
everywhere and its circumference nowhere." This train of thought
{524} might be a preparation for the reception of the Copernican
system; but it is very different from the doctrine that the Sun is
the centre of the Planetary Motions.




CHAPTER II.

THE COPERNICAN THEORY.


_The Moon's Rotation._

I HAVE said, in page 264, that a confusion of mind produced by the
double reference of motion to absolute space, and to a centre of
revolution, often leads persons to dispute whether the Moon, while
she revolves about the Earth, always turning to it the same face,
revolves about her axis or not.

This dispute has been revived very lately, and has been conducted in
a manner which shows that popular readers and writers have made
little progress in the clearness of their notions during the last
two or three centuries; and that they have accepted the Newtonian
doctrines in words with a very dim apprehension of their real import.

If the Moon were carried round the Earth by a rigid arm revolving
about the Earth as a centre, being rigidly fastened to this arm, as
a mimic Moon might be, in a machine constructed to represent her
motions, this contrivance, while it made her revolve round the Earth
would make her also turn the same face to the Earth: and if we were
to make such a machine the standard example of rotation, the Moon
might be said not to rotate on her axis.

But we are speedily led to endless confusion by taking this case as
the standard of rotation. For the selection of the centre of
rotation in a system which includes several bodies is arbitrary. The
Moon turns all her faces successively to the Sun, and therefore with
regard to the Sun, she does rotate on her axis; and yet she revolves
round the Sun as truly as she revolves round the Earth. And the only
really simple and consistent mode of speaking of rotation, is to
refer the motion not to any relative centre, but to absolute space.

This is the argument merely on the ground of simplicity and
consistency. But we find physical reasons, as well as mathematical,
for referring the motion to absolute space. If a cup of water be
carried round a centre so as to describe a circle, a straw floating
on the surface {525} of the water, if it point to the centre of the
circle at first, does not continue to do so, but remains parallel to
itself during the whole revolution. Now there is no cause to make
the water (and therefore the straw) rotate on its axis; and
therefore it is not a clear or convenient way of speaking, to say
that the water in this case does revolve on its axis. But if the
water in this case do not revolve on its axis, a body in the case of
the Moon does revolve on its axis.

The difficulty, as I have said in the text, is of the same nature as
that which the Copernicans at first found in the parallel motion of
the Earth's axis. In order to make the axis of the Earth's rotation
remain parallel to itself while the Earth revolves about the Sun, in
a mechanical representation, some machinery is needed _in addition_ to
the machinery which produces the revolution round the centre (the
Sun): but the simplest way of regarding the parallel motion is, to
conceive that the axis has no motion except that which carries it
round the central Sun. And it was seen, when the science of
Mechanics was established, that no force was needed in nature to
produce this parallelism of the Earth's axis. It was therefore the
only scientific course, to conceive this parallelism as not being a
rotation: and in like manner we are to conceive the parallelism of a
revolving body as not being a rotation.


_M. Foucault's Proofs of the Earth's Motion._

IT was hardly to be expected that we should discover, in our own
day, a new physical proof of the earth's motion, yet so it has been.
The experiments of M. Foucault have enabled us to see the Rotation
of the Earth on its axis, as taking place, we may say, before our
eyes. These experiments are, in fact, a result of what has been said
in speaking of the Moon's rotation: namely, That the mechanical
causes of motion operate with reference to absolute, not relative,
space; so that where there is no cause operating to change a motion,
it will retain its direction in _absolute_ space; and may on that
account seem to change, if regarded relatively in a _limited_ space.

In M. Foucault's first experiment, the motion employed was that of a
pendulum. If a pendulum oscillate quite freely, there is no cause
acting to change the vertical plane of oscillation _absolutely_; for
the forces which produce the oscillation are _in_ the vertical
plane. But if the vertical plane remain the same _absolutely_, at a
spot on the surface of the revolving Earth, it will change
_relatively_ to the spectator. He will see the pendulum oscillate in
a vertical plane which gradually {526} turns away from its first
position. Now this is what really happens; and thus the revolution
of the Earth in absolute space is experimentally proved.

In subsequent experiments, M. Foucault has used the rotation of a
body to prove the same thing. For when a body rotates freely, acted
upon by no power, there is nothing to change the position of the
axis of rotation in absolute space. But if the position of the axis
remain the same in absolute space, it will, in virtue of its
relative motion, change as seen by a spectator at any spot on the
rotating Earth. By taking a heavy disk or globe and making it rotate
on its axis rapidly, the force of absolute permanence (as compared
with the inevitable casual disturbances arising from the machinery
which supports the revolving disk) becomes considerable  and hence
the relative motion can, in this way also, be made visible.

Mr. De Morgan has said (_Comp. to Brit. Alm._ 1836, p. 18) that
astronomy does not supply any argument for the earth's motion which
is absolutely and demonstrably conclusive, till we come to the
Aberration of Light. But we may now venture to say that the
experiments of M. Foucault prove the diurnal motion of the Earth in
the most conclusive manner, by palpable and broad effects, if we
accept the doctrines of the Science of Mechanics: while Aberration
proves the annual motion, if we suppose that we can observe the
places of the fixed stars to the accuracy of a few seconds; and if
we accept, in addition to the doctrines of Mechanics, the doctrine
of the motion of light with a certain great velocity.




CHAPTER III.

SEQUEL TO COPERNICUS.


_English Copernicans._

PROFESSOR DE MORGAN has made numerous and interesting contributions
to the history of the progress and reception of the Copernican
System. These are given mainly in the _Companion to the British
Almanac_; especially in his papers entitled "Old Arguments against
the Motion of the Earth" (1836); "English Mathematical and
Astronomical Writers" (1837); "On the Difficulty of Correct {527}
Description of Books" (1853); "The Progress of the Doctrine of the
Earth's Motion between the Times of Copernicus and Galileo" (1855).
In these papers he insists very rightly upon the distinction between
the _mathematical_ and the _physical_ aspect of the doctrines of
Copernicus: a distinction corresponding very nearly with the
distinction which we have drawn between Formal and Physical
Astronomy; and in accordance with which we have given the history of
the Heliocentric Doctrine as a Formal Theory in Book v., and as a
Physical Theory in Book vii.

Another interesting part of Mr. De Morgan's researches are the
notices which he has given of the early assertors of the
heliocentric doctrine in England. These make their appearance as
soon as it was well possible they should exist. The work of
Copernicus was published, as we have said, in 1543. In September
1556, John Field published an Ephemeris for 1557, "juxta Copernici
et Reinholdi Canones," in the preface to which he avows his
conviction of the truth of the Copernican hypothesis. Robert
Recorde, the author of various works on Arithmetic, published among
others, "The Pathway to Knowledge" in 1551. In this book, the author
discusses the question of the "quietnes of the earth," and professes
to leave it undecided: but Mr. De Morgan (_Comp. A._ 1837, p. 33)
conceives that it appears from what is said, that he was really a
Copernican, but did not think the world ripe for any such doctrine.

Mr. Joseph Hunter also has brought to notice[29\A] the claims of
Field, whom he designates as the _Proto-Copernican_ of England. He
quotes the Address to the Reader prefixed to his first _Ephemeris_,
and dated May 31, 1556, in which he says that, since abler men
decline the task, "I have therefore published this Ephemeris of the
year 1557, following in it as my authorities, N. Copernicus and
Erasmus Reinhold, whose writings are established and founded on
true, certain, and authentic demonstrations." I conceive that this
passage, however, only shows that Field had adopted the Copernican
scheme as a basis for the calculation of Ephemerides; which, as Mr.
De Morgan has remarked, is a very different thing from accepting it
as a physical truth. Field, in this same address, makes mention of
the errors "illius turbæ quæ Alphonsi utitur hypothesi;" but the
word _hypothesis_ is still indecisive.

[Note 29\A: _Ast. Soc. Notices_, vol. iii. p. 3 (1833).]

As evidence that Field was regarded in his own day as a man who
{528} had rendered good service to science, Mr. Hunter notices that,
in 1558, the Heralds granted to him the right of using, with his
arms, the crest or additional device of a red right arm issuing from
the clouds, and presenting a golden armillary sphere.

Recorde's claims depend upon a passage in a Dialogue between
_Master_ and _Scholar_, in which the Master expounds the doctrine of
Copernicus, and the authorities against it; to which the Scholar
answers, taking the common view: "Nay, sir, in good faith I desire
not to hear such vaine phantasies, so far against common reason, and
repugnant to all the learned multitude of wryters, and therefore let
it passe for ever and a day longer." The Master, more sagely, warns
him against a hasty judgment, and says, "Another time I will so
declare his supposition, that you shall not only wonder to hear it,
but also peradventure be as earnest then to credit it, as you now
are now to condemne it." I conceive that this passage proves Mr. De
Morgan's assertion, that Recorde was a Copernican, and very likely
the first in England.

In 1555, also, Leonard Digges published his "Prognostication
Everlasting;" but this is, as Mr. De Morgan says (_Comp. A._ 1837, p.
40) a meteorological work. It was republished in 1592 by his son
Thomas Digges with additions; and as these have been the occasion of
some confusion among those who have written on the history of
astronomy, I am glad to be able, through the kindness of Professor
Walker of Oxford, to give a distinct account of the editions of the
work.

In the Bodleian Library, besides the editions of 1555 and 1592 of
the "Prognostication Everlasting," there is an edition of 1564. It
is still decidedly Ptolemaic, and contains a Diagram representing a
number of concentric circles, which are marked, in order, as--
"The Earth,
     Moone,
     Venus,
     Mercury,
     Sunne,
     Mars,
     Jupiter,
     Saturne,
 The Starrie Firmament,
 The Crystalline Heavens,
 The First Mover,
 The Abode of God and the Elect. Here the Learned do approve." {529}

The third edition, of 1592, contains an Addition, by the son, of
twenty pages. He there speaks of having found, apparently among his
father's papers, "A description or modile of the world and situation
of Spheres Cœlestiall and elementare according to the doctrine of
Ptolemie, whereunto all universities (led thereunto chiefly by the
authoritie of Aristotle) do consent." He adds: "But in this our age,
one rare witte (seeing the continuall errors that from time to time
more and more continually have been discovered, besides the infinite
absurdities in their Theoricks, which they have been forced to admit
that would not confesse any Mobilitie in the ball of the Earth) hath
by long studye, paynfull practise, and rare invention, delivered a
new Theorick or Model of the world, shewing that the Earth resteth
not in the Center of the whole world or globe of elements, which
encircled and enclosed in the Moone's orbe, and together with the
whole globe of mortalitye is carried yearely round about the Sunne,
which like a king in the middest of all, raygneth and giveth lawes
of motion to all the rest, sphærically dispersing his glorious
beames of light through all this sacred cœlestiall Temple. And the
Earth itselfe to be one of the Planets, having his peculiar and
strange courses, turning every 24 hours rounde upon his owne centre,
whereby the Sunne and great globe of fixed Starres seem to sway
about and turne, albeit indeed they remaine fixed--So many ways is
the sense of mortal man abused."

This Addition is headed:
"A Perfit Description of the Cœlestiall Orbes, according to the most
ancient doctrine of the Pythagoreans: lately revived by Copernicus,
and by Geometrical Demonstrations approved." Mr. De Morgan, not
having seen this edition, and knowing the title-page only as far as
the word "Pythagoreans," says "their _astrological_ doctrines we
presume, not their reputed _Copernican_ ones." But it now appears
that in this, as in other cases, the authority of the Pythagoreans
was claimed for the Copernican system. Antony a Wood quotes the
latter part of the title thus: "Cui subnectitur _orbium_
Copernicarum accurata descriptio;" which is inaccurate. Weidler,
still more inaccurately, cites it, "Cui subnectitur _operum_
Copernici accurata descriptio." Lalande goes still further,
attempting, it would seem, to recover the English title-page from
the Latin: we find in the _Bibl. Astron._ the following: "1592 . .
Leonard Digges, Accurate Description of the Copernican System to the
Astronomical perpetual Prognostication."

Thomas Digges appears, by others also of his writings, to have been
{530} a clear and decided Copernican. In his "Alæ sive Scalæ
Mathematicæ," 1573, he bestows high praise upon Copernicus and upon
his system: and appears to have been a believer in the real motion
of the Earth, and not merely an admirer of the system of Copernicus
as an explanatory hypothesis.


_Giordano Bruno._

The complete title of the work referred to is:

"Jordani Bruni Nolani De Monade Numero et Figura liber consequens
Quinque De Minimo Magno et Mensura, item De Innumerabilibus, Immenso
et Infigurabili; seu De Universo et Mundis libri octo. (Francofurti,
1591.)"

That the Reader may judge of the value of Bruno's speculations, I
give the following quotations:

Lib. iv. c. 11 (Index). "Tellurem totam habitabilem esse _intus_ et
extra, et innumerabilia animantium complecti tum nobis sensibilium
tum _occultorum_ genera."

C. 13. "Ut Mundorum Synodi in Universo et particulares Mundi in
Synodis ordinentur,' &c.

He says (Lib. v. c. 1, p. 461): "Besides the stars and the great
worlds there are smaller living creatures carried through the
etherial space, in the form of a small sphere which has the aspect
of a bright fire, and is by the vulgar regarded as a fiery beam.
They are below the clouds, and I saw one which seemed to touch the
roofs of the houses. Now this sphere, or beam as they call it, was
really a living creature (_animal_), which I once saw moving in a
straight path, and grazing as it were the roofs of the city of Nola,
as if it were going to impinge on Mount Cicada; which however it
went over."

There are two recent editions of the works of Giordano Bruno; by
Adolf Wagner, Leipsick, 1830, in two volumes; and by Gfrörer,
Berlin, 1833. Of the latter I do not know that more than one volume
(vol. ii.) has appeared.


_Did Francis Bacon reject the Copernican System?_

MR. DE MORGAN has very properly remarked (_Comp. B. A._ 1855, p. 11)
that the notice of the heliocentric question in the _Novum Organon_
must be considered one of the most important passages in his works
upon this point, as being probably the latest written and best {531}
matured. It occurs in Lib. ii. Aphorism xxxvi., in which he is
speaking of _Prerogative Instances_, of which he gives twenty-seven
species. In the passage now referred to, he is speaking of a kind of
Prerogative Instances, better known to ordinary readers than most of
the kinds by name, the _Instantia Crucis_: though probably the
metaphor from which this name is derived is commonly wrongly
apprehended. Bacon's meaning is _Guide-Post Instances_: and the
_Crux_ which he alludes to is not a Cross, but a Guide-Post at
Cross-roads. And among the cases to which such Instances may be
applied, he mentions the diurnal motion of the heavens from east to
west, and the special motion of the particular heavenly bodies from
west to east. And he suggests what he conceives may be an _Instantia
Crucis_ in each case. If, he says, we find any motion from east to
west in the bodies which surround the earth, slow in the ocean,
quicker in the air, quicker still in comets, gradually quicker in
planets according to their greater distance from the earth: _then_ we
may suppose that there is a cosmical diurnal motion, and the motion
of the earth must be denied.

With regard to the special motions of the heavenly bodies, he first
remarks that each body not coming quite so far westwards as before,
after one revolution of the heavens, and going to the north or the
south, does not imply any special motion; since it may be accounted
for by a modification of the diurnal motion in each, which produces
a defect of the return, and a spiral path; and he says that if we
look at the matter as common people[30\A] and disregard the devices
of astronomers, the motion is really so to the senses; and that he
has made an imitation of it by means of wires. The _instantia
crucis_ which he here suggests is, to see if we can find in any
credible history an account of any comet which did not share in the
diurnal revolution of the skies.

[Note 30\A: Et certissimum est si paulisper pro plebeiis nos geramus
(missis astronomorum et scholæ commentis, quibus illud in more est,
ut sensui in multis immerito vim faciant et obscuriora malint) talem
esse motum istum ad sensum qualem diximus.]

On his assertion that the motion of each separate planet is, to
sense, a spiral, we may remark that it is certainly true; but that
the business of science, here, as elsewhere, consists in _resolving_
the complex phenomenon into simple phenomena; the complex spiral
motion into simple circular motions.

With regard to the diurnal motion of the earth, it would seem as if
Bacon himself had a leaning to believe it when he wrote this
passage; for neither is he himself, nor are any of the
Anticopernicans, {532} accustomed to assert that the immensely rapid
motion of the sphere of the Fixed Stars graduates by a slower and
slower motion of Planets, Comets, Air, and Ocean, into the
immobility of the Earth. So that the conditions are not satisfied on
which he hypothetically says, "tum abnegandus est motus terræ."

With regard to the proper motions of the planets, this passage seems
to me to confirm what I have already said of him; that he does not
appear to have seen the full value and meaning of what had been
done, up to his time, in Formal Astronomy.

We may however fully agree with Mr. De Morgan; that the whole of
what he has said on this subject, when put together, does not
justify Hume's assertion that he rejected the Copernican system
"with the most positive disdain."

Mr. De Morgan, in order to balance the Copernican argument derived
from the immense velocity of the stars in their diurnal velocity on
the other supposition, has reminded us that those who reject this
great velocity as improbable, accept without scruple the greater
velocity of light. It is curious that Bacon also has made this
comparison, though using it for a different purpose; namely, to show
that the transmission of the visual impression may be instantaneous.
In Aphorism xlvi. of Book ii. of the _Novum Organon_ he is speaking
of what he calls _Instantiæ curriculi_, or _Instantiæ ad aquam_,
which we may call _Instances by the clock_: and he says that the
great velocity of the diurnal sphere makes the marvellous velocity
of the rays of light more credible.

"Immensa illa velocitas in ipso corpore, quæ cernitur in motu diurno
(quæ etiam viros graves ita obstupefecit ut _mallent credere motum
terræ_), facit motum illum ejaculationis ab ipsis [stellis] (licet
celeritate ut diximus admirabilem) magis credibilem." This passage
shows an inclination towards the opinion of the earth's being at
rest, but not a very strong conviction.


_Kepler persecuted._

WE have seen (p. 280) that Kepler writes to Galileo in 1597--"Be
trustful and go forwards. If Italy is not a convenient place for the
publication of your views, and if you are likely to meet with any
obstacles, perhaps Germany will grant us the necessary liberty."
Kepler however had soon afterwards occasion to learn that in Germany
also, the cultivators of science were exposed to persecution. It is
true that {533} in his case the persecution went mainly on the broad
ground of his being a Protestant, and extended to great numbers of
persons at that time. The circumstances of this and other portions of
Kepler's life have been brought to light only recently through an
examination of public documents in the Archives of Würtemberg and
unpublished letters of Kepler. (Johann Keppler's Leben und Wirken,
nach neuerlich aufgefundenen Manuscripten bearbeitet von J. L. C.
Freiherrn v. Breitschwart, K. Würtemberg. Staats-Rath. Stuttgart,
1831.)

Schiller, in his _History of the Thirty Years' War_, says that when
Ferdinand of Austria succeeded to the Archduchy of Stiria, and found
a great number of Protestants among his subjects, he suppressed
their public worship without cruelty and almost without noise. But
it appears now that the Protestants were treated with great
severity. Kepler held a professorship in Stiria, and had married, in
1507, Barbara Müller, who had landed property in that province. On
the 11th of June, 1598, he writes to his friend Mæstlin that the
arrival of the Prince out of Italy is looked forwards to with
terror. In December he writes that the Protestants had irritated the
Catholics by attacks from the pulpit and by caricatures; that
hereupon the Prince, at the prayer of the Estates, had declared the
Letter of License granted by his father to be forfeited, and had
ordered all the Evangelical Teachers to leave the country on pain of
death. They went to the frontiers of Hungary and Croatia; but after
a month, Kepler was allowed to return, on condition of keeping
quiet. His discoveries appear to have operated in his favor. But the
next year he found his situation in Stiria intolerable, and longed
to return to his native country of Würtemberg, and to find some
position there. This he did not obtain. He wrote a circular letter
to his Brother Protestants, to give them consolation and courage;
and this was held to be a violation of the conditions on which his
residence was tolerated. Fortunately, at this time he was invited to
join Tycho Brahe, who had also been driven from his native country,
and was living at Prague. The two astronomers worked together under
the patronage of the Emperor Rudolph II.; and when Tycho died in
1601, Kepler became the Imperial _Mathematicus_.

We are not to imagine that even among Protestants, astronomical
notions were out of the sphere of religious considerations. When
Kepler was established in Stiria, his first official business was
the calculation of the Calendar for the Evangelical Community. They
protested against the new Calendar, as manifestly calculated for the
furtherance of an impious papistry: and, say they, "We hold the Pope
for a {534} horrible roaring Lion. If we take his Calendar, we must
needs go into the church when he rings us in." Kepler however did
not fail to see, and to say, that the Papal Reformation of the
Calendar was a vast improvement.

Kepler, as court-astronomer, was of course required to provide such
observations of the heavens as were requisite for the calculations of
the Astrologers. That he considered Astrology to be valuable only as
the nurse of Astronomy, he did not hesitate to reveal. He wrote a work
with a title of which the following is the best translation which I
can give: "_Tertius interveniens_, or: A Warning to certain
_Theologi_, _Medici_, _Philosophi_, that while they reasonably reject
star-gazing superstition, they do not throw away the kernel with the
shell.[31\A] 1610." In this he says, "You over-clever Philosophers
blame this Daughter of Astronomy more than is reasonable. Do you not
know that she must maintain her mother with her charms? How many men
would be able to make Astronomy their business, if men did not cherish
the hope to read the Future in the skies?"

[Note 31\A: The German passage involves a curious image, borrowed, I
suppose, from some odd story: "dass sie mit billiger Verwerfung des
sternguckerischen Aberglaubens das Kind nicht mit dem Bade
ausschütten." "That they do not throw away the child along with the
dirty water of his bath."]


_Were the Papal Edicts against the Copernican System repealed?_

ADMIRAL SMYTH, in his _Cycle of Celestial Objects_, vol. i. p. 65,
says--"At length, in 1818, the voice of truth was so prevailing that
Pius VII. repealed the edicts against the Copernican system, and
thus, in the emphatic words of Cardinal Toriozzi, 'wiped off this
scandal from the Church.'"

A like story is referred to by Sir Francis Palgrave, in his
entertaining and instructive fiction, _The Merchant and the Friar_.

Having made inquiry of persons most likely to be well informed on
this subject, I have not been able to learn that there is any
further foundation for these statements than this: In 1818, on the
revisal of the _Index Expurgatorius_, Galileo's writings were, after
some opposition, expunged from that Catalogue.

Monsignor Marino Marini, an eminent Roman Prelate, had addressed to
the _Romana Accademia di Archeologia_, certain historico-critical
Memoirs, which he published in 1850, with the title _Galileo e
l'Inquisizione_. In these, he confirms the conclusion which, I
think, almost {535} all persons who have studied the facts have
arrived at;[32\A] that Galileo trifled with authority to which he
professed to submit, and was punished for obstinate contumacy, not
for heresy. M. Marini renders full justice to Galileo's ability, and
does not at all hesitate to regard his scientific attainments as
among the glories of Italy. He quotes, what Galileo himself quoted,
an expression of Cardinal Baronius, that "the intention of the Holy
Spirit was to teach how to go to heaven, not how heaven goes."[33\A]
He shows that Galileo pleaded (p. 62) that he had not held the
Copernican opinion after it had been intimated to him (by Bellarmine
in 1616), that he was not to hold it; and that his breach of promise
in this respect was the cause of the proceedings against him.

[Note 32\A: M. Marini (p. 29) mentions Leibnitz, Guizot, Spittler,
Eichhorn, Raumer, Ranke, among the "storici eterodossi" who have at
last done justice to the Roman Church.]

[Note 33\A: Come si vada al Cielo, e non come vada il Cielo.]

Those who admire Galileo and regard him as a martyr because, after
escaping punishment by saying "It _does not_ move," he forthwith
said "And yet it _does_ move," will perhaps be interested to know
that the former answer was suggested to him by friends anxious for
his safety. Niccolini writes to Bali Cioli (April 9, 1633) that
Galileo continued to be so persuaded of the truth of his opinions
that "he was resolved (some moments before his sentence) to defend
them stoutly; but I (continues Niccolini) exhorted him to make an
end of this; not to mind defending them; and to submit himself to
that which he sees that they may desire him to believe or to hold
about this matter of the motion of the earth. He was extremely
afflicted." But the Inquisition was satisfied with his answers, and
required no more.[34\A]

[Note 34\A: Marini, p. 61.]



{{536}}
BOOK VI.

MECHANICS.




CHAPTER III.

PRINCIPLES AND PROBLEMS.


_Significance of Analytical Mechanics._

IN the text, page 372, I have stated that Lagrange, near the end of
his life, expressed his sorrow that the methods of approximation
employed in Physical Astronomy rested on arbitrary processes, and
not on any insight into the results of mechanical action. From the
recent biography of Gauss, the greatest physical mathematician of
modern times, we learn that he congratulated himself on having
escaped this error. He remarked[35\A] that many of the most
celebrated mathematicians, Euler very often, Lagrange sometimes, had
trusted too much to the symbolical calculation of their problems,
and would not have been able to give an account of the meaning of
each successive step of their investigation. He said that he
himself, on the other hand, could assert that at every step which he
took, he always had the aim and purpose of his operations before his
eyes without ever turning aside from the way. The same, he remarked,
might be said of Newton.

[Note 35\A: Gauss, _Zum Gedächtniss, von W. Sartorius v.
Waltershausen_, p. 80.]


_Engineering Mechanics._

The principles of the science of Mechanics were discovered by
observations made upon bodies within the reach of men; as we have
seen in speaking of the discoveries of Stevinus, Galileo, and
others, up to the time of Newton. And when there arose the
controversy about _vis viva_ (Chap. v. Sect. 2 of this
Book);--namely, whether the "living force" of a body is measured by
the product of the weight into the {537} velocity, or of the weight
into the square of the velocity;--still the examples taken were
cases of action in machines and the like terrestrial objects. But
Newton's discoveries identified celestial with terrestrial
mechanics; and from that time the mechanical problems of the heavens
became more important and attractive to mathematicians than the
problems about earthly machines. And thus the generalizations of the
problems, principles, and methods of the mathematical science of
Mechanics from this period are principally those which have
reference to the motions of the heavenly bodies: such as the Problem
of Three Bodies, the Principles of the Conservation of Areas, and of
the Immovable Plane, the Method of Variation of Parameters, and the
like (Chap. vi. Sect. 7 and 14). And the same is the case in the
more recent progress of that subject, in the hands of Gauss, Bessel,
Hansen, and others.

But yet the science of Mechanics as applied to terrestrial
machines--_Industrial Mechanics_, as it has been termed--has made
some steps which it may be worth while to notice, even in a general
history of science. For the most part, all the most general laws of
mechanical action being already finally established, in the way
which we have had to narrate, the determination of the results and
conditions of any combination of materials and movements becomes
really a mathematical deduction from known principles. But such
deductions may be made much more easy and much more luminous by the
establishment of general terms and general propositions suited to
their special conditions. Among these I may mention a new abstract
term, introduced because a general mechanical principle can be
expressed by means of it, which has lately been much employed by the
mathematical engineers of France, MM. Poncelet, Navier, Morin, &c.
The abstract term is _Travail_, which has been translated _Laboring
Force_; and the principle which gives it its value, and makes it
useful in the solution of problems, is this;--that the _work done_
(in overcoming resistance or producing any other effect) is equal to
the _Laboring Force_, by whatever contrivances the force be applied.
This is not a new principle, being in fact mathematically equivalent
to the conservation of Vis Viva; but it has been employed by the
mathematicians of whom I have spoken with a fertility and simplicity
which make it the mark of a new school of _The Mechanics of
Engineering_.

The Laboring Force expended and the work done have been described by
various terms, as _Theoretical Effect_ and _Practical Effect_, and
the like. The usual term among English engineers for the work {538}
which an Engine usually does, is _Duty_; but as this word naturally
signifies what the engine _ought_ to do, rather than what it does,
we should at least distinguish between the Theoretical and the
Actual Duty.

The difference between the Theoretical and Actual Duty of a Machine
arises from this: that a portion of the Laboring Force is absorbed
in producing effects, that is, in doing work which is not reckoned
as Duty: for instance, overcoming the resistance and waste of the
machine itself. And so long as this resistance and waste are not
rightly estimated, no correspondence can be established between the
theoretical and the practical Duty. Though much had been written
previously upon the theory of the steam-engine, the correspondence
between the Force expended and the Work done was not clearly made
out till Comte De Pambour published his _Treatise on Locomotive
Engines_ in 1835, and his _Theory of the Steam-Engine_ in 1839.


_Strength of Materials._

Among the subjects which have specially engaged the attention of
those who have applied the science of Mechanics to practical
matters, is the strength of materials: for example, the strength of
a horizontal beam to resist being broken by a weight pressing upon
it. This was one of the problems which Galileo took up. He was led
to his study of it by a visit which he made to the arsenal and
dockyards of Venice, and the conclusions which he drew were
published in his _Dialogues_, in 1633. In his mode of regarding the
problem, he considers the section at which the beam breaks as the
short arm of a bent lever which resists fracture, and the part of
the beam which is broken off as the longer arm of the lever, the
lever turning about the fracture as a hinge. So far this is true;
and from this principle he obtained results which are also true  as,
that the strength of a rectangular beam is proportional to the
breadth multiplied into the square of the depth:--that a hollow beam
is stronger than a solid beam of the same mass; and the like.

But he erred in this, that he supposed the hinge about which the
breaking beam turns, to be exactly at the unrent surface, that
surface resisting all change, and the beam being rent all the way
across. Whereas the fact is, that the unrent surface yields to
compression, while the opposite surface is rent; and the hinge about
which the breaking beam turns is at an intermediate point, where the
extension {539} and rupture end, and the compression and crushing
begin: a point which has been called _the neutral axis_. This was
pointed out by Mariotte; and the notion, once suggested, was so
manifestly true that it was adopted by mathematicians in general.
James Bernoulli,[36\A] in 1705, investigated the strength of beams
on this view; and several eminent mathematicians pursued the
subject; as Varignon, Parent, and Bulfinger; and at a later period,
Dr. Robison in our own country.

[Note 36\A: _Opera_, ii. p. 976.]

But along with the fracture of beams, the mathematicians considered
also another subject, the flexure of beams, which they undergo
before they break, in virtue of their elasticity. What is the
_elastic curve_?--the curve into which an elastic line forms itself
under the pressure of a weight--is a problem which had been proposed
by Galileo, and was fully solved, as a mathematical problem, by
Euler and others.

But beams in practice are not mere lines: they are solids. And their
resistance to flexure, and the amount of it, depends upon the
resistance of their internal parts to extension and compression, and
is different for different substances. To measure these differences,
Dr. Thomas Young introduced the notion of the _Modulus of
Elasticity_:[37\A] meaning thereby a column of the substance of the
same diameter, such as would by its weight produce a compression
equal to the whole length of the beam, the rate of compression being
supposed to continue the same throughout. Thus if a rod of any kind,
100 inches long, were compressed 1 inch by a weight 1000 pounds, the
weight of its modulus of elasticity would be 100,000 pounds. This
notion assumes Hooke's law that the extension of a substance is as
its tension; and extends this law to compression also.

[Note 37\A: Lecture xiii. The height of the modulus is the same for
the same substance, whatever its breadth and thickness may be; for
atmospheric air it is about five miles, and for steel nearly 1500
miles.]

There is this great advantage in introducing the definition of the
Modulus of Elasticity,--that it applies equally to the flexure of a
substance and to the minute vibrations which propagate sound, and
the like. And the notion was applied so as to lead to curious and
important results with regard to the power of beams to resist
flexure, not only when loaded transversely, but when pressed in the
direction of their length, and in any oblique direction.

But in the fracture of beams, the resistance to extension and to
compression are not practically equal; and it was necessary to
determine {540} the difference of these two forces by experiments.
Several persons pursued researches on this subject; especially Mr.
Barlow, of the Royal Military Academy,[38\A] who investigated the
subject with great labor and skill, so far as wood is concerned. But
the difference between the resistance to tension and to compression
requires more special study in the case of iron; and has been
especially attended to in recent times, in consequence of the vast
increase in the number of iron structures, and in particular,
railways. It appears that wrought iron yields to compressive
somewhat more easily than to tensile force, while cast iron yields
far more easily to tensile than to compressive strains. In all cases
the power of a beam to resist fracture resides mainly in the upper
and the under side, for there the tenacity of the material acts at
the greatest leverage round the hinge of fracture. Hence the
practice was introduced of making iron beams with a broad _flange_
at the upper and another flange at the under side, connected by a
vertical plate or _web_, of which the office was to keep the two
flanges asunder. Mr. Hodgkinson made many valuable experiments, on a
large scale, to determine the forms and properties of such beams.

[Note 38\A: _An Essay on the Strength and Shape of Timber_. 3d
edition, 1826.]

But though engineers were, by such experiments and reasonings,
enabled to calculate the strength of a given iron beam, and the
dimensions of a beam which should bear a given load, it would hardly
have occurred to the boldest speculator, a few years ago, to predict
that there might be constructed beams nearly 500 feet long, resting
merely on their two extremities, of which it could be known
beforehand, that they would sustain, without bending or yielding in
any perceptible degree, the weight of a railroad train, and the jar
of its unchecked motion. Yet of such beams, constructed beforehand
with the most perfect confidence, crowned with the most complete
success, is composed the great tubular bridge which that consummate
engineer, Mr. Robert Stephenson, has thrown across the Menai Strait,
joining Wales with the island of Anglesey. The upper and under
surfaces of this quadrangular tube are the flanges of the beam, and
the two sides are the webs which connect them. In planning this
wonderful structure, the point which required especial care was to
make the upper surface strong enough to resist the compressive force
which it has to sustain; and this was done by constructing the upper
part of the beam of a series of cells, made of iron plate. The
application of the arch, of the dome, and of groined vaulting, to
the widest space over which they have ever been thrown, {541} are
achievements which have, in the ages in which they occurred, been
received with great admiration and applause; but in those cases the
principle of the structure had been tried and verified for ages upon
a smaller scale. Here not only was the space thus spanned wider than
any ever spanned before, but the principle of such a beam with a
cellular structure of its parts, was invented for this very purpose,
experimentally verified with care, and applied with the most exact
calculation of its results.


_Roofs--Arches--Vaults._

The calculations of the mechanical conditions of structures
consisting of several beams, as for instance, the frames of roofs,
depends upon elementary principles of mechanics; and was a subject
of investigation at an early period of the science. Such frames may
be regarded as assemblages of levers. The parts of which they
consist are rigid beams which sustain and convey force, and _Ties_
which resist such force by their tension. The former parts must be
made rigid in the way just spoken of with regard to iron beams; but
ties may be rods merely. The wide structures of many of the roofs of
railway stations, compared with the massive wooden roofs of ancient
buildings, may show us how boldly and how successfully this
distinction has been carried out in modern times. The investigation
of the conditions and strength of structures consisting of wooden
beams has been cultivated by Mathematicians and Engineers, and is
often entitled _Carpentry_ in our Mechanical Treatises. In our own
time, Dr. Robison and Dr. Thomas Young have been two of the most
eminent mathematicians who have written upon this subject.

The properties of the simple machines have been known, as we have
narrated, from the time of the Ancient Greeks. But it is plain that
such machines are prevented from producing their full effect by
various causes. Among the rest, the rubbing of one part of the
machine upon another produces an obstacle to the effectiveness of a
machine: for instance, the rubbing of the axle of a wheel in the
hole in which it rests, the rubbing of a screw against the sides of
its hollow screw; the rubbing of a wedge against the sides of its
notch; the rubbing of a cord against its pulley. In all these cases,
the effect of the machine to produce motion is diminished by the
friction. And this _Friction_ may be measured and its effects
calculated; and thus we have a new branch of mechanics, which has
been much cultivated. {542}

Among the effects of friction, we may notice the standing of a stone
arch. For each of the vaulting stones of an arch is a truncated
wedge; and though a collection of such stones might be so
proportioned in their weights as to balance exactly, yet this
balance would be a tottering equilibrium, which the slightest shock
would throw down, and which would not practically subsist. But the
friction of the vaulting stones against one another prevents this
instability from being a practical inconvenience; and makes an
equilibrated arch to be an arch strong for practical purposes. The
_Theory of Arches_ is a portion of Mechanics which has been much
cultivated, and which has led to conclusions of practical use, as
well as of theoretical beauty.

I have already spoken of the invention of the Arch, the Dome, and
Groined Vaulting, as marked steps in building. In all these cases the
invention was devised by practical builders; and mechanical theory,
though it can afterwards justify these structures, did not originally
suggest them. They are not part of the result, nor even of the
application of theory, but only of its exemplification. The authors of
all these inventions are unknown; and the inventions themselves may be
regarded as a part of the Prelude of the science of mechanics, because
they indicate that the ideas of mechanical pressure and support, in
various forms, are acquiring clearness and fixity.

In this point of view, I spoke (Book iv. chap. v. sect. 5) of the
Architecture of the Middle Ages as indicating a progress of thought
which led men towards the formation of Statics as a science.

As particular instances of the operation of such ideas, we have the
_Flying Buttresses_ which support stone vaults; and especially, as
already noted, the various contrivances by which stone vaults are
made to intersect one another, so as to cover a complex pillared
space below with _Groined Vaulting_. This invention, executed as it
was by the builders of the twelfth and succeeding centuries, is the
most remarkable advance in the mechanics of building, after the
invention of the _Arch_ itself.

It is curious that it has been the fortune of our times, among its
many inventions, to have produced one in this department, of which
we may say that it is the most remarkable step in the mechanics of
arches which has been made since the introduction of pointed groined
vaults. I speak of what are called _Skew Arches_, in which the
courses of stone or brick of which the bridge is built run obliquely
to the walls of the bridge. Such bridges have become very common in
the works of railroads; for they save space and material, and the
{543} invention once made, the cost of the ingenuity is nothing. Of
course, the mechanical principles involved in such structures are
obvious to the mathematician, when the problem has been practically
solved. And in this case, as in the previous cardinal inventions in
structure, though the event has taken place within a few years, no
single person, so far as I am aware, can be named as the
inventor.[39\A]

[Note 39\A: Since this was written, I have been referred to Rees's
_Cyclopædia_, Article _Oblique Arches_, where this invention is
correctly explained, and is claimed for an engineer named Chapman.
It is there said, that the first arch of this kind was erected in
1787 at Naas, near Kildare in Ireland.]



{{544}}
BOOK VII.

PHYSICAL ASTRONOMY.




CHAPTER I.

PRELUDE TO NEWTON.


_The Ancients._

EXPRESSIONS in ancient writers which may be interpreted as
indicating a notion of gravitation in the Newtonian sense, no doubt
occur. But such a notion, we may be sure, must have been in the
highest degree obscure, wavering, and partial. I have mentioned
(Book i. Chap. 3) an author who has fancied that he traces in the
works of the ancients the origin of most of the vaunted discoveries
of the moderns. But to ascribe much importance to such expressions
would be to give a false representation of the real progress of
science. Yet some of Newton's followers put forward these passages
as well deserving notice; and Newton himself appears to have had
some pleasure in citing such expressions; probably with the feeling
that they relieved him of some of the odium which, he seems to have
apprehended, hung over new discoveries. The Preface to the
_Principia_, begins by quoting[40\A] the authority of the ancients,
as well as the moderns, in favor of applying the science of
Mechanics to Natural Philosophy. In the Preface to David Gregory's
_Astronomiæ Physicæ et Geometricæ Elementa_, published in 1702, is a
large array of names of ancient authors, and of quotations, to prove
the early and wide diffusion of the doctrine of the gravity of the
Heavenly Bodies. And it appears to be now made out, that this
collection of ancient authorities {545} was supplied to Gregory by
Newton himself. The late Professor Rigaud, in his _Historical Essay
on the First Publication of Sir Isaac Newton's Principia_, says (pp.
80 and 101) that having been allowed to examine Gregory's papers, he
found that the quotations given by him in his Preface are copied or
abridged from notes which Newton had supplied to him in his own
handwriting. Some of the most noticeable of the quotations are those
taken from Plutarch's Dialogue _on the Face which appears in the
Moon's Disk_: it is there said, for example, by one of the speakers,
that the Moon is perhaps prevented from falling to the earth by the
rapidity of her revolution round it; as a stone whirled in a sling
keeps it stretched. Lucretius also is quoted, as teaching that all
bodies would descend with an equal celerity in a vacuum:
  Omnia quapropter debent per inane quietum
  Æque ponderibus non æquis concita ferri.
         Lib. ii. v. 238.

[Note 40\A: Cum veteres _Mechanicam_ (uti author est _Pappus_), in
rerum Naturalium investigatione maximi fecerint, et recentiores,
missis formis substantialibus et qualitatibus occultis, Phenonmena
Naturæ ad leges mathematicas revocare aggressa sunt; visum est in
hoc Tractatu _Mathesin_ excolere quatenus ea ad _Philosophiam_
spectat.]

It is asserted in Gregory's Preface that Pythagoras was not
unacquainted with the important law of gravity, the inverse squares
of the distances from the centre. For, it is argued, the seven
strings of Apollo's lyre mean the seven planets; and the proportions
of the notes of strings are reciprocally as the inverse squares of
the weights which stretch them.

I have attempted, throughout this work, to trace the progress of the
discovery of the great truths which constitute real science, in a
more precise manner than that which these interpretations of ancient
authors exemplify.


_Jeremiah Horrox._

In describing the Prelude to the Epoch of Newton, I have spoken (p.
395) of a group of philosophers in England who began, in the first
half of the seventeenth century, to knock at the door where Truth
was to be found, although it was left for Newton to force it open;
and I have there noticed the influence of the civil wars on the
progress of philosophical studies. To the persons thus tending
towards the true physical theory of the solar system, I ought to
have added Jeremy Horrox, whom I have mentioned in a former part
(Book v. chap. 5) as one of the earliest admirers of Kepler's
discoveries. He died at the early age of twenty-two, having been the
first person who ever saw Venus pass across the disk of the Sun
according to astronomical prediction, which took place in 1639. His
_Venus in sole visa_, {546} in which this is described, did not
appear till 1661, when it was published by Hevelius of Dantzic. Some
of his papers were destroyed by the soldiers in the English civil
wars; and his remaining works were finally published by Wallis, in
1673. The passage to which I here specially wish to refer is
contained in a letter to his astronomical ally, William Crabtree,
dated 1638. He appears to have been asked by his friend to suggest
some cause for the motion of the aphelion of a planet; and in reply,
he uses an experimental illustration which was afterwards employed
by Hooke in 1666. A ball at the end of a string is made to swing so
that it describes an oval. This contrivance Hooke employed to show
the way in which an orbit results from the combination of a
projectile motion with a central force. But the oval does not keep
its axis constantly in the same position. The apsides, as Horrox
remarked, move in the same direction as the pendulum, though much
slower. And it is true, that this experiment does illustrate, in a
general way, the cause of the motion of the aphelia of the Planetary
Orbits; although the form of the orbit is different in the
experiment and in the solar system; being an ellipse with the centre
of force in the centre of the ellipse, in the former case, and an
ellipse with the centre of force in the focus, in the latter case.
These two forms of orbits correspond to a central force varying
directly as the distance, and a central force varying inversely as
the square of the distance; as Newton proved in the _Principia_. But
the illustration appears to show that Horrox pretty clearly saw how
an orbit arose from a central force. So far, and no further,
Newton's contemporaries could get; and then he had to help them
onwards by showing what was the law of the force, and what larger
truths were now attainable.


_Newton's Discovery of Gravitation._

[Page 402.] As I have already remarked, men have a willingness to
believe that great discoveries are governed by casual coincidences,
and accompanied by sudden revolutions of feeling. Newton had
entertained the thought of the moon being retained in her orbit by
gravitation as early as 1665 or 1666. He resumed the subject and
worked the thought out into a system in 1684 and 5. What induced him
to return to the question? What led to his success on this last
occasion? With what feelings was the success attended? It is easy to
make an imaginary connection of facts. "His optical discoveries had
recommended him to the Royal Society, and he was now a member. He
{547} _there_ learned the accurate measurement of the Earth by
Picard, differing very much from the estimation by which he had made
his calculation in 1666; and he thought his conjecture now more
likely to be just."[41\A] M. Biot gives his assent to this
guess.[42\A] The English translation of M. Biot's biography[43\A]
converts the guess into an assertion. But, says Professor
Rigaud,[44\A] Picard's measurement of the Earth was well known to
the Fellows of the Royal Society as early as 1675, there being an
account of the results of it given in the _Philosophical
Transactions_ for that year. Moreover, Norwood, in his _Seaman's
Practice_, dated 1636, had given a much more exact measure than
Newton employed in 1666. But Norwood, says Voltaire, had been buried
in oblivion by the civil wars. No, again says the exact and
truth-loving Professor Rigaud, Norwood was in communication with the
Royal Society in 1667 and 1668. So these guesses at the accident
which made the apple of 1665 germinate in 1684, are to be carefully
distinguished from history.

[Note 41\A: Robison's _Mechanical Philosophy_, vol. iii. p. 94.
(Art. 195.)]

[Note 42\A: _Biographie Universelle_.]

[Note 43\A: _Library of Useful Knowledge_.]

[Note 44\A: _Historical Essay on the First Publication of the
Principia_ (1838).]

But with what feelings did Newton attain to his success? Here again
we have, I fear, nothing better than conjecture. "He went home, took
out his old papers, and resumed his calculations. As they drew near
to a close, he was so much agitated that he was obliged to desire a
friend to finish them. His former conjecture was now found to agree
with the phænomena with the utmost precision."[45\A] This
conjectural story has been called "a tradition;" but he who relates
it does not call it so. Every one must decide, says Professor
Rigaud, from his view of Newton's character, how far he thinks it
consistent with this statement. Is it likely that Newton, so calm
and so indifferent to fame as he generally showed himself, should be
thus agitated on such an occasion? "No," says Sir David Brewster;
"it is not supported by what we know of Newton's character."[46\A]
To this we may assent; and this conjectural incident we must
therefore, I conceive, separate from history. I had incautiously
admitted it into the text of the first Edition.

[Note 45\A: Robison, ibid.]

[Note 46\A: _Life of Newton_, vol. i. p. 292.]

Newton appears to have discovered the method of demonstrating that a
body might describe an ellipse when acted upon by a force residing
in the focus, and varying inversely as the square of the distance,
in 1669, upon occasion of his correspondence with Hooke. In 1684,
{548} at Halley's request, he returned to the subject; and in
February, 1685 there was inserted in the Register of the Royal
Society a paper of Newton's (_Isaaci Newtoni Propositiones de
Motu_), which contained some of the principal propositions of the
first two Books of the _Principia_. This paper, however, does not
contain the proposition "Lunam gravitare in Terram," nor any of the
propositions of the Third Book.




CHAPTER  III.

THE PRINCIPIA.


_Sect._ 2.--_Reception of the Principia._

LORD BROUGHAM has very recently (_Analytical View of Sir Isaac
Newton's Principia_, 1855) shown a strong disposition still to
maintain, what he says has frequently been alleged, that the
reception of the work was not, even in this country, "such as might
have been expected." He says, in explanation of the facts which I
have adduced, showing the high estimation in which Newton was held
immediately after the publication of the _Principia_, that Newton's
previous fame was great by former discoveries. This is true; but the
effect of this was precisely what was most honorable to Newton's
countrymen, that they received with immediate acclamations this new
and greater discovery. Lord Brougham adds, "after its appearance the
_Principia_ was more admired than studied;" which is probably true
of the _Principia_ still, and of all great works of like novelty and
difficulty at all times. But, says Lord Brougham, "there is no
getting over the inference on this head which arises from the dates
of the two first editions. There elapsed an interval of no less than
twenty-seven years between them; and although Cotes [in his Preface]
speaks of the copies having become scarce and in very great demand
when the second edition appeared in 1713, yet had this urgent demand
been of many years' continuance, the reprinting could never have
been so long delayed." But Lord Brougham might have learnt from Sir
David Brewster's _Life of Newton_ (vol. i. p. 312), which he extols
so emphatically, that already in 1691 (only four years after the
publication), a copy of the _Principia_ could hardly be procured,
and that even at that {549} time an improved edition was in
contemplation; that Newton had been pressed by his friends to
undertake it, and had refused.

When Bentley had induced Newton to consent that a new edition should
be printed, he announces his success with obvious exultation to
Cotes, who was to superintend the work. And in the mean time the
_Astronomy_ of David Gregory, published in 1702, showed in every
page how familiar the Newtonian doctrines were to English
philosophers, and tended to make them more so, as the sermons of
Bentley himself had done in 1692.

Newton's Cambridge contemporaries were among those who took a part
in bringing the _Principia_ before the world. The manuscript draft
of it was conveyed to the Royal Society (April 28, 1686) by Dr.
Vincent, Fellow of Clare Hall, who was the tutor of Whiston,
Newton's deputy in his professorship; and he, in presenting the
work, spoke of the novelty and dignity of the subject. There exists
in the library of the University of Cambridge a manuscript
containing the early Propositions of the _Principia_ as far as Prop.
xxxiii. (which is a part of Section vii., about Falling Bodies).
This appears to have been a transcript of Newton's Lectures,
delivered as Lucasian Professor: it is dated October, 1684.


_Is Gravitation proportional to Quantity of Matter?_

It was a portion of Newton's assertion in his great discovery, that
all the bodies of the universe attract each other with forces which
are _as the quantity of matter_ in each: that is, for instance, the
sun attracts the satellites of any planet just as much as he
attracts the planet itself, in proportion to the quantity of matter
in each; and the planets attract one another just as much as they
attract the sun, according to the quantity of matter.

To prove this part of the law _exactly_ is a matter which requires
careful experiments; and though proved experimentally by Newton, has
been considered in our time worthy of re-examination by the great
astronomer Bessel. There was some ground for doubt; for the mass of
Jupiter, as deduced from the perturbations of Saturn, was only 1/1070
of the mass of the sun; the mass of the same planet as deduced from
the perturbations of Juno and Pallas was 1/1045 of that of the Sun. If
this difference were to be confirmed by accurate observations and
calculations, it would follow that the attractive power exercised by
Jupiter upon the minor planets was greater than that exercised upon
{550} Saturn. And in the same way, if the attraction of the Earth had
any _specific_ relation to different kinds of matter, the time of
oscillation of a pendulum of equal length composed wholly or in part
of the two substances would be different. If, for instance, it were
more intense for magnetized iron than for stone, the iron pendulum
would oscillate more quickly. Bessel showed[47\A] that it was possible
to assume hypothetically a constitution of the sun, planets, and their
appendages, such that the attraction of the Sun on the Planets and
Satellites should be proportional to the quantity of matter in each;
but that the attraction of the Planets on one another would not be on
the same scale.

[Note 47\A: _Berlin Mem._ 1824.]

Newton had made experiments (described in the _Principia_, Book
iii., Prop. vi.) by which it was shown that there could be no
considerable or palpable amount of such specific difference among
terrestrial bodies, but his experiments could not be regarded as
exact enough for the requirements of modern science. Bessel
instituted a laborious series of experiments (presented to the
Berlin Academy in 1832) which completely disproved the conjecture of
such a difference; every substance examined having given exactly the
same coefficient of gravitating intensity as compared with inertia.
Among the substances examined were metallic and stony masses of
meteoric origin, which might be supposed, if any bodies could, to
come from other parts of the solar system.




CHAPTER IV.

VERIFICATION AND COMPLETION OF THE NEWTONIAN THEORY.


_Tables of the Moon and Planets._

THE Newtonian discovery of Universal Gravitation, so remarkable in
other respects, is also remarkable as exemplifying the immense
extent to which the verification of a great truth may be carried,
the amount of human labor which may be requisite to do it justice,
and the striking extension of human knowledge to which it may lead.
I have said that it is remarked as a beauty in the first fixation of
a theory that its measures or elements are established by means of a
few {551} data; but that its excellence when established is in the
number of observations which it explains. The multiplicity of
observations which are explained by astronomy, and which are made
because astronomy explains them, is immense, as I have noted in the
text. And the multitude of observations thus made is employed for
the purpose of correcting the first adopted elements of the theory.
I have mentioned some of the examples of this process: I might
mention many others in order to continue the history of this part of
Astronomy up to the present time. But I will notice only those which
seem to me the most remarkable.

In 1812, Burckhardt's _Tables de la Lune_ were published by the
French Bureau des Longitudes. A comparison of these and Burg's with
a considerable number of observations, gave 9-100ths of a second as
the mean error of the former in the Moon's longitude, while the mean
error of Burg's was 18-100ths. The preference was therefore accorded
to Burckhardt's.

Yet the Lunar Tables were still as much as thirty seconds wrong in
single observations. This circumstance, and Laplace's expressed wish,
induced the French Academy to offer a prize for a complete and purely
theoretical determination of the Lunar path, instead of determinations
resting, as hitherto, partly upon theory and partly upon observations.
In 1820, two prize essays appeared, the one by Damoiseau, the other by
Plana and Carlini. And some years afterwards (in 1824, and again in
1828), Damoiseau published _Tables de la Lune formées sur la seule
Théorie d'Attraction_. These agree very closely with observation. That
we may form some notion of the complexity of the problem, I may state
that the longitude of the Moon is in these Tables affected by no fewer
than forty-seven _equations_; and the other quantities which determine
her place are subject to inequalities not much less in number.

Still I had to state in the second Edition, published in 1847, that
there remained an unexplained discordance between theory and
observation in the motions of the Moon; an inequality of long period
as it seemed, which the theory did not give.

A careful examination of a long series of the best observations of
the Moon, compared throughout with the theory in its most perfect
form, would afford the means both of correcting the numerical
elements of the theory, and of detecting the nature, and perhaps the
law, of any still remaining discrepancies. Such a work, however,
required vast labor, as well as great skill and profound
mathematical knowledge. {552} Mr. Airy undertook the task; employing
for that purpose, the Observations of the Moon made at Greenwich
from 1750 to 1830. Above 8000 observed places of the Moon were
compared with theory by the computation of the same number of
places, each separately and independently calculated from Plana's
Formulæ. A body of calculators (sometimes sixteen), at the expense
of the British Government, was employed for about eight years in
this work. When we take this in conjunction with the labor which the
observations themselves imply, it may serve to show on what a scale
the verification of the Newtonian theory has been conducted. The
first results of this labor were published in two quarto volumes;
the final deductions as to correction of elements, &c., were given
in the Memoirs of the Astronomical Society in 1848.[48\A]

[Note 48\A: The total expense of computers, to the end of reading
the proof-sheets, was 4300_l._

Mr. Airy's estimate of days' works [made before beginning], for the
heavy part of calculations only, was thirty-six years of one computer.
This was somewhat exceeded, but not very greatly, in that part.]

Even while the calculations were going on, it became apparent that
there were some differences between the observed places of the Moon,
and the theory so far as it had then been developed. M. Hansen, an
eminent German mathematician who had devised new and powerful
methods for the mathematical determination of the results of the law
of gravitation, was thus led to explore still further the motions of
the Moon in pursuance of this law. The result was that he found
there must exist two lunar inequalities, hitherto not known; the one
of 273, and the other of 239 years, the coefficients of which are
respectively 27 and 23 seconds. Both these originate in the
attraction of Venus; one of them being connected with the long
inequality in the Solar Tables, of which Mr. Airy had already proved
the existence, as stated in Chap. vi. Sect. 6 of this Book.

These inequalities fell in with the discrepancies between the actual
observations and the previously calculated Tables, which Mr. Airy
had discovered. And again, shortly afterwards, M. Hansen found that
there resulted from the theory two other new equations of the Moon;
one in latitude and one in longitude, agreeing with two which were
found by Mr. Airy in deducing from the observations the correction
of the elements of the Lunar Tables. And again, a little later,
there was detected by these mathematicians a theoretical correction
for the {553} motion of the Node of the Moon's orbit, coinciding
exactly with one which had been found to appear in the observations.

Nothing can more strikingly exhibit the confirmation which increased
scrutiny brings to light between the Newtonian theory on the one
hand, and the celestial motions on the other. We have here a very
large mass of the best observations which have ever been made,
systematically examined, with immense labor, and with the set
purpose of correcting at once all the elements of the Lunar Tables.
The corrections of the elements thus deduced imply of course some
error in the theory as previously developed. But at the same time,
and with the like determination thoroughly to explore the subject,
the theory is again pressed to yield its most complete results, by
the invention of new and powerful mathematical methods; and the
event is, that residual errors of the old Tables, several in number,
following the most diverse laws, occurring in several detached
parts, agree with the residual results of the Theory thus newly
extracted from it. And thus every additional exactness of scrutiny
into the celestial motions on the one hand and the Newtonian theory
on the other, has ended, sooner or later, in showing the exactness
of their coincidence.

The comparison of the theory with observation in the case of the
motions of the Planets, the motion of each being disturbed by the
attraction of all the others, is a subject in some respects still
more complicated and laborious. This work also was undertaken by the
same indefatigable astronomer; and here also his materials belonged
to the same period as before; being the admirable observations made
at Greenwich from 1750 to 1830, during the time that Bradley,
Maskelyne, and Pond were the Astronomers Royal.[49\A] These
Planetary observations were deduced, and the observed places were
compared with the tabular places: with Lindenau's Tables of Mercury,
Venus, and Mars; and with Bouvard's Tables of Jupiter, Saturn, and
Uranus; and thus, while the received theory and its elements were
confirmed, the means of testing any improvement which may hereafter
be proposed, either in the form of the theoretical results or in the
constant elements which they involved, was placed within the reach
of the {554} astronomers of all future time. The work appeared in
1845; the expense of the compilations and the publication being
defrayed by the British Government.

[Note 49\A: The observations of stars made by Bradley, who preceded
Maskelyne at Greenwich, had already been discussed by Bessel, a
great German astronomer; and the results published in 1818, with a
title that well showed the estimation in which he held those
materials: _Fundamenta Astronomiæ pro anno_ 1775, _deducta ex
Ohservationibus viri incomparabilis James Bradley in specula
Astronomica Grenovicensi per annos_ 1750-1762 _institutis_.]


_The Discovery of Neptune._

The theory of gravitation was destined to receive a confirmation
more striking than any which could arise from any explanation,
however perfect, given by the motions of a known planet; namely, in
revealing the existence of an unknown planet, disclosed to
astronomers by the attraction which it exerted upon a known one. The
story of the discovery of Neptune by the calculations of Mr. Adams
and M. Le Verrier was partly told in the former edition of this
History. I had there stated (vol. ii. p. 306) that "a deviation of
observation from the theory occurs at the very extremity of the
solar system, and that its existence appears to be beyond doubt.
Uranus does not conform to the Tables calculated for him on the
theory of gravitation. In 1821, Bouvard said in the Preface to the
Tables of this Planet, "the formation of these Tables offers to us
this alternative, that we cannot satisfy modern observations to the
requisite degree of precision without making our Tables deviate from
the ancient observations." But when we have done this, there is
still a discordance between the Tables and the more modern
observations, and this discordance goes on increasing. At present
the Tables make the Planet come upon the meridian about eight
seconds later than he really does. This discrepancy has turned the
thoughts of astronomers to the effects which would result from a
planet external to Uranus. It appears that the observed motion would
be explained by applying a planet at twice the distance of Uranus
from the Sun to exercise a disturbing force, and it is found that
the present longitude of this disturbing body must be about 325
degrees.

I added, "M. Le Verrier (_Comptes Rendus_, Jan. 1, 1846) and, as I
am informed by the Astronomer Royal, Mr. Adams, of St. John's
College, Cambridge, have both arrived independently at this result."

To this Edition I added a Postscript, dated, Nov. 7, 1846, in which
I said:

"The planet exterior to Uranus, of which the existence was inferred
by M. Le Verrier and Mr. Adams from the motions of Uranus (vol. ii.
Note (L.)), has since been discovered. This confirmation of
calculations founded upon the doctrine of universal gravitation, may
be looked upon as the most remarkable event of the kind since the
return of Halley's comet in 1757  and in some respects, as a more
striking event {555} even than that; inasmuch as the new planet had
never been seen at all, and was discovered by mathematicians
entirely by their feeling of its influence, which they perceived
through the organ of mathematical calculation.

"There can be no doubt that to M. Le Verrier belongs the glory of
having first published a prediction of the place and appearance of the
new planet, and of having thus occasioned its discovery by
astronomical observers. M. Le Verrier's first prediction was published
in the _Comptes Rendus de l'Acad. des Sciences_, for _June_ 1, 1846
(not _Jan._ 1, as erroneously printed in my Note). A subsequent paper
on the subject was read Aug. 31. The planet was seen by M. Galle, at
the Observatory of Berlin, on September 23, on which day he had
received an express application from M. Le Verrier, recommending him
to endeavor to recognize the stranger by its having a visible disk.
Professor Challis, at the Observatory of Cambridge, was looking out
for the new planet from July 29, and saw it on August 4, and again on
August 12, but without recognizing it, in consequence of his plan of
not comparing his observations till he had accumulated a greater
number of them. On Sept. 29, having read for the first time M. Le
Verrier's second paper, he altered his plan, and paid attention to the
physical appearance rather than the position of the star. On that very
evening, not having then heard of M. Galle's discovery, he singled out
the star by its seeming to have a disk.

"M. Le Verrier's mode of discussing the circumstances of Uranus's
motion, and inferring the new planet from these circumstances, is in
the highest degree sagacious and masterly. Justice to him cannot
require that the contemporaneous, though unpublished, labors of Mr.
Adams, of St John's College, Cambridge, should not also be recorded.
Mr. Adams made his first calculations to account for the anomalies
in the motion of Uranus, on the hypothesis of a more distant planet,
in 1843. At first he had not taken into account the earlier
Greenwich observations; but these were supplied to him by the
Astronomer Royal, in 1844. In September, 1845, Mr. Adams
communicated to Professor Challis values of the elements of the
supposed disturbing body; namely, its mean distance, mean longitude
at a given epoch, longitude of perihelion, eccentricity of orbit,
and mass. In the next month, he communicated to the Astronomer Royal
values of the same elements, somewhat corrected. The note (L.), vol.
ii., of the present work (2d Ed.), in which the names of MM. Le
Verrier and Adams are mentioned in conjunction, was in the press in
August, 1846, a {556} month before the planet was seen. As I have
stated in the text, Mr. Adams and M. Le Verrier assigned to the
unseen planet nearly the same position; they also assigned to it
nearly the same mass; namely, 2½ times the mass of Uranus. And
hence, supposing the density to be not greater than that of Uranus,
it followed that the visible diameter would be about 3", an apparent
magnitude not much smaller than Uranus himself.

"M. Le Verrier has mentioned for the new planet the name _Neptunus_;
and probably, deference to his authority as its discoverer, will
obtain general currency for this name."

Mr. Airy has given a very complete history of the circumstances
attending the discovery of Neptune, in the Memoirs of the
Astronomical Society (read November 13, 1846). In this he shows that
the probability of some disturbing body beyond Uranus had suggested
itself to M. A. Bouvard and Mr. Hussey as early as 1834. Mr. Airy
himself then thought that the time was not ripe for making out the
nature of any external action on the planets. But Mr. Adams soon
afterwards proceeded to work at the problem. As early as 1841 (as he
himself informs me) he conjectured the existence of a planet
exterior to Uranus, and recorded in a memorandum his design of
examining its effect; but deferred the calculations till he had
completed his preparations for the University examination which he
was to undergo in January, 1843, in order to receive the Degree of
Bachelor of Arts. He was the Senior Wrangler of that occasion, and
soon afterwards proceeded to carry his design into effect; applying
to the Astronomer Royal for recorded observations which might aid
him in his task. On one of the last days of October, 1845, Mr. Adams
went to the Observatory at Greenwich; and finding the Astronomer
Royal abroad, he left there a paper containing the elements of the
extra-Uranian Planet: the longitude was in this paper stated as 323½
degrees. It was, as we have seen, in June, 1846, that M. Le
Verrier's Memoir appeared, in which he assigned to the disturbing
body a longitude of 325 degrees. The coincidence was striking. "I
cannot sufficiently express," says Mr. Airy, "the feeling of delight
and satisfaction which I received from the Memoir of M. Le Verrier."
This feeling communicated itself to others. Sir John Herschel said
in September, 1846, at a meeting of the British Association at
Southampton, "We see it (the probable new planet) as Columbus saw
America from the shores of Spain. Its movements have been felt,
trembling along the far-reaching line of our analysis, with a
certainty hardly inferior to that of ocular demonstration." {557}

In truth, at the moment when this was uttered, the new Planet had
already been seen by Professor Challis; for, as we have said, he had
seen it in the early part of August. He had included it in the net
which he had cast among the stars for this very purpose; but
employing a slow and cautious process, he had deferred for a time
that examination of his capture which would have enabled him to
detect the object sought. As soon as he received M. Le Verrier's
paper of August 31 on September 29, he was so much impressed with
the sagacity and clearness of the limitations of the field of
observation there laid down, that he instantly changed his plan of
observation, and noted the planet, as an object having a visible
disk, on the evening of the same day.

In this manner the theory of gravitation predicted and produced the
discovery. Thus to predict unknown facts found afterwards to be
true, is, as I have said, a confirmation of a theory which in
impressiveness and value goes beyond any explanation of known facts.
It is a confirmation which has only occurred a few times in the
history of science; and in the case only of the most refined and
complete theories, such as those of Astronomy and Optics. The
mathematical skill which was requisite in order to arrive at such a
discovery, may in some measure be judged of by the account which we
have had to give of the previous mathematical progress of the theory
of gravitation. It there appeared that the lives of many of the most
acute, clear-sighted, and laborious of mankind, had been employed
for generations in solving the problem. Given the planetary bodies,
to find their mutual perturbations: but here we have the inverse
problem--Given the perturbations, to find the planets.[50\A]

[Note 50\A: This may be called the _inverse_ problem with reference
to the older and more familiar problem; but we may remark that the
usual phraseology of the Problem of Central Forces differs from this
analogy. In Newton's _Principia_, the earlier Sections, in which the
motion is given to find the force, are spoken of as containing the
Direct Problem of Central Forces: the Eighth Section of the First
Book, where the Force is given to find the orbit, is spoken of as
containing the _Inverse_ Problem of Central Forces.]


_The Minor Planets._

The discovery of the Minor Planets which revolve between the orbits
of Mars and Jupiter was not a consequence or confirmation of the
Newtonian theory. That theory gives no reason for the distance of
{558} the Planets from the Sun; nor does any theory yet devised give
such reason. But an empirical formula proposed by the Astronomer
Bode of Berlin, gives a law of these distances (_Bode's Law_),
which, to make it coherent, requires a planet between Mars and
Jupiter. With such an addition, the distance of Mercury, Venus,
Earth, Mars, the Missing Planet, Jupiter, Saturn, and Uranus, are
nearly as the numbers 4, 7, 10, 16, 28, 52, 100, 196, in which the
excesses of each number above the preceding are the series 3, 3, 6,
12, 24, 48, 96. On the strength of this law the Germans wrote _on the
long-expected Planet_, and formed themselves into associations for
the discovery of it.

Not only did this law stimulate the inquiries for the Missing
Planet, and thus lead to the discovery of the Minor Planets, but it
had also a share in the discovery of Neptune. According to the law,
a planet beyond Uranus may be expected to be at the distance
represented by 388. Mr. Adams and M. Le Verrier both of them began
by assuming a distance of nearly this magnitude for the Planet which
they sought; that is, a distance more than 38 times the earth's
distance. It was found afterwards that the distance of Neptune is
only 30 times that of the earth; yet the assumption was of essential
use in obtaining the result  and Mr. Airy remarks that the history
of the discovery shows the importance of using any received theory
as far as it will go, even if the theory can claim no higher merit
than that of being plausible.[51\A]

[Note 51\A: Account of the Discovery of Neptune, &c., _Mem. Ast.
Soc._, vol. xvi. p. 414.]

The discovery of Minor Planets in a certain region of the interval
between Mars and Jupiter has gone on to such an extent, that their
number makes them assume in a peculiar manner the character of
representatives of a Missing Planet. At first, as I have said in the
text, it was supposed that all these portions must pass through or
near a common node; this opinion being founded on the very bold
doctrine, that the portions must at one time have been united in one
Planet, and must then have separated. At this node, as I have
stated, Olbers lay in wait for them, as for a hostile army at a
defile. Ceres, Pallas, and Juno had been discovered in this way in
the period from 1801 to 1804; and Vesta was caught in 1807. For a
time the chase for new planets in this region seemed to have
exhausted the stock. But after thirty-eight years, to the
astonishment of astronomers, they began to be again detected in
extraordinary numbers. In 1845, M. Hencke of {559} Driessen
discovered a fifth of these planets, which was termed Astræa. In
various quarters the chase was resumed with great ardor. In 1847
were found Hebe, Iris, and Flora; in 1848, Metis; in 1849, Hygæa; in
1850, Parthenope, Victoria, and Egeria; in 1861, Irene and Eunomia;
in 1852, Psyche, Thetis, Melpomene, Fortuna, Massilia, Lutetia,
Calliope. To these we have now (at the close of 1856) to add
_nineteen_ others; making up the whole number of these Minor Planets
at present known to _forty-two_.

As their enumeration will show, the ancient practice has been
continued of giving to the Planets mythological names. And for a
time, till the numbers became too great, each of the Minor Planets
was designated in astronomical books by some symbol appropriate to
the character of the mythological person; as from ancient times Mars
has been denoted by a mark indicating a spear, and Venus by one
representing a looking-glass. Thus, when a Minor Planet was
discovered at London in 1851, the year in which the peace of the
world was, in a manner, celebrated by the Great Exhibition of the
Products of All Nations, held at that metropolis, the name _Irene_
was given to the new star, as a memorial of the auspicious time of
its discovery. And it was agreed, for awhile, that its symbol should
be a dove with an olive-branch. But the vast multitude of the Minor
Planets, as discovery went on, made any mode of designation, except
a numerical one, practically inconvenient. They are now denoted by a
small circle inclosing a figure in the order of their discovery.
Thus, _Ceres_ is (1), _Irene_ is (14), and _Isis_ is (42).

The rapidity with which these discoveries were made was owing in
part to the formation of star-maps, in which all known fixed stars
being represented, the existence of a new and movable star might be
recognized by comparison of the sky with the map. These maps were
first constructed by astronomers of different countries at the
suggestion of the Academy of Berlin; but they have since been
greatly extended, and now include much smaller stars than were
originally laid down.

I will mention the number of planets discovered in each year. After
the start was once made, by Hencke's discovery of Astræa in 1845,
the same astronomer discovered Hebe in 1847; and in the same year
Mr. Hind, of London, discovered two others, Iris and Flora. The
years 1848 and 1849 each supplied one; the year 1850, three; 1851,
two; 1852 was marked by the extraordinary discovery of _eight_ new
members of the planetary system. The year 1853 supplied four; 1854,
six; 1855, four; and 1856 has already given us five. {560}

These discoveries have been distributed among the observatories of
Europe. The bright sky of Naples has revealed seven new planets to
the telescope of Signer Gasparis. Marseilles has given us one;
Germany, four, discovered by M. Luther at Bilk; Paris has furnished
seven; and Mr. Hind, in Mr. Bishop's private observatory in London,
notwithstanding our turbid skies, has discovered no less than ten
planets; and there also Mr. Marth discovered (29) Amphitrite. Mr.
Graham, at the private observatory of Mr. Cooper, in Ireland,
discovered (9) Metis.

America has supplied its planet, namely (31) Euphrosyne, discovered
by Mr. Ferguson at Washington  and the most recent of these
discoveries is that by Mr. Pogson, of Oxford, who has found the
forty-second of these Minor Planets, which has been named
Isis.[52\A]

[Note 52\A: I take this list from a Memoir of M. Bruhns, Berlin,
1856.]

I may add that it appears to follow from the best calculations that
the total mass of all these bodies is very small. Herschel reckoned
the diameters of Ceres at 35, and of Pallas at 26 miles. It has
since been calculated[53\A] that some of them are smaller still;
Victoria having a diameter of 9 miles, Lutetia of 8, and Atalanta of
little more than 4. It follows from this that the whole mass would
probably be less than the sixth part of our moon. Hence their
perturbing effects on each other or on other planets are null; but
they are not the less disturbed by the action of the other planets,
and especially of Jupiter.

[Note 53\A: Bruhns, as above.]


_Anomalies in the Action of Gravitation._

The complete and exact manner in which the doctrine of gravitation
explains the motions of the Comets as well as of the Planets, has
made astronomers very bold in proposing hypotheses to account for
any deviations from the motion which the theory requires. Thus
Encke's Comet is found to have its motion accelerated by about
one-eighth of a day in every revolution. This result was conceived
to be established by former observations, and is confirmed by the
facts of the appearance of 1852.[54\A] The hypothesis which is
proposed in order to explain this result is, that the Comet moves in
a resisting medium, which makes it fall inwards from its path,
towards the Sun, and thus, by narrowing its orbit, diminishes its
periodic time. On the other hand, M. Le Verrier has found that
Mercury's mean motion has gone on diminishing; {561} as if the
planet were, in the progress of his revolutions, receding further
from the Sun. This is explained, if we suppose that there is, in the
region of Mercury, a resisting medium which moves round the Sun in
the same direction as the Planets move. Evidence of a kind of
nebulous disk surrounding the Sun, and extending beyond the orbits
of Mercury and Venus, appears to be afforded us by the phenomenon
called the _Zodiacal Light_; and as the Sun itself rotates on its
axis, it is most probable that this kind of atmosphere rotates
also.[55\A] On the other hand, M. Le Verrier conceives that the
Comets which now revolve within the ordinary planetary limits have
not always done so, but have been caught and detained by the Planets
among which they move. In this way the action of Jupiter has brought
the Comets of Faye and Vico into their present limited orbits, as it
drew the Comet of Lexell out of its known orbit, when the Comet passed
over the Planet in 1779, since which time it has not been seen.

[Note 54\A: _Berlin Memoirs_, 1854.]

[Note 55\A: M. Le Verrier, _Annales de l'Obs. de Paris_, vol. i.
p. 89.]

Among the examples of the boldness with which astronomers assume the
doctrine of gravitation even beyond the limits of the solar system
to be so entirely established, that hypotheses may and must be
assumed to explain any apparent irregularity of motion, we may
reckon the mode of accounting for certain supposed irregularities in
the proper motion of Sirius, which has been proposed by Bessel, and
which M. Peters thinks is proved to be true by his recent researches
(_Astr. Nach._ xxxi. p. 219, and xxxii. p. 1). The hypothesis is,
that Sirius has a companion star, dark, and therefore invisible to
us; and that the two, revolving round their common centre as the
system moves on, the motion of Sirius is seen to be sometimes
quicker and sometimes slower.


_The Earth's Density._

"Cavendish's experiment," as it is commonly called--the measure of
the attractions of manageable masses by the torsion balance, in
order to determine the density of the Earth--has been repeated
recently by Professor Reich at Freiberg, and by Mr. Baily in
England, with great attention to the means of attaining accuracy.
Professor Reich's result for the density of the Earth is 5·44; Mr.
Baily's is 5·92. Cavendish's result was 5·48; according to recent
revisions[56\A] it is 5·52. {562}

[Note 56\A: The calculation has been revised by M. Edward Schmidt.
Humboldt's _Kosmos_, ii. p. 425.]

But the statical effect of the attraction of manageable masses, or
even of mountains, is very small. The effect of a small change in
gravity may be accumulated by being constantly repeated in the
oscillations of a pendulum, and thus may become perceptible. Mr.
Airy attempted to determine the density of the Earth by a method
depending on this view. A pendulum oscillating at the surface was to
be compared with an equal pendulum at a great depth below the
surface. The difference of their rates would disclose the different
force of gravity at the two positions; and hence, the density of the
Earth. In 1826 and 1828, Mr. Airy attempted this experiment at the
copper mine of Dolcoath in Cornwall, but failed from various causes.
But in 1854, he resumed it at the Harton coal mine in Durham, the
depth of which is 1260 feet; having in this new trial, the advantage
of transmitting the time from one station to the other by the
instantaneous effect of galvanism, instead of by portable watches.
The result was a density of 6·56; which is much larger than the
preceding results, but, as Mr. Airy holds, is entitled to compete
with the others on at least equal terms.


_Tides._

I should be wanting in the expression of gratitude to those who have
practically assisted me in Researches on the Tides, if I did not
mention the grand series of Tide Observations made on the coast of
Europe and America in June, 1835, through the authority of the Board
of Admiralty, and the interposition of the late Duke of Wellington, at
that time Foreign Secretary. Tide observations were made for a
fortnight at all the Coast-guard stations of Great Britain and Ireland
in June, 1834; and these were repeated in June, 1835, with
corresponding observations on all the coasts of Europe, from the North
Cape of Norway to the Straits of Gibraltar; and from the mouth of the
St. Lawrence to the mouth of the Mississippi. The results of these
observations, which were very complete so far as the coast tides were
concerned, were given in the _Philosophical Transactions_ for 1836.

Additional accuracy respecting the Tides of the North American coast
may be expected from the survey now going on under the direction of
Superintendent A. Bache. The Tides of the English Channel have been
further investigated, and the phenomena presented under a new point of
view by Admiral Beechey. {563}

The Tides of the Coast of Ireland have been examined with great care
by Mr. Airy. Numerous and careful observations were made with a view,
in the first instance, of determining what was to be regarded as "the
Level of the Sea;" but the results were discussed so as to bring into
view the laws and progress, on the Irish coast, of the various
inequalities of the Tides mentioned in Chap. iv. Sect. 9 of this Book.

I may notice as one of the curious results of the Tide Observations
of 1836, that it appeared to me, from a comparison of the
Observations, that there must be a point in the German Ocean, about
midway between Lowestoft on the English coast, and the Brill on the
Dutch coast, where the tide would vanish: and this was ascertained
to be the case by observation; the observations being made by
Captain Hewett, then employed in a survey of that sea.

_Cotidal Lines_ supply, as I conceive, a good and simple method of
representing the progress and connection of _littoral_ tides. But to
draw cotidal lines across oceans, is a very precarious mode of
representing the facts, except we had much more knowledge on the
subject than we at present possess. In the _Phil. Trans._ for 1848,
I have resumed the subject of the Tides of the Pacific; and I have
there expressed my opinion, that while the littoral tides are
produced by progressive waves, the oceanic tides are more of the
nature of stationary undulations.

But many points of this kind might be decided, and our knowledge on
this subject might be brought to a condition of completeness, if a
ship or ships were sent expressly to follow the phenomena of the
Tides from point to point, as the observations themselves might
suggest a course. Till this is done, our knowledge cannot be
completed. Detached and casual observations, made _aliud agendo_,
can never carry us much beyond the point where we at present are.


_Double Stars._

Sir John Herschel's work, referred to in the History (2d Ed.) as
then about to appear, was published in 1847.[57\A] In this work,
besides a vast amount of valuable observations and reasonings on
other subjects {564} (as Nebulæ, the Magnitude of Stars, and the
like), the orbits of several double stars are computed by the aid of
the new observations. But Sir John Herschel's conviction on the
point in question, the operation of the Newtonian law of gravitation
in the region of the stars, is expressed perhaps more clearly in
another work which he published in 1849.[58\A] He there speaks of
Double Stars, and especially of _gamma Virginis_, the one which has
been most assiduously watched, and has offered phenomena of the
greatest interest.[59\A] He then finds that the two components of
this star revolve round each other in a period of 182 years; and
says that the elements of the calculated orbit represent the whole
series of recorded observations, comprising an angular movement of
nearly nine-tenths of a complete circuit, both in angle and
distance, with a degree of exactness fully equal to that of
observation itself. "No doubt can therefore," he adds, "remain as to
the **prevalence in this remote system of the Newtonian Law of
Gravitation."

[Note 57\A: _Results of Astronomical Observations made during the
years_ 1834, 5, 6, 7, 8, _at the Cape of Good Hope, being the
completion of a Telescopic Survey of the whole Surface of the
visible Heavens commenced in_ 1825.]

[Note 58\A: _Outlines of Astronomy_.]

[Note 59\A: _Out._ 844.]

Yet M. Yvon de Villarceau has endeavored to show[60\A] that this
conclusion, however probable, is not yet proved. He holds, even for
the Double Stars, which have been most observed, the observations are
only equivalent to seven or eight really distinct data, and that seven
data are not sufficient to determine that an ellipse is described
according to the Newtonian law. Without going into the details of this
reasoning, I may remark, that the more rapid relative angular motion
of the components of a Double Star when they are more near each other,
proves, as is allowed on all hands, that they revolve under the
influence of a mutual attractive force, obeying the Keplerian Law of
Areas. But that, whether this force follows the law of the inverse
square or some other law, can hardly have been rigorously proved as
yet, we may easily conceive, when we recollect the manner in which
that law was proved for the Solar System. It was by means of an error
of _eight minutes_, observed by Tycho, that Kepler was enabled, as he
justly boasted, to reform the scheme of the Solar System,--to show,
that is, that the planetary orbits are ellipses with the sun in the
focus. Now, the observations of Double Stars cannot pretend to such
accuracy as this; and therefore the Keplerian theorem cannot, as yet,
have been fully demonstrated from those observations. But when we know
{565} that Double Stars are held together by a central force, to prove
that this force follows a different law from the only law which has
hitherto been found to obtain in the universe, and which obtains
between all the known masses of the universe, would require very clear
and distinct evidence, of which astronomers have as yet seen no trace.

[Note 60\A: _Connaissance des Temps_, for 1852; published in 1849.]




CHAPTER  VI.


_Sect._ 1. _Instruments._--2. _Clocks._

IN page 473, I have described the manner in which astronomers are able
to observe the transit of a star, and other astronomical phenomena, to
the exactness of a tenth of a second of time. The mode of observation
there described implies that the observer at the moment of observation
compares the impressions of the eye and of the ear. Now it is found
that the habit which the observer must form of doing this operates
differently in different observers, so that one observer notes the
same fact as happening a fraction of a second earlier or later than
another observer does; and this in every case. Thus, using the term
_equation_, as we use it in Astronomy, to express a correction by
which we get regularity from irregularity, there is a _personal
equation_ belonging to this mode of observation, showing that it is
liable to error. Can this error be got rid of?

It is at any rate much diminished by a method of observation recently
introduced into observatories, and first practised in America. The
essential feature of this mode of observation consists in combining
the impression of sight with that of touch, instead of with that of
hearing. The observer at the moment of observation presses with his
finger so as to make a mark on a machine which by its motion measures
time with great accuracy and on a large scale; and thus small
intervals of time are made visible.

A universal, though not a necessary, part of this machinery, as
hitherto adopted, is, that a galvanic circuit has been employed in
conveying the impression from the finger to the part where time is
measured and marked. The facility with which galvanic wires can {566}
thus lead the impression by any path to any distance, and increase its
force in any degree, has led to this combination, and almost
identification, of observation by touch with its record by galvanism.

The method having been first used by Mr. Bond at Cambridge, in North
America, has been adopted elsewhere, and especially at Greenwich,
where it is used for all the instruments; and consequently a
collection of galvanic batteries is thus as necessary a part of the
apparatus of the establishment as its graduated circles and arcs.




END OF VOL. I.




HISTORY
OF THE
INDUCTIVE SCIENCES.

VOLUME II.


HISTORY
OF THE
INDUCTIVE SCIENCES,
FROM
THE EARLIEST TO THE PRESENT TIME.
BY WILLIAM WHEWELL, D. D.,
MASTER OF TRINITY COLLEGE, CAMBRIDGE.
_THE THIRD EDITION, WITH ADDITIONS._
IN TWO VOLUMES.


VOLUME II.


NEW YORK:
D. APPLETON AND COMPANY,
549 & 551 BROADWAY.
1875.




CONTENTS

OF THE SECOND VOLUME.

_THE SECONDARY MECHANICAL SCIENCES._

BOOK VIII.

HISTORY OF ACOUSTICS.

                                                                 PAGE
Introduction.                                                      23

CHAPTER I.--PRELUDE TO THE SOLUTION OF PROBLEMS IN ACOUSTICS.      24

CHAPTER II.--PROBLEM OF THE VIBRATIONS OF STRINGS.                 28

CHAPTER III.--PROBLEM OF THE PROPAGATION OF SOUND.                 32

CHAPTER IV.--PROBLEM OF DIFFERENT SOUNDS OF THE SAME STRING.       36

CHAPTER V.--PROBLEM OF THE SOUNDS OF PIPES.                        38

CHAPTER VI.--PROBLEM OF DIFFERENT MODES OF VIBRATION OF BODIES IN
GENERAL.                                                           41

BOOK IX.

HISTORY OF OPTICS, FORMAL AND PHYSICAL.

Introduction.                                                      51
{8}

_FORMAL OPTICS._

CHAPTER I.--PRIMARY INDUCTION OF OPTICS.--RAYS OF LIGHT AND LAWS
OF REFLECTION.                                                     53

CHAPTER II.--DISCOVERY OF THE LAW OF REFRACTION.                   54

CHAPTER III.--DISCOVERY OF THE LAW OF DISPERSION BY REFRACTION.    58

CHAPTER IV.--DISCOVERY OF ACHROMATISM.                             66

CHAPTER V.--DISCOVERY OF THE LAWS OF DOUBLE REFRACTION.            69

CHAPTER VI.--DISCOVERY OF THE LAWS OF POLARIZATION.                72

CHAPTER VII.--DISCOVERY OF THE LAWS OF THE COLORS OF THIN PLATES.  76

CHAPTER VIII.--ATTEMPTS TO DISCOVER THE LAWS OF OTHER PHENOMENA.   78

CHAPTER IX.--DISCOVERY OF THE LAWS OF PHENOMENA OF DIPOLARIZED
LIGHT.                                                             80

_PHYSICAL OPTICS._

CHAPTER X.--PRELUDE TO THE EPOCH OF YOUNG AND FRESNEL.             85

CHAPTER XI.--EPOCH OF YOUNG AND FRESNEL.

_Sect._ 1. Introduction.                                           92
_Sect._ 2. Explanation of the Periodical Colors of Thin Plates and
Shadows by the Undulatory Theory.                                  93
_Sect._ 3. Explanation of Double Refraction by the Undulatory
Theory.                                                            98
_Sect._ 4. Explanation of Polarization by the Undulatory Theory.  100
_Sect._ 5. Explanation of Dipolarization by the Undulatory
Theory.                                                           105
{9}

CHAPTER XII.--SEQUEL TO THE EPOCH OF YOUNG AND
FRESNEL.--RECEPTION OF THE UNDULATORY THEORY.                     111

CHAPTER XIII.--CONFIRMATION AND EXTENSION OF THE UNDULATORY
THEORY.                                                           118

1. Double Refraction of Compressed Glass.                         119
2. Circular Polarization.                                         119
3. Elliptical Polarization in Quartz.                             122
4. Differential Equations of Elliptical Polarization.             122
5. Elliptical Polarization of Metals.                             123
6. Newton's Rings by Polarized Light.                             124
7. Conical Refraction.                                            124
8. Fringes of Shadows.                                            126
9. Objections to the Theory.                                      126
10. Dispersion, on the Undulatory Theory.                         128
11. Conclusion.                                                   128

BOOK X.

HISTORY OF THERMOTICS AND ATMOLOGY.

Introduction.                                                     137

_THERMOTICS PROPER._

CHAPTER I.--THE DOCTRINES OF CONDUCTION AND RADIATION.

_Sect._ 1. Introduction of the Doctrine of Conduction.            139
_Sect._ 2.      "          "        "       Radiation.            142
_Sect._ 3. Verification of the Doctrines of Conduction and
Radiation.                                                        143
_Sect._ 4. The Geological and Cosmological Application of
Thermotics.                                                       144
                1. Effect of Solar Heat on the Earth.             145
                2. Climate.                                       146
                3. Temperature of the Interior of the Earth.      147
                4. Heat of the Planetary Spaces.                  148
_Sect._ 5. Correction of Newton's Law of Cooling.                 149
_Sect._ 6. Other Laws of Phenomena with respect to Radiation.     151
_Sect._ 7. Fourier's Theory of Radiant Heat.                      152
_Sect._ 8. Discovery of the Polarization of Heat.                 153
{10}

CHAPTER II.--THE LAWS OF CHANGES OCCASIONED BY HEAT.

_Sect._ 1. Expansion by Heat.--The Law of Dalton and Gay-Lussac
for Gases.                                                        157
_Sect._ 2. Specific Heat.--Change of Consistence.                 159
_Sect._ 3. The Doctrine of Latent Heat.                           160

_ATMOLOGY._

CHAPTER III.--THE RELATION OF VAPOR AND AIR.

_Sect._ 1. The Boylean Law of the Air's Elasticity.               163
_Sect._ 2. Prelude to Dalton's Doctrine of Evaporation.           165
_Sect._ 3. Dalton's Doctrine of Evaporation.                      170
_Sect._ 4. Determination of the Laws of the Elastic Force of
Steam.                                                            172
_Sect._ 5. Consequences of the Doctrine of
Evaporation.--Explanation of Rain, Dew, and Clouds.               176

CHAPTER IV.--PHYSICAL THEORIES OF HEAT.

Thermotical Theories.                                             181
Atmological Theories.                                             184
Conclusion.                                                       187

_THE MECHANICO-CHEMICAL SCIENCES._

BOOK XI.

HISTORY OF ELECTRICITY.

Introduction.                                                     191

CHAPTER I.--DISCOVERY OF LAWS OF ELECTRIC PHENOMENA.              193

CHAPTER II.--THE PROGRESS OF ELECTRICAL THEORY.                   201

Question of One or Two Fluids.                                    210
Question of the Material Reality of the Electric Fluid.           212
{11}

BOOK XII.

HISTORY OF MAGNETISM.

CHAPTER I.--DISCOVERY OF LAWS OF MAGNETIC PHENOMENA.              217

CHAPTER II.--PROGRESS OF MAGNETIC THEORY.

Theory of Magnetic Action.                                        220
Theory of Terrestrial Magnetism.                                  224
Conclusion.                                                       232

BOOK XIII.

HISTORY OF GALVANISM, OR VOLTAIC ELECTRICITY.

CHAPTER I.--DISCOVERY OF VOLTAIC ELECTRICITY.                     237

CHAPTER II.--RECEPTION AND CONFIRMATION OF THE DISCOVERY OF
VOLTAIC ELECTRICITY.                                              240

CHAPTER III.--DISCOVERY OF THE LAWS OF THE MUTUAL ATTRACTION AND
REPULSION OF VOLTAIC CURRENTS.--AMPÈRE.                           242

CHAPTER IV.--DISCOVERY OF ELECTRO-MAGNETIC ACTION.--OERSTED.      243

CHAPTER V.--DISCOVERY OF THE LAWS OF ELECTRO-MAGNETIC ACTION.     245

CHAPTER VI.--THEORY OF ELECTRODYNAMICAL ACTION.

Ampère's Theory.                                                  246
Reception of Ampère's Theory.                                     249

CHAPTER VII.--CONSEQUENCES OF THE ELECTRODYNAMIC THEORY.          250

Discovery of Diamagnetism.                                        252
{12}

CHAPTER VIII.--DISCOVERY OF THE LAWS OF MAGNETO-ELECTRIC
INDUCTION.--FARADAY.                                              253

CHAPTER IX.--TRANSITION TO CHEMICAL SCIENCE.                      256

_THE ANALYTICAL SCIENCE._

BOOK XIV.

HISTORY OF CHEMISTRY.

CHAPTER I.--IMPROVEMENT OF THE NOTION OF CHEMICAL ANALYSIS, AND
RECOGNITION OF IT AS THE SPAGIRIC ART.                            261

CHAPTER II.--DOCTRINE OF ACID AND ALKALI.--SYLVIUS.               262

CHAPTER III.--DOCTRINE OF ELECTIVE ATTRACTIONS.--GEOFFROY.
BERGMAN.                                                          265

CHAPTER IV.--DOCTRINE OF ACIDIFICATION AND COMBUSTION.--PHLOGISTIC
THEORY.

Publication of the Theory by Beccher and Stahl.                   267
Reception and Application of the Theory.                          271

CHAPTER V.--CHEMISTRY OF GASES.--BLACK. CAVENDISH.                272

CHAPTER VI.--EPOCH OF THE THEORY OF OXYGEN.--LAVOISIER.

_Sect._ 1. Prelude to the Theory.--Its Publication.               275
_Sect._ 2. Reception and Confirmation of the Theory of Oxygen.    278
_Sect._ 3. Nomenclature of the Oxygen Theory.                     281

CHAPTER VII.--APPLICATION AND CORRECTION OF THE OXYGEN THEORY.    282
{13}

CHAPTER VIII.--THEORY OF DEFINITE, RECIPROCAL, AND MULTIPLE
PROPORTIONS.

_Sect._ 1. Prelude to the Atomic Theory, and its Publication by
Dalton.                                                           285
_Sect._ 2. Reception and Confirmation of the Atomic Theory.       288
_Sect._ 3. The Theory of Volumes.--Gay-Lussac.                    290

CHAPTER IX.--EPOCH OF DAVY AND FARADAY.

_Sect._ 1. Promulgation of the Electro-chemical Theory by Davy.   291
_Sect._ 2. Establishment of the Electro-chemical Theory by
Faraday.                                                          296
_Sect._ 3. Consequences of Faraday's Discoveries.                 302
_Sect._ 4. Reception of the Electro-chemical Theory.              303

CHAPTER X.--TRANSITION FROM THE CHEMICAL TO THE CLASSIFICATORY
SCIENCES.                                                         305

_THE ANALYTICO-CLASSIFICATORY SCIENCE._

BOOK XV.

HISTORY OF MINERALOGY.

INTRODUCTION

_Sect._  1. Of the Classificatory Sciences.                       313
_Sect._  2. Of Mineralogy as the Analytico-classificatory
Science.                                                          314

_CRYSTALLOGRAPHY._

CHAPTER I.--PRELUDE TO THE EPOCH OF DE LISLE AND HAÜY.            316

CHAPTER II.--EPOCH OF ROMÉ DE LISLE AND HAÜY.--ESTABLISHMENT OF
THE FIXITY OF CRYSTALLINE ANGLES, AND THE SIMPLICITY OF THE LAWS
OF DERIVATION.                                                    320

CHAPTER III.--RECEPTION AND CORRECTIONS OF THE HAUÏAN
CRYSTALLOGRAPHY.                                                  324
{14}

CHAPTER IV.--ESTABLISHMENT OF THE DISTINCTION OF SYSTEMS OF
CRYSTALLIZATION.--WEISS AND MOHS.                                 326

CHAPTER V.--RECEPTION AND CONFIRMATION OF THE DISTINCTION OF
SYSTEMS OF CRYSTALLIZATION.

Diffusion of the Distinction of Systems.                          330
Confirmation of the Distinction of Systems by the Optical
Properties of Minerals.--Brewster.                                331

CHAPTER VI.--CORRECTION OF THE LAW OF THE SAME ANGLE FOR THE SAME
SUBSTANCE.

Discovery of Isomorphism.--Mitscherlich.                          334
Dimorphism.                                                       336

CHAPTER VII.--ATTEMPTS TO ESTABLISH THE FIXITY OF OTHER PHYSICAL
PROPERTIES.--WERNER.                                              336

_SYSTEMATIC MINERALOGY._

CHAPTER VIII.--ATTEMPTS AT THE CLASSIFICATION OF MINERALS.

_Sect._ 1. Proper Object of Classification.                       339
_Sect._ 2. Mixed Systems of Classification.                       340

CHAPTER IX.--ATTEMPTS AT THE REFORM OF MINERALOGICAL
SYSTEMS.--SEPARATION OF THE CHEMICAL AND NATURAL HISTORY METHODS.

_Sect._  1. Natural History System of Mohs.                       344
_Sect._  2. Chemical System of Berzelius and others.              347
_Sect._  3. Failure of the Attempts at Systematic Reform.         349
_Sect._  4. Return to Mixed Systems with Improvements.            351

_CLASSIFICATORY SCIENCES._

BOOK XVI.

HISTORY OF SYSTEMATIC BOTANY AND ZOOLOGY.

Introduction.                                                     357
{15}

CHAPTER I.--IMAGINARY KNOWLEDGE OF PLANTS.                        358

CHAPTER II.--UNSYSTEMATIC KNOWLEDGE OF PLANTS.                    361

CHAPTER III.--FORMATION OF A SYSTEM OF ARRANGEMENT OF PLANTS.

_Sect._ 1. Prelude to the Epoch of Cæsalpinus.                    369
_Sect._ 2. Epoch of Cæsalpinus.--Formation of a System of
Arrangement.                                                      373
_Sect._ 3. Stationary Interval.                                   378
_Sect._ 4. Sequel to the Epoch of Cæsalpinus.--Further Formation
and Adoption of Systematic Arrangement.                           382

CHAPTER IV.--THE REFORM OF LINNÆUS.

_Sect._ 1. Introduction of the Reform.                            387
_Sect._ 2. Linnæan Reform of Botanical Terminology.               389
_Sect._ 3.    "       "         "      Nomenclature.              391
_Sect._ 4. Linnæus's Artificial System,                           395
_Sect._ 5. Linnæus's Views on a Natural Method.                   396
_Sect._ 6. Reception and Diffusion of the Linnæan Reform.         400

CHAPTER V.--PROGRESS TOWARDS A NATURAL SYSTEM OF BOTANY.          404

CHAPTER VI.--THE PROGRESS OF SYSTEMATIC ZOOLOGY.                  412

CHAPTER VII.--THE PROGRESS OF ICHTHYOLOGY.                        419

Period of Unsystematic Knowledge.                                 420
Period of Erudition.                                              421
Period of Accumulation of Materials.--Exotic Collections.         422
Epoch of the Fixation of Characters.--Ray and Willoughby.         422
Improvement of the System.--Artedi.                               423
Separation of the Artificial and Natural Methods in Ichthyology.  426

_ORGANICAL SCIENCES._

BOOK XVII.

HISTORY OF PHYSIOLOGY AND COMPARATIVE ANATOMY.

Introduction.                                                     435
{16}

CHAPTER I.--DISCOVERY OF THE ORGANS OF VOLUNTARY MOTION.

_Sect._ 1. Knowledge of Galen and his Predecessors.               438
_Sect._ 2. Recognition of Final Causes in Physiology.--Galen.     442

CHAPTER II.--DISCOVERY OF THE CIRCULATION OF THE BLOOD.

_Sect._ 1. Prelude to the Discovery.                              444
_Sect._ 2. The Discovery of the Circulation made by Harvey.       447
_Sect._ 3. Reception of the Discovery.                            448
_Sect._ 4. Bearing of the Discovery on the Progress of
Physiology.                                                       449

CHAPTER III.--DISCOVERY OF THE MOTION OF THE CHYLE, AND CONSEQUENT
SPECULATIONS.

_Sect._ 1. The Discovery of the Motion of the Chyle.              452
_Sect._ 2. The Consequent Speculations. Hypotheses of Digestion.  453

CHAPTER IV.--EXAMINATION OF THE PROCESS OF REPRODUCTION IN
ANIMALS AND PLANTS, AND CONSEQUENT SPECULATIONS.

_Sect._ 1. The Examination of the Process of Reproduction in
Animals.                                                          455
_Sect._ 2.          "        "       "             "      in
Vegetables.                                                       457
_Sect._ 3. The Consequent Speculations.--Hypotheses of
Generation.                                                       459

CHAPTER V.--EXAMINATION OF THE NERVOUS SYSTEM, AND CONSEQUENT
SPECULATIONS.

_Sect._ 1. The Examination of the Nervous System.                 461
_Sect._ 2. The Consequent Speculations. Hypotheses respecting
Life, Sensation, and Volition.                                    464

CHAPTER VI.--INTRODUCTION OF THE PRINCIPLE OF DEVELOPED AND
METAMORPHOSED SYMMETRY.

_Sect._ 1. Vegetable Morphology.--Göthe. De Candolle.             468
_Sect._ 2. Application of Vegetable Morphology.                   474

CHAPTER VII.--PROGRESS OF ANIMAL MORPHOLOGY.

_Sect._ 1. Rise of Comparative Anatomy.                           475
_Sect._ 2. Distinction of the General Types of the Forms of
Animals.--Cuvier.                                                 478
_Sect._ 3. Attempts to establish the Identity of the Types of
Animal Forms.                                                     480
{17}

CHAPTER VIII.--THE DOCTRINE OF FINAL CAUSES IN PHYSIOLOGY.

_Sect._ 1. Assertion of the Principle of Unity of Plan.           482
_Sect._ 2. Estimate of the Doctrine of Unity of Plan.             487
_Sect._ 3. Establishment and Application of the Principle of the
Conditions of Existence of Animals.--Cuvier.                      492

_THE PALÆTIOLOGICAL SCIENCES._

BOOK XVIII.

HISTORY OF GEOLOGY.

Introduction.                                                     499

_DESCRIPTIVE GEOLOGY._

CHAPTER I.--PRELUDE TO SYSTEMATIC DESCRIPTIVE GEOLOGY.

_Sect._ 1. Ancient Notices of Geological Facts.                   505
_Sect._ 2. Early Descriptions and Collections of Fossils.         506
_Sect._ 3. First Construction of Geological Maps.                 509

CHAPTER II.--FORMATION OF SYSTEMATIC DESCRIPTIVE GEOLOGY.

_Sect._ 1. Discovery of the Order and Stratification of the
Materials of the Earth.                                           511
_Sect._ 2. Systematic Form given to Descriptive
Geology.--Werner.                                                 513
_Sect._ 3. Application of Organic Remains as a Geological
Character.--Smith.                                                515
_Sect._ 4. Advances in Palæontology.--Cuvier.                     517
_Sect._ 5. Intellectual Characters of the Founders of Systematic
Descriptive Geology.                                              520

CHAPTER III.--SEQUEL TO THE FORMATION OF SYSTEMATIC DESCRIPTIVE
GEOLOGY.

_Sect._ 1. Reception and Diffusion of Systematic Geology.         523
_Sect._ 2. Application of Systematic Geology.--Geological Surveys
and Maps.                                                         526
_Sect._ 3. Geological Nomenclature.                               527
_Sect._ 4. Geological Synonymy, or Determination of Geological
Equivalents.                                                      531
{18}

CHAPTER IV.--ATTEMPTS TO DISCOVER GENERAL LAWS IN GEOLOGY.

_Sect._ 1. General Geological Phenomena.                          537
_Sect._ 2. Transition to Geological Dynamics.                     541

_GEOLOGICAL DYNAMICS._

CHAPTER V.--INORGANIC GEOLOGICAL DYNAMICS.

_Sect._ 1. Necessity and Object of a Science of Geological
Dynamics.                                                         542
_Sect._ 2. Aqueous Causes of Change.                              545
_Sect._ 3. Igneous Causes of Change.--Motions of the Earth's
Surface.                                                          549
_Sect._ 4. The Doctrine of Central Heat.                          554
_Sect._ 5. Problems respecting Elevations and Crystalline
Forces.                                                           556
_Sect._ 6. Theories of Changes of Climate.                        559

CHAPTER VI.--PROGRESS OF THE GEOLOGICAL DYNAMICS OF ORGANIZED
BEINGS.

_Sect._ 1. Objects of this Science.                               561
_Sect._ 2. Geography of Plants and Animals.                       562
_Sect._ 3. Questions of the Transmutation of Species.             563
_Sect._ 4. Hypothesis of Progressive Tendencies.                  565
_Sect._ 5. Question of Creation as related to Science.            568
_Sect._ 6. The Hypothesis of the Regular Creation and Extinction
of Species.                                                       573
                 1. Creation of Species.                          573
                 2. Extinction of Species.                        576
_Sect._ 7. The Imbedding of Organic Remains.                      577

_PHYSICAL GEOLOGY._

CHAPTER VII.--PROGRESS OF PHYSICAL GEOLOGY.

_Sect._ 1. Object and Distinctions of Physical Geology.           579
_Sect._ 2. Of Fanciful Geological Opinions.                       580
_Sect._ 3. Of Premature Geological Theories.                      584

CHAPTER VIII.--THE TWO ANTAGONIST DOCTRINES OF GEOLOGY.

_Sect._ 1. Of the Doctrine of Geological Catastrophes.            586
_Sect._ 2.   "       "            "      Uniformity.              588
{19}

_ADDITIONS TO THE THIRD EDITION._

BOOK VIII.--ACOUSTICS.

SOUND.

The Velocity of Sound in Water.                                   599

BOOK IX.--OPTICS.

Photography.                                                      601
Fluorescence.                                                     601

UNDULATORY THEORY.

Direction of the Transverse Vibrations in Polarization.           603
Final Disproof of the Emission Theory.                            604

BOOK X.--THERMOTICS.--ATMOLOGY.

THE RELATION OF VAPOR AND AIR.

Force of Steam.                                                   606
Temperature of the Atmosphere.                                    607

THEORIES OF HEAT.

The Dynamical Theory of Heat.                                     608

BOOK XI.--ELECTRICITY.

General Remarks.                                                  610
Dr. Faraday's Views of Statical Electrical Induction.             611

BOOK XII.--MAGNETISM.

Recent Progress of Terrestrial Magnetism.                         613
Correction of Ships' Compasses.                                   616
{20}

BOOK XIII.--VOLTAIC ELECTRICITY.

MAGNETO-ELECTRIC INDUCTION.

Diamagnetlc Polarity.                                             620
Magneto-optic Effects and Magnecrystallic Polarity.               621
Magneto-electric Machines.                                        623
Applications of Electrodynamic Discoveries.                       623

BOOK XIV.--CHEMISTRY.

THE ELECTRO-CHEMICAL THEORY.

The Number of Elementary Substances.                              625

BOOK XV.--MINERALOGY.

Crystallography.                                                  627
Optical Properties of Minerals.                                   629
Classification of Minerals.                                       630

BOOK XVI.--CLASSIFICATORY SCIENCES.

Recent Views of Botany.                                           631
   "      "     Zoology.                                          634

BOOK XVII.--PHYSIOLOGICAL AND COMPARATIVE ANATOMY.

VEGETABLE MORPHOLOGY.                                             636
ANIMAL MORPHOLOGY.                                                638
Final Causes.                                                     642

BOOK XVIII.

GEOLOGY.                                                          646



{{21}}
BOOK VIII.


_THE SECONDARY MECHANICAL SCIENCES._


HISTORY OF ACOUSTICS.


  .  .  .  .  .  .  Go, demand
  Of mighty Nature, if 'twas ever meant
  That we should pry far off and be unraised,
  That we should pore, and dwindle as we pore,
  Viewing all objects unremittingly
  In disconnexion dead and spiritless;
  And still dividing, and dividing still,
  Break down all grandeur, still unsatisfied
  With the perverse attempt, while littleness
  May yet become more little; waging thus
  An impious warfare 'gainst the very life
  Of our own souls.      WORDSWORTH, _Excursion_.

  .  .  .  .  .  .  Ἐσσυμένη δὲ
  Ἠερίην ἀψῖδα διεῤῥοίζησε πεδίλῳ
  Εἰς δόμον ἉΡΜΟΝIΗΣ παμμητόρος, ὁππόθι νύμφη
  Ἴκελον οἶκον ἐναίε τύπῳ τετράζυγι κόσμου
  Αὐτοπαγῆ              NONNUS. _Dionysiac_. xli. 275.

  Along the skiey arch the goddess trode,
  And sought Harmonia's august abode;
  The universal plan, the mystic Four,
  Defines the figure of the palace-floor.
  Solid and square the ancient fabric stands,
  Raised by the labors of unnumbered hands.



{{23}}
BOOK VIII.



INTRODUCTION.


_The Secondary Mechanical Sciences._

IN the sciences of Mechanics and Physical Astronomy, Motion and
Force are the direct and primary objects of our attention. But there
is another class of sciences in which we endeavor to reduce
phenomena, not evidently mechanical, to a known dependence upon
mechanical properties and laws. In the cases to which I refer, the
facts do not present themselves to the senses as modifications of
position and motion, but as _secondary qualities_, which are found
to be in some way derived from those primary attributes. Also, in
these cases the phenomena are reduced to their mechanical laws and
causes in a secondary manner; namely, by treating them as the
operation of a _medium_ interposed between the object and the organ
of sense. These, then, we may call _Secondary Mechanical Sciences_.
The sciences of this kind which require our notice are those which
treat of the sensible qualities, Sound, Light, and Heat; that is.
Acoustics, Optics, and Thermotics.

It will be recollected that our object is not by any means to give a
full statement of all the additions which have been successively
made to our knowledge on the subjects under review, or a complete
list of the persons by whom such additions have been made; but to
present a view of the progress of each of those branches of
knowledge _as a theoretical science_;--to point out the Epochs of
the discovery of those general principles which reduce many facts to
one theory; and to note all that is most characteristic and
instructive in the circumstances and persons which bear upon such
Epochs. A history of any science, written with such objects, will
not need to be long; but it will fail in its purpose altogether, if
it do not distinctly exhibit some well-marked and prominent
features. {24}

We begin our account of the Secondary Mechanical Sciences with
Acoustics, because the progress towards right theoretical views,
was, in fact, made much earlier in the science of Sound, than in
those of Light and of Heat; and also, because a clear comprehension
of the theory to which we are led in this case, is the best
preparation for the difficulties (by no means inconsiderable) of the
reasonings of theorists on the other subjects.




CHAPTER I.

PRELUDE TO THE SOLUTION OF PROBLEMS IN ACOUSTICS.


IN some measure the true theory of sound was guessed by very early
speculators on the subject; though undoubtedly conceived in a very
vague and wavering manner. That sound is caused by some motion of
the sounding body, and conveyed by some motion of the air to the
ear, is an opinion which we trace to the earliest times of physical
philosophy. We may take Aristotle as the best expounder of this
stage of opinion. In his Treatise _On Sound and Hearing_, he says,
"Sound takes place when bodies strike the air, not by the air having
a _form_ impressed upon it (σχηματίζομενον), as some think, but by
its being moved in a corresponding manner; (probably he means in a
manner corresponding to the impulse;) the air being contracted, and
expanded, and overtaken, and again struck by the impulses of the
breath and of the strings. For when the breath falls upon and
strikes the air which is next it, the air is carried forwards with
an impetus, and that which is contiguous to the first is carried
onwards; so that the same voice spreads every way as far as the
motion of the air takes place."

As is the case with all such specimens of ancient physics, different
persons would find in such a statement very different measures of
truth and distinctness. The admirers of antiquity might easily, by
pressing the language closely, and using the light of modern
discovery, detect in this passage an exact account of the production
and propagation of sound: while others might maintain that in
Aristotle's own mind, there were only vague notions, and verbal
generalizations. This {25} latter opinion is very emphatically
expressed by Bacon.[1\8] "The collision or thrusting of air, which
they will have to be the cause of sound, neither denotes the _form_
nor the latent process of sound; but is a term of ignorance and of
superficial contemplation." Nor can it be justly denied, that an
exact and distinct apprehension of the kind of motion of the air by
which sound is diffused, was beyond the reach of the ancient
philosophers, and made its way into the world long afterwards. It
was by no means easy to reconcile the nature of such motion with
obvious phenomena. For the process is not evident as motion; since,
as Bacon also observes,[2\8] it does not visibly agitate the flame
of a candle, or a feather, or any light floating substance, by which
the slightest motions of the air are betrayed. Still, the persuasion
that sound is some motion of the air, continued to keep hold of
men's minds, and acquired additional distinctness. The illustration
employed by Vitruvius, in the following passage, is even now one of
the best we can offer.[3\8] "Voice is breath, flowing, and made
sensible to the hearing by striking the air. It moves in infinite
circumferences of circles, as when, by throwing a stone into still
water, you produce innumerable circles of waves, increasing from the
centre and spreading outwards, till the boundary of the space, or
some obstacle, prevents their outlines from going further. In the
same manner the voice makes its motion in circles. But in water the
circle moves breadthways upon a level plain; the voice proceeds in
breadth, and also successively ascends in height."

[Note 1\8: _Hist. Son. et Aud._ vol. ix. p. 68.]

[Note 2\8: _Ibid._]

[Note 3\8: _De Arch._ v. 3.]

Both the comparison, and the notice of the difference of the two
cases, prove the architect to have had very clear notions on the
subject; which he further shows by comparing the resonance of the
walls of a building to the disturbance of the outline of the waves
of water when they meet with a boundary, and are thrown back.
"Therefore, as in the outlines of waves in water, so in the voice,
if no obstacle interrupt the foremost, it does not disturb the
second and the following ones, so that all come to the ears of
persons, whether high up or low down, without resonance. But when
they strike against obstacles, the foremost, being thrown back,
disturb the lines of those which follow." Similar analogies were
employed by the ancients in order to explain the occurrence of
Echoes. Aristotle says,[4\8] "An Echo takes place, when the air,
being as one body in consequence of the vessel which bounds it, and
being prevented from being thrust forwards, is reflected {26} back
like a ball." Nothing material was added to such views till modern
times.

[Note 4\8: _De Animâ_, ii. 8.]

Thus the first conjectures of those who philosophized concerning
sound, led them to an opinion concerning its causes and laws, which
only required to be distinctly understood, and traced to mechanical
principles, in order to form a genuine science of Acoustics. It was,
no doubt, a work which required a long time and sagacious reasoners,
to supply what was thus wanting; but still, in consequence of this
peculiar circumstance in the early condition of the prevalent
doctrine concerning sound, the history of Acoustics assumes a
peculiar form. Instead of containing, like the history of Astronomy
or of Optics, a series of generalizations, each including and rising
above preceding generalizations; in this case, the highest
generalization is in view from the first; and the object of the
philosopher is to determine its precise meaning and circumstances in
each example. Instead of having a series of inductive Truths,
successively dawning on men's minds, we have a series of
Explanations, in which certain experimental facts and laws are
reconciled, as to their mechanical principles and their measures,
with the general doctrine already in our possession. Instead of
having to travel gradually towards a great discovery, like Universal
Gravitation, or Luminiferous Undulations, we take our stand upon
acknowledged truths, the production and propagation of sound by the
motion of bodies and of air; and we connect these with other truths,
the laws of motion and the known properties of bodies, as, for
instance, their elasticity. Instead of _Epochs of Discovery_, we
have _Solutions of Problems_; and to these we must now proceed.

We must, however, in the first place, notice that these Problems
include other subjects than the mere production and propagation of
sound generally. For such questions as these obviously occur:--what
are the laws and cause of the differences of sounds;--of acute and
grave, loud and low, continued and instantaneous;--and, again, of
the differences of articulate sounds, and of the quality of
different voices and different instruments? The first of these
questions, in particular, the real nature of the difference of acute
and grave sounds, could not help attracting attention; since the
difference of notes in this respect was the foundation of one of the
most remarkable mathematical sciences of antiquity. Accordingly, we
find attempts to explain this difference in the ancient writers on
music. In Ptolemy's _Harmonics_, the third Chapter of the first Book
is entitled, "How the {27} acuteness and graveness of notes is
produced;" and in this, after noting generally the difference of
sounds, and the causes of difference (which he states to be the
force of the striking body, the physical constitution of the body
struck, and other causes), he comes to the conclusion, that "the
things which produce acuteness in sounds, are a greater density and
a smaller size; the things which produce graveness, are a greater
rarity and a bulkier form." He afterwards explains this so as to
include a considerable portion of truth. Thus he says, "That in
strings, and in pipes, other things remaining the same, those which
are stopped at the smaller distance from the bridge give the most
acute note; and in pipes, those notes which come through holes
nearest to the mouth-hole are most acute." He even attempts a
further generalization, and says that the greater acuteness arises,
in fact, from the body being more tense; and that thus "hardness may
counteract the effect of greater density, as we see that brass
produces a more acute sound than lead." But this author's notions of
tension, since they were applied so generally as to include both the
tension of a string, and the tension of a piece of solid brass, must
necessarily have been very vague. And he seems to have been
destitute of any knowledge of the precise nature of the motion or
impulse by which sound is produced; and, of course, still more
ignorant of the mechanical principles by which these motions are
explained. The notion of _vibrations_ of the parts of sounding
bodies, does not appear to have been dwelt upon as an essential
circumstance; though in some cases, as in sounding strings, the fact
is very obvious. And the notion of vibrations of the air does not at
all appear in ancient writers, except so far as it may be conceived
to be implied in the comparison of aërial and watery waves, which we
have quoted from Vitruvius. It is however, very unlikely that, even
in the case of water, the motions of the particles were distinctly
conceived, for such conception is far from obvious.

The attempts to apprehend distinctly, and to explain mechanically,
the phenomena of sound, gave rise to a series of Problems, of which
we most now give a brief history. The questions which more peculiarly
constitute the Science of Acoustics, are the questions concerning
those motions or affections of the air by which it is the medium of
hearing. But the motions of sounding bodies have both so much
connexion with those of the medium, and so much resemblance to them,
that we shall include in our survey researches on that subject also.
{28}



CHAPTER II.

PROBLEM OF THE VIBRATIONS OF STRINGS.


THAT the continuation of sound depends on a continued minute and
rapid motion, a shaking or trembling, of the parts of the sounding
body, was soon seen. Thus Bacon says,[5\8] "The duration of the
sound of a bell or a string when struck, which appears to be
prolonged and gradually extinguished, does not proceed from the
first percussion; but the trepidation of the body struck perpetually
generates a new sound. For if that trepidation be prevented, and the
bell or string be stopped, the sound soon dies: as in _spinets_, as
soon as the _spine_ is let fall so as to touch the string, the sound
ceases." In the case of a stretched string, it is not difficult to
perceive that the motion is a motion back and forwards across the
straight line which the string occupies when at rest. The further
examination of the quantitative circumstances of this oscillatory
motion was an obvious problem; and especially after oscillations,
though of another kind (those of a pendulous body), had attracted
attention, as they had done in the school of Galileo. Mersenne, one
of the promulgators of Galileo's philosophy in France, is the first
author in whom I find an examination of the details of this case
(_Harmonicorum Liber_, Paris, 1636). He asserts,[6\8] that the
differences and concords of acute and grave sounds depend on the
rapidity of vibrations, and their ratio; and he proves this doctrine
by a series of experimental comparisons. Thus he finds[7\8] that the
note of a string is as its length, by taking a string first twice,
and then four times as long as the original string, other things
remaining the same. This, indeed, was known to the ancients, and was
the basis of that numerical indication of the notes which the
proposition expresses. Mersenne further proceeds to show the effect
of thickness and tension. He finds (Prop. 7) that a string must be
four times as thick as another, to give the octave below; he finds,
also (Prop. 8), that the tension must be about four times as great
in order to produce the octave above. From these proportions various
others are deduced, and the _law of the_ {29} _phenomena_ of this
kind may be considered as determined. Mersenne also undertook to
_measure_ the phenomena numerically, that is to determine the number
of vibrations of the string in each of such cases; which at first
might appear difficult, since it is obviously impossible to count
with the eye the passages of a sounding string backwards and
forwards. But Mersenne rightly assumed, that the number of
vibrations is the same so long as the tone is the same, and that the
ratios of the numbers of vibrations of different strings may be
determined from the numerical relations of their notes. He had,
therefore, only to determine the number of vibrations of one certain
string, or one known note, to know those of all others. He took a
musical string of three-quarters of a foot long, stretched with a
weight of six pounds and five eighths, which he found gave him by
its vibrations a certain standard note in his organ: he found that a
string of the same material and tension, fifteen feet, that is,
twenty times as long, made ten recurrences in a second; and he
inferred that the number of vibrations of the shorter string must
also be twenty times as great; and thus such a string must make in
one second of time two hundred vibrations.

[Note 5\8:  _Hist. Son. et Aud._ vol. ix. p. 71.]

[Note 6\8: L. i. Prop. 15.]

[Note 7\8: L. ii. Prop. 6.]

This determination of Mersenne does not appear to have attracted due
notice; but some time afterwards attempts were made to ascertain the
connexion between the sound and its elementary pulsations in a more
direct manner. Hooke, in 1681, produced sounds by the striking of
the teeth of brass wheels,[8\8] and Stancari, in 1706, by whirling
round a large wheel in air, showed, before the Academy of Bologna,
how the number of vibrations in a given note might be known.
Sauveur, who, though deaf for the first seven years of his life, was
one of the greatest promoters of the science of sound, and gave it
its name of _Acoustics_, endeavored also, about the same time, to
determine the number of vibrations of a standard note, or, as he
called it, Fixed Sound. He employed two methods, both ingenious and
both indirect. The first was the method of _beats_. Two organ-pipes,
which form a discord, are often heard to produce a kind of _howl_,
or _wavy_ noise, the sound swelling and declining at small intervals
of time. This was readily and rightly ascribed to the coincidences
of the pulsations of sound of the two notes after certain cycles.
Thus, if the number of vibrations of the notes were as fifteen to
sixteen in the same time, every fifteenth vibration of the one would
coincide with every {30} sixteenth vibration of the other, while all
the intermediate vibrations of the two tones would, in various
degrees, disagree with each other; and thus every such cycle, of
fifteen and sixteen vibrations, might be heard as a separate beat of
sound. Now, Sauveur wished to take a case in which these beats were
so slow as to be counted,[9\8] and in which the ratio of the
vibrations of the notes was known from a knowledge of their musical
relations. Thus if the two notes form an interval of a semitone,
their ratio will be that above supposed, fifteen to sixteen; and if
the beats be found to be six in a second, we know that, in that
time, the graver note makes ninety and the acuter ninety-six
vibrations. In this manner Sauveur found that an open organ-pipe,
five feet long, gave one hundred vibrations in a second.

[Note 8\8: _Life_, p. xxiii.]

[Note 9\8: _Ac. Sc. Hist._ 1700, p. 131.]

Sauveur's other method is more recondite, and approaches to a
mechanical view of the question.[10\8] He proceeded on this basis; a
string, horizontally stretched, cannot be drawn into a mathematical
straight line, but always hangs in a very flat curve, or _festoon_.
Hence Sauveur assumed that its transverse vibrations may be
conceived to be identical with the lateral swingings of such a
festoon. Observing that the string C, in the middle of a
harpsichord, hangs in such a festoon to the amount of 1⁄323rd of an
inch, he calculates, by the laws of pendulums, the time of
oscillation, and finds it 1⁄122nd of a second. Thus this C, his
_fixed note_, makes one hundred and twenty-two vibrations in a
second. It is curious that this process, seemingly so arbitrary, is
capable of being justified on mechanical principles; though we can
hardly give the author credit for the views which this justification
implies. It is, therefore, easy to understand that it agreed with
other experiments, in the laws which it gave for the dependence of
the tone on the length and tension.

[Note 10\8: _Ac. Sc. Hist._ 1713.]

The problem of satisfactorily explaining this dependence, on
mechanical principles, naturally pressed upon the attention of
mathematicians when the law of the phenomena was thus completely
determined by Mersenne and Sauveur. It was desirable to show that
both the circumstances and the measure of the phenomena were such as
known mechanical causes and laws would explain. But this problem, as
might be expected, was not attacked till mechanical principles, and
the modes of applying them, had become tolerably familiar.

As the vibrations of a string are produced by its tension, it
appeared to be necessary, in the first place, to determine the law
of the tension {31} which is called into action by the motion of the
string; for it is manifest that, when the string is drawn aside from
the straight line into which it is stretched, there arises an
additional tension, which aids in drawing it back to the straight
line as soon as it is let go. Hooke (_On Spring_, 1678) determined
the law of this additional tension, which he expressed in his noted
formula, "Ut tensio sic vis," the Force is as the Tension; or
rather, to express his meaning more clearly, the Force of tension is
as the Extension, or, in a string, as the increase of length. But,
in reality, this principle, which is important in many acoustical
problems, is, in the one now before us, unimportant; the force which
urges the string towards the straight line, depends, with such small
extensions as we have now to consider, not on the extension, but on
the curvature; and the power of treating the mathematical difficulty
of curvature, and its mechanical consequences, was what was
requisite for the solution of this problem.

The problem, in its proper aspect, was first attacked and mastered
by Brook Taylor, an English mathematician of the school of Newton,
by whom the solution was published in 1715, in his _Methodus
Incrementorum_. Taylor's solution was indeed imperfect, for it only
pointed out a form and a mode of vibration, with which the string
_might_ move consistently with the laws of mechanics; not the mode
in which it _must_ move, supposing its form to be any whatever. It
showed that the curve might be of the nature of that which is called
_the companion to the cycloid_; and, on the supposition of the curve
of the string being of this form, the calculation confirmed the
previously established laws by which the tone, or the time of
vibration, had been discovered to depend on the length, tension, and
bulk of the string. The mathematical incompleteness of Taylor's
reasoning must not prevent us from looking upon his solution of the
problem as the most important step in the progress of this part of
the subject: for the difficulty of applying mechanical principles to
the question being once overcome, the extension and correction of
the application was sure to be undertaken by succeeding
mathematicians; and, accordingly, this soon happened. We may add,
moreover, that the subsequent and more general solutions require to
be considered with reference to Taylor's, in order to apprehend
distinctly their import; and further, that it was almost evident to
a mathematician, even before the general solution had appeared, that
the dependence of the time of vibration on the length and tension,
would be the same in the general case as in the {32} Taylorian
curve; so that, for the ends of physical philosophy, the solution
was not very incomplete.

John Bernoulli, a few years afterwards,[11\8] solved the problem of
vibrating chords on nearly the same principles and suppositions as
Taylor; but a little later (in 1747), the next generation of great
mathematicians, D'Alembert, Euler, and Daniel Bernoulli, applied the
increased powers of analysis to give generality to the mode of
treating this question; and especially the calculus of partial
differentials, invented for this purpose. But at this epoch, the
discussion, so far as it bore on physics, belonged rather to the
history of another problem, which comes under our notice hereafter,
that of the composition of vibrations; we shall, therefore, defer
the further history of the problem of vibrating strings, till we
have to consider it in connexion with new experimental facts.

[Note 11\8: _Op._ iii. p. 207.]




CHAPTER III.

PROBLEM OF THE PROPAGATION OF SOUND.


WE have seen that the ancient philosophers, for the most part, held
that sound was transmitted, as well as produced, by some motion of
the air, without defining what kind of motion this was; that some
writers, however, applied to it a very happy similitude, the
expansive motion of the circular waves produced by throwing a stone
into still water; but that notwithstanding, some rejected this mode
of conception, as, for instance, Bacon, who ascribed the
transmission of sound to certain "spiritual species."

Though it was an obvious thought to ascribe the motion of sound to
some motion of air; to conceive what kind of motion could and did
produce this effect, must have been a matter of grave perplexity at
the time of which we are speaking; and is far from easy to most
persons even now. We may judge of the difficulty of forming this
conception, when we recollect that John Bernoulli the younger[12\8]
declared, that he could not understand Newton's proposition on this
subject. The difficulty consists in this; that the movement of the
parts of air, in which sound consists, travels along, but that the
parts {33} of air themselves do not so travel. Accordingly Otto
Guericke,[13\8] the inventor of the air-pump, asks, "How can sound
be conveyed by the motion of the air? when we find that it is better
conveyed through air that is still, than when there is a wind." We
may observe, however, that he was partly misled by finding, as he
thought, that a bell could be heard in the vacuum of his air-pump; a
result which arose, probably, from some imperfection in his
apparatus.

[Note 12\8:_ Prize Dis. on Light_, 1736.]

[Note 13\8: _De Vac. Spat._ p. 138.]

Attempts were made to determine, by experiment, the circumstances of
the motion of sound; and especially its velocity. Gassendi[14\8] was
one of the first who did this. He employed fire-arms for the
purpose, and thus found the velocity to be 1473 Paris feet in a
second. Roberval found a velocity so small (560 feet) that it threw
uncertainty upon the rest, and affected Newton's reasonings
subsequently.[15\8] Cassini, Huyghens, Picard, Römer, found a
velocity of 1172 Paris feet, which is more accurate than the former.
Gassendi had been surprised to find that the velocity with which
sounds travel, is the same whether they are loud or gentle.

[Note 14\8: Fischer, _Gesch. d. Physik_. vol. i. 171.]

[Note 15\8: Newt. _Prin._ B. ii. P. 50, Schol.]

The explanation of this constant velocity of sound, and of its
amount, was one of the problems of which a solution was given in the
Great Charter of modern science, Newton's _Principia_ (1687). There,
for the first time, were explained the real nature of the motions
and mutual action of the parts of the air through which sound is
transmitted. It was shown[16\8] that a body vibrating in an elastic
medium, will propagate _pulses_ through the medium; that is, the parts
of the medium will move forwards and backwards, and this motion will
affect successively those parts which are at a greater and greater
distance from the origin of motion. The parts, in going forwards,
produce condensation; in returning to their first places, they allow
extension; and the play of the elasticities developed by these
expansions and contractions, supplies the forces which continue to
propagate the motion.

[Note 16\8: Newt. _Prin._ B. ii. P. 43.]

The idea of such a motion as this, is, as we have said, far from
easy to apprehend distinctly: but a distinct apprehension of it is a
step essential to the physical part of the sciences now under
notice; for it is by means of such _pulses_, or _undulations_, that
not only sound, but light, and probably heat, are propagated. We
constantly meet with evidence of the difficulty which men have in
conceiving this undulatory motion, and in separating it from a local
motion of the medium as a {34} mass. For instance, it is not easy at
first to conceive the waters of a great river flowing constantly
_down_ towards the sea, while waves are rolling _up_ the very same
part of the stream; and while the great elevation, which makes the
tide, is travelling from the sea perhaps with a velocity of fifty
miles an hour. The motion of such a wave, or elevation, is distinct
from any stream, and is of the nature of undulations in general. The
parts of the fluid stir for a short time and for a small distance,
so as to accumulate themselves on a neighboring part, and then
retire to their former place; and this movement affects the parts in
the order of their places. Perhaps if the reader looks at a field of
standing corn when gusts of wind are sweeping over it in visible
waves, he will have his conception of this matter aided; for he will
see that here, where each ear of grain is anchored by its stalk,
there can be no permanent local motion of the substance, but only a
successive stooping and rising of the separate straws, producing
hollows and waves, closer and laxer strips of the crowded ears.

Newton had, moreover, to consider the mechanical consequences which
such condensations and rarefactions of the elastic medium, air,
would produce in the parts of the fluid itself. Employing known laws
of the elasticity of air, he showed, in a very remarkable
proposition,[17\8] the law according to which the particles of air
might vibrate. We may observe, that in this solution, as in that of
the vibrating string already mentioned, a rule was exhibited
according to which the particles _might_ oscillate, but not the law
to which they _must_ conform. It was proved that, by taking the
motion of each particle to be perfectly similar to that of a
pendulum, the forces, developed by contraction and expansion, were
precisely such as the motion required; but it was not shown that no
other type of oscillation would give rise to the same accordance of
force and motion. Newton's reasoning also gave a determination of
the speed of propagation of the pulses: it appeared that sound ought
to travel with the velocity which a body would acquire by falling
freely through half _the height of a homogeneous atmosphere_; "the
height of a homogeneous atmosphere" being the height which the air
must have, in order to produce, at the earth's surface, the actual
atmospheric pressure, supposing no diminution of density to take
place in ascending. This height is about 29,000 feet; and hence it
followed that the velocity was 968 feet. This velocity is really
considerably less than that of sound; but at the time of which {35}
we speak, no accurate measure had been established; and Newton
persuaded himself, by experiments made in the cloister of Trinity
College, his residence, that his calculation was not far from the
fact. When, afterwards, more exact experiments showed the velocity
to be 1142 English feet, Newton attempted to explain the difference
by various considerations, none of which were adequate to the
purpose;--as, the dimensions of the solid particles of which the
fluid air consists;--or the vapors which are mixed with it. Other
writers offered other suggestions; but the true solution of the
difficulty was reserved for a period considerably subsequent.

[Note 17\8: _Princ._ B. ii. P. 48.]

Newton's calculation of the motion of sound, though logically
incomplete, was the great step in the solution of the problem; for
mathematicians could not but presume that his result was not
restricted to the hypothesis on which he had obtained it; and the
extension of the solution required only mere ordinary talents. The
logical defect of his solution was assailed, as might have been
expected. Cranmer (professor at Geneva), in 1741, conceived that he
was destroying the conclusiveness of Newton's reasoning, by showing
that it applied equally to other modes of oscillation. This, indeed,
contradicted the enunciation of the 48th Prop. of the Second Book of
the _Principia_; but it confirmed and extended all the general
results of the demonstration; for it left even the velocity of sound
unaltered, and thus showed that the velocity did not depend
mechanically on the type of the oscillation. But the satisfactory
establishment of this physical generalization was to be supplied
from the vast generalizations of analysis, which mathematicians were
now becoming able to deal with. Accordingly this task was performed
by the great master of analytical generalization, Lagrange, in 1759,
when, at the age of twenty-three, he and two friends published the
first volume of the _Turin Memoirs_. Euler, as his manner was, at
once perceived the merit of the new solution, and pursued the
subject on the views thus suggested. Various analytical improvements
and extensions were introduced into the solution by the two great
mathematicians; but none of these at all altered the formula by
which the velocity of sound was expressed; and the discrepancy
between calculation and observation, about one-sixth of the whole,
which had perplexed Newton, remained still unaccounted for.

The merit of satisfactorily explaining this discrepancy belongs to
Laplace. He was the first to remark[18\8] that the common law of the
{36} changes of elasticity in the air, as dependent on its
compression, cannot be applied to those rapid vibrations in which
sound consists, since the sudden compression produces a degree of
heat which additionally increases the elasticity. The ratio of this
increase depended on the experiments by which the relation of heat
and air is established. Laplace, in 1816, published[19\8] the
theorem on which the correction depends. On applying it, the
calculated velocity of sound agreed very closely with the best
antecedent experiments, and was confirmed by more exact ones
instituted for that purpose.

[Note 18\8: _Méc. Cél._ t. v. l. xii. p. 96.]

[Note 19\8: _Ann. Phys. et Chim._ t. iii. p. 288.]

This step completes the solution of the problem of the propagation
of sound, as a mathematical induction, obtained from, and verified
by, facts. Most of the discussions concerning points of analysis to
which the investigations on this subject gave rise, as, for
instance, the admissibility of _discontinuous functions_ into the
solutions of partial differential equations, belong to the history
of pure mathematics. Those which really concern the physical theory
of sound may be referred to the problem of the motion of air in
tubes, to which we shall soon have to proceed; but we must first
speak of another form which the problem of vibrating strings assumed.

It deserves to be noticed that the ultimate result of the study of
the undulations of fluids seems to show that the comparison of the
motion of air in the diffusion of sound with the motion of circular
waves from a centre in water, which is mentioned at the beginning of
this chapter, though pertinent in a certain way, is not exact. It
appears by Mr. Scott's recent investigations concerning waves,[20\8]
that the circular waves are oscillating waves of the Second order,
and are _gregarious_. The sound-wave seems rather to resemble the
great solitary Wave of Translation of the First order, of which we
have already spoken in Book vi. chapter vi.

[Note 20\8: _Brit. Ass. Reports for_ 1844, p. 361.]




CHAPTER IV.

PROBLEM OF DIFFERENT SOUNDS OF THE SAME STRING.


IT had been observed at an early period of acoustical knowledge,
that one string might give several sounds. Mersenne and others {37}
had noticed[21\8] that when a string vibrates, one which is in
unison with it vibrates without being touched. He was also aware
that this was true if the second string was an octave or a twelfth
below the first. This was observed as a new fact in England in 1674,
and communicated to the Royal Society by Wallis.[22\8] But the later
observers ascertained further, that the longer string divides itself
into two, or into three equal parts, separated by _nodes_, or points
of rest; this they proved by hanging bits of paper on different
parts of the string. The discovery so modified was again made by
Sauveur[23\8] about 1700. The sounds thus produced in one string by
the vibration of another, have been termed _Sympathetic Sounds_.
Similar sounds are often produced by performers on stringed
instruments, by touching the string at one of its aliquot divisions,
and are then called the _Acute harmonics_. Such facts were not
difficult to explain on Taylor's view of the mechanical condition of
the string; but the difficulty was increased when it was noticed
that a sounding body could produce these different notes _at the
same time_. Mersenne had remarked this, and the fact was more
distinctly observed and pursued by Sauveur. The notes thus produced
in addition to the genuine note of the string, have been called
_Secondary Notes_; those usually heard are, the Octave, the Twelfth,
and the Seventeenth above the note itself. To supply a mode of
conceiving distinctly, and explaining mechanically, vibrations which
should allow of such an effect, was therefore a requisite step in
acoustics.

[Note 21\8: _Harm._ lib. iv. Prop. 28 (1636).]

[Note 22\8: _Ph. Tr._ 1677, April.]

[Note 23\8: _A. P._ 1701.]

This task was performed by Daniel Bernoulli in a memoir published in
1755.[24\8] He there stated and proved the Principle of _the
coexistence of small vibrations_. It was already established, that a
string might vibrate either in a single _swelling_ (if we use this
word to express the curve between two nodes which Bernoulli calls a
_ventre_), or in two or three or any number of equal swellings with
immoveable nodes between. Daniel Bernoulli showed further, that
these nodes might be combined, each taking place as if it were the
only one. This appears sufficient to explain the coexistence of the
harmonic sounds just noticed. D'Alembert, indeed, in the article
_Fundamental_ in the French _Encyclopédie_, and Lagrange in his
_Dissertation on Sound_ in the _Turin Memoirs_,[25\8] offer several
objections to this explanation; and it cannot be denied that the
subject has its difficulties; but {38} still these do not deprive
Bernoulli of the merit of having pointed out the principle of
Coexistent Vibrations, or divest that principle of its value in
physical science.

[Note 24\8: _Berlin Mem._ 1753, p. 147.]

[Note 25\8: T. i. pp. 64, 103.]

Daniel Bernoulli's Memoir, of which we speak, was published at a
period when the clouds which involve the general analytical
treatment of the problem of vibrating strings, were thickening about
Euler and D'Alembert, and darkening into a controversial hue; and as
Bernoulli ventured to interpose his view, as a solution of these
difficulties, which, in a mathematical sense, it is not, we can
hardly be surprised that he met with a rebuff. The further
prosecution of the different modes of vibration of the same body
need not be here considered.

The sounds which are called _Grave Harmonics_, have no analogy with
the Acute Harmonics above-mentioned; nor do they belong to this
section; for in the case of Grave Harmonics, we have one sound from
the co-operation of two strings, instead of several sounds from one
string. These harmonics are, in fact, connected with beats, of which
we have already spoken; the beats becoming so close as to produce a
note of definite musical quality. The discovery of the Grave
Harmonics is usually ascribed to Tartini, who mentions them in 1754;
but they are first noticed[26\8] in the work of Sorge _On tuning
Organs_, 1744. He there expresses this discovery in a query. "Whence
comes it, that if we tune a fifth (2 : 3), a _third_ sound is
faintly heard, the octave below the lower of the two notes? Nature
shows that with 2 : 3, she still requires the unity, to perfect the
order 1, 2, 3." The truth is, that these numbers express the
frequency of the vibrations, and thus there will be coincidences of
the notes 2 and 3, which are of the frequency 1, and consequently
give the octave below the sound 2. This is the explanation given by
Lagrange,[27\8] and is indeed obvious.

[Note 26\8: Chladni. _Acoust._ p. 254.]

[Note 27\8: _Mem. Tur._ i. p. 104.]




CHAPTER V.

PROBLEM OF THE SOUNDS OF PIPES.


IT was taken for granted by those who reasoned on sounds, that the
sounds of flutes, organ-pipes, and wind-instruments in general, {39}
consisted in vibrations of some kind; but to determine the nature
and laws of these vibrations, and to reconcile them with mechanical
principles, was far from easy. The leading facts which had been
noticed were, that the note of a pipe was proportional to its
length, and that a flute and similar instruments might be made to
produce some of the acute harmonics, as well as the genuine note. It
had further been noticed,[28\8] that pipes closed at the end,
instead of giving the series of harmonics 1, ½, ⅓, ¼, &c., would
give only those notes which answer to the odd numbers 1, ⅓, ⅕, &c.
In this problem also, Newton[29\8] made the first step to the
solution. At the end of the propositions respecting the velocity of
sound, of which we have spoken, he noticed that it appeared by
taking Mersenne's or Sauveur's determination of the number of
vibrations corresponding to a given note, that the pulse of air runs
over twice the length of the pipe in the time of each vibration. He
does not follow out this observation, but it obviously points to the
theory, that the sound of a pipe consists of pulses which travel
back and forwards along its length, and are kept in motion by the
breath of the player. This supposition would account for the
observed dependence of the note on the length of the pipe. The
subject does not appear to have been again taken up in a theoretical
way till about 1760; when Lagrange in the second volume of the
_Turin Memoirs_, and D. Bernoulli in the _Memoirs of the French
Academy_ for 1762, published important essays, in which some of the
leading facts were satisfactorily explained, and which may therefore
be considered as the principal solutions of the problem.

[Note 28\8: D. Bernoulli, _Berlin. Mem._ 1753, p. 150.]

[Note 29\8: _Princip._ Schol. Prop. 50.]

In these solutions there was necessarily something hypothetical. In
the case of vibrating strings, as we have seen, the Form of the
vibrating curve was guessed at only, but the existence and position
of the Nodes could be rendered visible to the eye. In the vibrations
of air, we cannot see either the places of nodes, or the mode of
vibration; but several of the results are independent of these
circumstances. Thus both of the solutions explain the fact, that a
tube closed at one end is in unison with an open tube of double the
length; and, by supposing nodes to occur, they account for the
existence of the odd series of harmonics alone, 1, 3, 5, in closed
tubes, while the whole series, 1, 2, 3, 4, 5, &c., occurs in open
ones. Both views of the nature of the vibration appear to be nearly
the same; though Lagrange's is expressed with an analytical
generality which renders it obscure, and Bernoulli has perhaps {40}
laid down an hypothesis more special than was necessary.
Lagrange[30\8] considers the vibration of open flutes as "the
oscillations of a fibre of air," under the condition that its
elasticity at the two ends is, during the whole oscillation, the
same as that of the surrounding atmosphere. Bernoulli supposes[31\8]
the whole inertia of the air in the flute to be collected into one
particle, and this to be moved by the whole elasticity arising from
this displacement. It may be observed that both these modes of
treating the matter come very near to what we have stated as
Newton's theory; for though Bernoulli supposes all the air in the
flute to be moved at once, and not successively, as by Newton's
pulse, in either case the whole elasticity moves the whole air in
the tube, and requires more time to do this according to its
quantity. Since that time, the subject has received further
mathematical developement from Euler,[32\8] Lambert,[33\8] and
Poisson;[34\8] but no new explanation of facts has arisen. Attempts
have however been made to ascertain experimentally the places of the
nodes. Bernoulli himself had shown that this place was affected by
the amount of the opening, and Lambert[35\8] had examined other
cases with the same view. Savart traced the node in various musical
pipes under different conditions; and very recently Mr. Hopkins, of
Cambridge, has pursued the same experimental inquiry.[36\8] It
appears from these researches, that the early assumptions of
mathematicians with regard to the position of the nodes, are not
exactly verified by the facts. When the air in a pipe is made to
vibrate so as to have several nodes which divide it into equal
parts, it had been supposed by acoustical writers that the part
adjacent to the open end was half of the other parts; the outermost
node, however, is found experimentally to be _displaced_ from the
position thus assigned to it, by a quantity depending on several
collateral circumstances.

[Note 30\8: _Mém. Turin_, vol. ii. p. 154.]

[Note 31\8: _Mém. Berlin_, 1753, p. 446.]

[Note 32\8: _Nov. Act. Petrop._ tom. xvi.]

[Note 33\8: _Acad. Berlin_, 1775.]

[Note 34\5: _Journ. Ec. Polyt._ cap. 14.]

[Note 35\8: _Acad. Berlin_, 1775.]

[Note 36\8: _Camb. Trans._ vol. v. p. 234.]

Since our purpose was to consider this problem only so far as it has
tended towards its mathematical solution, we have avoided saying
anything of the dependence of the mode of vibration on the cause by
which the sound is produced; and consequently, the researches on the
effects of reeds, embouchures, and the like, by Chladni, Savart,
Willis, and others, do not belong to our subject. It is easily seen
that the complex effect of the elasticity and other properties of
the reed and of the air together, is a problem of which we can
hardly {41} hope to give a complete solution till our knowledge has
advanced much beyond its present condition.

Indeed, in the science of Acoustics there is a vast body of facts to
which we might apply what has just been said; but for the sake of
pointing out some of them, we shall consider them as the subjects of
one extensive and yet unsolved problem.




CHAPTER VI.

PROBLEM OF DIFFERENT MODES OF VIBRATION OF BODIES IN GENERAL.


NOT only the objects of which we have spoken hitherto, strings and
pipes, but almost all bodies are capable of vibration. Bells, gongs,
tuning-forks, are examples of solid bodies; drums and tambourines,
of membranes; if we run a wet finger along the edge of a glass
goblet, we throw the fluid which it contains into a regular
vibration; and the various character which sounds possess according
to the room in which they are uttered, shows that large masses of
air have peculiar modes of vibration. Vibrations are generally
accompanied by sound, and they may, therefore, be considered as
acoustical phenomena, especially as the sound is one of the most
decisive facts in indicating the mode of vibration. Moreover, every
body of this kind can vibrate in many different ways, the vibrating
segments being divided by Nodal Lines and Surfaces of various form
and number. The mode of vibration, selected by the body in each
case, is determined by the way in which it is held, the way in which
it is set in vibration, and the like circumstances.

The general problem of such vibrations includes the discovery and
classification of the phenomena; the detection of their formal laws;
and, finally, the explanation of these on mechanical principles. We
must speak very briefly of what has been done in these ways. The
facts which indicate Nodal Lines had been remarked by Galileo, on
the sounding board of a musical instrument; and Hooke had proposed
to observe the vibrations of a bell by strewing flour upon it. But
it was Chladni, a German philosopher, who enriched acoustics with
the discovery of the vast variety of symmetrical figures of Nodal
Lines, which are exhibited on plates of regular forms, when {42}
made to sound. His first investigations on this subject,
_Entdeckungen über die Theorie des Klangs_, were published 1787; and
in 1802 and 1817 he added other discoveries. In these works he not
only related a vast number of new and curious facts, but in some
measure reduced some of them to order and law. For instance, he has
traced all the vibrations of square plates to a resemblance with
those forms of vibration in which Nodal Lines are parallel to one
side of the square, and those in which they are parallel to another
side; and he has established a notation for the modes of vibration
founded on this classification. Thus, 5-2 denotes a form in which
there are five nodal lines parallel to one side, and two to another;
or a form which can be traced to a disfigurement of such a standard
type. Savart pursued this subject still further; and traced, by
actual observation, the forms of the Nodal Surfaces which divide
solid bodies, and masses of air, when in a state of vibration.

The dependence of such vibrations upon their physical cause, namely,
the elasticity of the substance, we can conceive in a general way;
but the mathematical theory of such cases is, as might be supposed,
very difficult, even if we confine ourselves to the obvious question
of the mechanical possibility of these different modes of vibration,
and leave out of consideration their dependence upon the mode of
excitation. The transverse vibrations of elastic rods, plates, and
rings, had been considered by Euler in 1779; but his calculation
concerning plates had foretold only a small part of the curious
phenomena observed by Chladni;[37\8] and the several notes which,
according to his calculation, the same ring ought to give, were not
in agreement with experiment.[38\8] Indeed, researches of this kind,
as conducted by Euler, and other authors,[39\8] rather were, and
were intended for, examples of analytical skill, than explanations
of physical facts. James Bernoulli, after the publication of
Chladni's experiments in 1787, attempted to solve the problem for
plates, by treating a plate as a collection of fibres; but, as
Chladni observes, the justice of this mode of conception is
disproved, by the disagreement of the results with experiment.

[Note 37\8: Fischer, vi. 587.]

[Note 38\8: Ib. vi. 596.]

[Note 39\8: See Chladni, p. 474.]

The Institute of France, which had approved of Chladni's labours,
proposed, in 1809, the problem now before us as a
prize-question:[40\8]--"To give the mathematical theory of the
vibrations of elastic {43} surfaces, and to compare it with
experiment." Only one memoir was sent in as a candidate for the
prize; and this was not crowned, though honorable mention was made
of it.[41\8] The formulæ of James Bernoulli were, according to M.
Poisson's statement, defective, in consequence of his not taking
into account the normal force which acts at the exterior boundary of
the plate.[42\8] The author of the anonymous memoir corrected this
error, and calculated the note corresponding to various figures of
the nodal lines; and he found an agreement with experiment
sufficient to justify his theory. He had not, however, proved his
fundamental equation, which M. Poisson demonstrated in a Memoir,
read in 1814.[43\8] At a more recent period also, MM. Poisson and
Cauchy (as well as a lady, Mlle. Sophie Germain) have applied to
this problem the artifices of the most improved analysis. M.
Poisson[44\8] determined the relation of the notes given by the
longitudinal and the transverse vibrations of a rod; and solved the
problem of vibrating circular plates when the nodal lines are
concentric circles. In both these cases, the numerical agreement of
his results with experience, seemed to confirm the justice of his
fundamental views.[45\8] He proceeds upon the hypothesis, that
elastic bodies are composed of separate particles held together by
the attractive forces which they exert upon each other, and
distended by the repulsive force of heat. M. Cauchy[46\8] has also
calculated the transverse, longitudinal, and rotatory vibrations of
elastic rods, and has obtained results agreeing closely with
experiment through a considerable list of comparisons. The combined
authority of two profound analysts, as MM. Poisson and Cauchy are,
leads us to believe that, for the simpler cases of the vibrations of
elastic bodies, Mathematics has executed her task; but most of the
more complex cases remain as yet unsubdued.

[Note 40\8: See Chladni, p. 357.]

[Note 41\8: Poisson's _Mém. in Ac. Sc._ 1812, p. 169.]

[Note 42\8: Ib. p. 220.]

[Note 43\8: Ib. 1812, p. 2.]

[Note 44\8: Ib. t. viii. 1829.]

[Note 45\8: _An. Chim._ tom. xxxvi. 1827, p. 90.]

[Note 46\8: _Exercices de Mathématique_, iii. and iv.]

The two brothers, Ernest and William Weber, made many curious
observations on undulations, which are contained in their
_Wellenlehre_, (Doctrine of Waves,) published at Leipsig in 1825.
They were led to suppose, (as Young had suggested at an earlier
period,) that Chladni's figures of nodal lines in plates were to be
accounted for by the superposition of undulations.[47\8] Mr.
Wheatstone[48\8] has undertaken to account for Chladni's figures of
vibrating _square_ plates by this {44} superposition of two or more
simple and obviously allowable modes of nodal division, which have
the same time of vibration. He assumes, for this purpose, certain
"primary figures," containing only _parallel_ nodal lines; and by
combining these, first in twos, and then in fours, he obtains most
of Chladni's observed figures, and accounts for their transitions
and deviations from regularity.

[Note 47\8: _Wellenlehre_, p. 474.]

[Note 48\8: _Phil. Trans._ 1833, p. 593.]

The principle of the superposition of vibrations is so solidly
established as a mechanical truth, that we may consider an
acoustical problem as satisfactorily disposed of when it is reduced
to that principle, as well as when it is solved by analytical
mechanics: but at the same time we may recollect, that the right
application and limitation of this law involves no small difficulty;
and in this case, as in all advances in physical science, we cannot
but wish to have the new ground which has been gained, gone over by
some other person in some other manner; and thus secured to us as a
permanent possession.

_Savart's Laws._--In what has preceded, the vibrations of bodies
have been referred to certain general classes, the separation of
which was suggested by observation; for example, the _transverse_,
_longitudinal_, and _rotatory_,[49\8] vibrations of rods. The
transverse vibrations, in which the rod goes backwards and forwards
across the line of its length, were the only ones noticed by the
earlier acousticians: the others were principally brought into
notice by Chladni. As we have already seen in the preceding pages,
this classification serves to express important laws; as, for
instance, a law obtained by M. Poisson which gives the relation of
the notes produced by the transverse and longitudinal vibrations of
a rod. But this distinction was employed by M. Felix Savart to
express laws of a more general kind; and then, as often happens in
the progress of science, by pursuing these laws to a higher point of
generality, the distinction again seemed to vanish. A very few words
will explain these steps.

[Note 49\8: Vibrations tournantes.]

It was long ago known that vibrations may be communicated by
contact. The distinction of transverse and longitudinal vibrations
being established, Savart found that if one rod touched another
perpendicularly, the longitudinal vibrations of the first occasion
transverse vibrations in the second, and _vice versâ_. This is the
more remarkable, since the two sets of vibrations are not equal in
rapidity, and therefore cannot sympathize in any obvious
manner.[50\8] Savart found himself {45} able to generalize this
proposition, and to assert that in any combination of rods, strings,
and laminæ, at right angles to each other, the longitudinal and
transverse vibrations affect respectively the rods in the one and
other direction,[51\8] so that when the horizontal rods, for example,
vibrate in the one way, the vertical rods vibrate in the other.

[Note 50\8: _An. Chim._ 1819, tom. xiv. p. 138.]

[Note 51\8: _An. Chim._ p. 152.]

This law was thus expressed in terms of that classification of
vibrations of which we have spoken. Yet we easily see that we may
express it in a more general manner, without referring to that
classification, by saying, that vibrations are communicated so as
always to be parallel to their original direction. And by following
it out in this shape by means of experiment, M. Savart was led, a
short time afterwards, to deny that there is any essential
distinction in these different kinds of vibration. "We are thus
led," he says[52\8] in 1822, "to consider _normal_ [transverse]
vibrations as only one circumstance in a more general motion common
to all bodies, analogous to _tangential_ [longitudinal and rotatory]
vibrations; that is, as produced by small _molecular oscillations_,
and differently modified according to the direction which it
affects, relatively to the dimensions of the vibrating body."

[Note 52\8: Ib. t. xxv. p. 33.]

These "inductions," as he properly calls them, are supported by a
great mass of ingenious experiments; and may be considered as well
established, when they are limited to molecular oscillations,
employing this phrase in the sense in which it is understood in the
above statement; and also when they are confined to bodies in which
the play of elasticity is not interrupted by parts more rigid than
the rest, as the sound-post of a violin.[53\8] And before I quit the
subject, I may notice a consequence which M. Savart has deduced from
his views, and which, at first sight, appears to overturn most of
the earlier doctrines respecting vibrating bodies. It was formerly
held that tense strings and elastic rods could vibrate only in a
determinate series of modes of division, with no intermediate steps.
But M. Savart maintains,[54\8] on the contrary, that they produce
sounds which are gradually transformed into one another, by
indefinite intermediate degrees. The reader may naturally ask, what
is the solution of this apparent {46} contradiction between the
earliest and the latest discoveries in acoustics. And the answer
must be, that these intermediate modes of vibration are complex in
their nature, and difficult to produce; and that those which were
formerly believed to be the only possible vibrating conditions, are
so eminent above all the rest by their features, their simplicity,
and their facility, that we may still, for common purposes, consider
them as a class apart; although for the sake of reaching a general
theorem, we may associate them with the general mass of cases of
molecular vibrations. And thus we have no exception here, as we can
have none in any case, to our maxim, that what formed part of the
early discoveries of science, forms part of its latest systems.

[Note 53\8: For the suggestion of the necessity of this limitation I
am indebted to Mr. Willis.]

[Note 54\8: _An. Chim._ 1826, t. xxxii. p. 384.]

We have thus surveyed the progress of the science of sound up to
recent times, with respect both to the discovery of laws of
phenomena, and the reduction of these to their mechanical causes.
The former branch of the science has necessarily been inductively
pursued; and therefore has been more peculiarly the subject of our
attention. And this consideration will explain why we have not dwelt
more upon the deductive labors of the great analysts who have
treated of this problem.

To those who are acquainted with the high and deserved fame which
the labors of D'Alembert, Euler, Lagrange, and others, upon this
subject, enjoy among mathematicians, it may seem as if we had not
given them their due prominence in our sketch. But it is to be
recollected here, as we have already observed in the case of
hydrodynamics, that even when the general principles are
uncontested, mere mathematical deductions from them do not belong to
the history of physical science, except when they point out laws
which are intermediate between the general principle and the
individual facts, and which observation may confirm.

The business of constructing any science may be figured as the task
of forming a road on which our reason can travel through a certain
province of the external world. We have to throw a bridge which may
lead from the chambers of our own thoughts, from our speculative
principles, to the distant shore of material facts. But in all cases
the abyss is too wide to be crossed, except we can find some
intermediate points on which the piers of our structure may rest.
Mere facts, without connexion or law, are only the rude stones hewn
from the opposite bank, of which our arches may, at some time, be
built. But mere hypothetical mathematical calculations are only
plans of projected structures; and those plans which exhibit only
one vast {47} and single arch, or which suppose no support but that
which our own position supplies, will assuredly never become
realities. We must have a firm basis of intermediate generalizations
in order to frame a continuous and stable edifice.

In the subject before us, we have no want of such points of
intermediate support, although they are in many instances
irregularly distributed and obscurely seen. The number of observed
laws and relations of the phenomena of sound, is already very great;
and though the time may be distant, there seems to be no reason to
despair of one day uniting them by clear ideas of mechanical
causation, and thus of making acoustics a perfect secondary
mechanical science.

The historical sketch just given includes only such parts of
acoustics as have been in some degree reduced to general laws and
physical causes; and thus excludes much that is usually treated of
under that head. Moreover, many of the numerical calculations
connected with sound belong to its agreeable effect upon the ear; as
the properties of the various systems of _Temperament_. These are
parts of Theoretical Music, not of Acoustics; of the Philosophy of
the Fine Arts, not of Physical Science; and may be referred to in a
future portion of this work, so far as they bear upon our object.

The science of Acoustics may, however, properly consider other
differences of sound than those of acute and grave,--for instance,
the _articulate_ differences, or those by which the various letters
are formed. Some progress has been made in reducing this part of the
subject to general rules; for though Kempelen's "talking machine"
was only a work of art, Mr. Willis's machine,[55\8] which exhibits
the relation among the vowels, gives us a law such as forms a step
in science. We may, however, consider this instrument as a
_phthongometer_, or measure of vowel quality; and in that point of
view we shall have to refer to it again when we come to speak of
such measures.

[Note 55\8: On the Vowel Sounds, and on Reed Organ-pipes. _Camb.
Trans._ iii. 237.]



{{49}}
BOOK IX.


_SECONDARY MECHANICAL SCIENCES._

(CONTINUED)


HISTORY OF OPTICS,

FORMAL AND PHYSICAL.



  Ω Διὸς ὑψιμέλαθρον ἔχων κράτος αἰὲν ἀτειρὲς
  Ἄστρων, Ἠελίου τε, Σεληναίης τε μέρισμα
  Πανδαμάτωρ, πυρίπνου, πᾶσιν ζωοῖσιν ἔναυσμα
  **Ὑψιφάνης ἌIϴΗΡ, κόσμου στοιχεῖον, **ἄριστον·
  Ἀγλαὸν ὦ βλάστημα, σελασφόρον, ἀστεροφεγγὲς
  Κικλήσκων λίτομαι σε, κεκραμένον **εὔδιον εἶναι.
          ORPHEUS. HYMN.

  O thou who fillest the palaces of Jove;
  Who flowest round moon, and sun, and stars above;
  Pervading, bright, life-giving element,
  Supernal ETHER, fair and excellent;
  Fountain of hope and joy, of light and day,
  We own at length thy tranquil, steady sway.



{{51}}
INTRODUCTION.

_Formal and Physical Optics._


THE history of the science of Optics, written at length, would be
very voluminous; but we shall not need to make our history so; since
our main object is to illustrate the nature of science and the
conditions of its progress. In this way Optics is peculiarly
instructive; the more so, as its history has followed a course in
some respects different from both the sciences previously reviewed.
Astronomy, as we have seen, advanced with a steady and continuous
movement from one generation to another, from the earliest time,
till her career was crowned by the great unforeseen discovery of
Newton; Acoustics had her extreme generalization in view from the
first, and her history consists in the correct application of it to
successive problems; Optics advanced through a scale of
generalizations as remarkable as those of Astronomy; but for a long
period she was almost stationary; and, at last, was rapidly impelled
through all those stages by the energy of two or three discoverers.
The highest point of generality which Optics has reached is little
different from that which Acoustics occupied at once; but in the
older and earlier science we still want that palpable and pointed
confirmation of the general principle, which the undulatory theory
receives from optical phenomena. Astronomy has amassed her vast
fortune by long-continued industry and labor; Optics has obtained
hers in a few years by sagacious and happy speculations; Acoustics,
having early acquired a competence, has since been employed rather
in improving and adorning than in extending her estate.

The successive inductions by which Optics made her advances, might,
of course, be treated in the same manner as those of Astronomy, each
having its prelude and its sequel. But most of the discoveries in
Optics are of a smaller character, and have less employed the minds
of men, than those of Astronomy; and it will not be necessary to
exhibit them in this detailed manner, till we come to the great
generalization by which the theory was established. I shall,
therefore, now pass rapidly in review the earlier optical
discoveries, without any such division of the series. {52}

Optics, like Astronomy, has for its object of inquiry, first, the
laws of phenomena, and next, their causes; and we may hence divide
this science, like the other, into _Formal Optics_ and _Physical
Optics_. The distinction is clear and substantive, but it is not
easy to adhere to it in our narrative; for, after the theory had
begun to make its rapid advance, many of the laws of phenomena were
studied and discovered in immediate reference to the theoretical
cause, and do not occupy a separate place in the history of science,
as in Astronomy they do. We may add, that the reason why Formal
Astronomy was almost complete before Physical Astronomy began to
exist, was, that it was necessary to construct the science of
Mechanics in the mean time, in order to be able to go on; whereas,
in Optics, mathematicians were able to calculate the results of the
undulatory theory as soon as it had suggested itself from the earlier
facts, and while the great mass of facts were only becoming known.

We shall, then, in the first _nine_ chapters of the History of
Optics treat of the Formal Science, that is, the discovery of the
laws of phenomena. The classes of phenomena which will thus pass
under oar notice are numerous; namely, reflection, refraction,
chromatic dispersion, achromatization, double refraction,
polarization, dipolarization, the colors of thin plates, the colors
of thick plates, and the fringes and bands which accompany shadows.
All these cases had been studied, and, in most of them, the laws had
been in a great measure discovered, before the physical theory of
the subject gave to our knowledge a simpler and more solid form.



{{53}}
FORMAL OPTICS.



CHAPTER I.

PRIMARY INDUCTION OF OPTICS.--RAYS OF LIGHT AND LAWS OF REFLECTION.


IN speaking of the Ancient History of Physics, we have already
noticed that the optical philosophers of antiquity had satisfied
themselves that vision is performed in straight lines;--that they
had fixed their attention upon those straight lines, or _rays_, as
the proper object of the science;--they had ascertained that rays
reflected from a bright surface make the _angle of reflection_ equal
to the _angle of incidence_;--and they had drawn several
consequences from these principles.

We may add to the consequences already mentioned, the art of
_perspective_, which is merely a corollary from the doctrine of
rectilinear visual rays; for if we suppose objects to be referred by
such rays to a plane interposed between them and the eye, all the
rules of perspective follow directly. The ancients practised this
art, as we see in the pictures which remain to us and we learn from
Vitruvius,[1\9] that they also wrote upon it. Agatharchus, who had
been instructed by Eschylus in the art of making decorations for the
theatre, was the first author on this subject, and Anaxagoras, who
was a pupil of Agatharchus, also wrote an _Actinographia_, or
doctrine of drawing by rays: but none of these treatises are come
down to us. The moderns re-invented the art in the flourishing times
of the art of painting, that is, about the end of the fifteenth
century; and, belonging to that period also, we have treatises[2\9]
upon it.

[Note 1\9: _De Arch._ ix. Mont. i. 707.]

[Note 2\9: Gauricus, 1504.]

But these are only deductive applications of the most elementary
optical doctrines; we must proceed to the inductions by which
further discoveries were made. {54}




CHAPTER II.

DISCOVERY OF THE LAW OF REFRACTION.


WE have seen in the former part of this history that the Greeks had
formed a tolerably clear conception of the refraction as well as the
reflection of the rays of light; and that Ptolemy had measured the
amount of refraction of glass and water at various angles. If we
give the names of the _angle of incidence_ and the _angle of
refraction_ respectively to the angles which a ray of light makes
with the line perpendicular to surface of glass or water (or any
other medium) within and without the medium, Ptolemy had observed
that the angle of refraction is always less than the angle of
incidence. He had supposed it to be less in a given proportion, but
this opinion is false; and was afterwards rightly denied by the
Arabian mathematician Alhazen. The optical views which occur in the
work of Alhazen are far sounder than those of his predecessors; and
the book may be regarded as the most considerable monument which we
have of the scientific genius of the Arabians; for it appears, for
the most part, not to be borrowed from Greek authorities. The author
not only asserts (lib. vii.), that refraction takes place towards
the perpendicular, and refers to experiment for the truth of this:
and that the quantities of the refraction differ according to the
magnitudes of the angles which the directions of the incidental rays
(_primæ lineæ_) make with the perpendiculars to the surface; but he
also says distinctly and decidedly that the angles of refraction do
not follow the proportion of the angles of incidence.

[2nd Ed.] [There appears to be good ground to assent to the
assertion of Alhazen's originality, made by his editor Risner, who
says, "Euclideum hic vel Ptolemaicum nihil fere est." Besides the
doctrine of reflection and refraction of light, the Arabian author
gives a description of the eye. He distinguishes three fluids,
_humor aqueus_, _crystallinus_, _vitreus_, and four coats of the
eye, _tunica adherens_, _cornea_, _uvea_, _tunica reti similis_. He
distinguishes also three kinds of vision: "Visibile percipitur aut
solo visu, aut visu et syllogismo, aut visu et anticipatâ notione."
He has several propositions relating to what we sometimes call the
Philosophy of Vision: for instance this: "E visibili sæpius viso
remanet in anima generalis notio," &c.] {55}

The assertion, that the angles of refraction are not proportional to
the angles of incidence, was an important remark; and if it had been
steadily kept in mind, the next thing to be done with regard to
refraction was to go on experimenting and conjecturing till the true
law of refraction was discovered; and in the mean time to apply the
principle as far as it was known. Alhazen, though he gives
directions for making experimental measures of refraction, does not
give any Table of the results of such experiments, as Ptolemy had
done. Vitello, a Pole, who in the 13th century published an
extensive work upon Optics, does give such a table; and asserts it
to be deduced from experiment, as I have already said (vol. i.). But
this assertion is still liable to doubt in consequence of the table
containing impossible observations.

[2nd Ed.] [As I have already stated, Vitello asserts that his Tables
were derived from his own observations. Their near agreement with
those of Ptolemy does not make this improbable: for where the
observations were only made to half a degree, there was not much
room for observers to differ. It is not unlikely that the
observations of refraction out of air into water and glass, and out
of water into glass, were actually made; while the impossible values
which accompany them, of the refraction out of water and glass into
air, and out of glass into water, were calculated, and calculated
from an erroneous rule.]

The principle that a ray refracted in glass or water is turned
towards the perpendicular, without knowing the exact law of
refraction, enabled mathematicians to trace the effects of
transparent bodies in various cases. Thus in Roger Bacon's works we
find a tolerably distinct explanation of the effect of a convex
glass; and in the work of Vitello the effect of refraction at the
two surfaces of a glass globe is clearly traceable.

Notwithstanding Alhazen's assertion of the contrary, the opinion was
still current among mathematicians that the angle of refraction was
proportional to the angle of incidence. But when Kepler's attention
was drawn to the subject, he saw that this was plainly inconsistent
with the observations of Vitello for large angles; and he convinced
himself by his own experiments that the true law was something
different from the one commonly supposed. The discovery of this true
law excited in him an eager curiosity; and this point had the more
interest for him in consequence of the introduction of a correction
for atmospheric refraction into astronomical calculations, which had
been made by Tycho, and of the invention of the telescope. In {56}
his _Supplement to Vitello_, published in 1604, Kepler attempts to
reduce to a rule the measured quantities of refraction. The reader
who recollects what we have already narrated, the manner in which
Kepler attempted to reduce to law the astronomical observations of
Tycho,--devising an almost endless variety of possible formulæ,
tracing their consequences with undaunted industry, and relating,
with a vivacious garrulity, his disappointments and his hopes,--will
not be surprised to find that he proceeded in the same manner with
regard to the Tables of Observed Refractions. He tried a variety of
constructions by triangles, conic sections, &c., without being able
to satisfy himself; and he at last[3\9] is obliged to content
himself with an approximate rule, which makes the refraction partly
proportional to the angle of incidence, and partly, to the secant of
that angle. In this way he satisfies the observed refractions within
a difference of less than half a degree each way. When we consider
how simple the law of refraction is, (that the ratio of the sines of
the angles of incidence and refraction is constant for the same
medium,) it appears strange that a person attempting to discover it,
and drawing triangles for the purpose, should fail; but this lot of
missing what afterwards seems to have been obvious, is a common one
in the pursuit of truth.

[Note 3\9: L. U. K. _Life of Kepler_, p. 115.]

The person who did discover the Law of the Sines, was Willebrord
Snell, about 1621; but the law was first published by Descartes, who
had seen Snell's papers.[4\9] Descartes does not acknowledge this
law to have been first detected by another; and after his manner,
instead of establishing its reality by reference to experiment, he
pretends to prove _à priori_ that it must be true,[5\9] comparing,
for this purpose, the particles of light to balls striking a
substance which _accelerates_ them.

[Note 4\9: Huyghens, _Dioptrica_, p. 2.]

[Note 5\9: _Diopt._ p. 53.]

[2nd Ed.] [Huyghens says of Snell's papers, "Quæ et nos vidimus
aliquando, et Cartesium quoque vidisse accepimus, et hinc fortasse
mensuram illam quæ in sinibus consistit elicuerit." Isaac Vossius,
_De Lucis Naturâ et Proprietate_, says that he also had seen this
law in Snell's unpublished optical Treatise. The same writer says,
"Quod itaque (Cartesius) habet, refractionum momenta non exigenda
esse ad angulos sed ad lineas, id tuo Snellio, acceptum ferre
debuisset, cujus nomen _more solito_ dissimulavit." "Cartesius got
his law from Snell, and _in his usual way_, concealed it." {57}

Huyghens' assertion, that Snell did not _attend to_ the proportion
of the sines, is very captious; and becomes absurdly so, when it is
made to mean that Snell did not _know_ the law of the sines. It is
not denied that Snell knew the true law, or that the true law is the
law of the sines. Snell does not use the trigonometrical term
_sine_, but he expresses the law in a geometrical form more simply.
Even if he _had_ attended to the law of the sines, he might
reasonably have preferred his own way of stating it.

James Gregory also independently discovered the true law of
refraction; and, in publishing it, states that he had learnt that it
had already been published by Descartes.]

But though Descartes does not, in this instance, produce any good
claims to the character of an inductive philosopher, he showed
considerable skill in tracing the consequences of the principle when
once adopted. In particular we must consider him as the genuine
author of the explanation of the rainbow. It is true that
Fleischer[6\9] and Kepler had previously ascribed this phenomenon to
the rays of sunlight which, falling on drops of rain, are refracted
into each drop, reflected at its inner surface, and refracted out
again: Antonio de Dominis had found that a glass globe of water,
when placed in a particular position with respect to the eye,
exhibited bright colors; and had hence explained the circular form
of the bow, which, indeed, Aristotle had done before.[7\9] But none
of these writers had shown why there was a narrow bright circle of a
definite diameter; for the drops which send rays to the eye after
two refractions and a reflection, occupy a much wider space in the
heavens. Descartes assigned the reason for this in the most
satisfactory manner,[8\9] by showing that the rays which, after two
refractions and a reflection, come to the eye at an angle of about
forty-one degrees with their original direction, are far more dense
than those in any other position. He showed, in the same manner,
that the existence and position of the _secondary bow_ resulted from
the same laws. This is the complete and adequate account of the
state of things, so far as the brightness of the bows only is
concerned; the explanation of the colors belongs to the next article
of our survey.

[Note 6\9: Mont. i. 701.]

[Note 7\9: _Meteorol._ iii. 3.]

[Note 8\9: _Meteorum_, cap. viii. p. 196.]

The explanation of the rainbow and of its magnitude, afforded by
Snell's law of sines, was perhaps one of the leading points in the
verification of the law. The principle, being once established, was
applied, by the aid of mathematical reasoning, to atmospheric
refractions, {58} optical instruments, _diacaustic_ curves, (that
is, the curves of intense light produced by refraction,) and to
various other cases; and was, of course, tested and confirmed by
such applications. It was, however, impossible to pursue these
applications far, without a due knowledge of the laws by which, in
such cases, colors are produced. To these we now proceed.

[2nd Ed.] [I have omitted many interesting parts of the history of
Optics about this period, because I was concerned with the
_inductive_ discovery of laws, rather than with mathematical
_deductions_ from such laws when established, or _applications_ of
them in the form of instruments. I might otherwise have noticed the
discovery of Spectacle Glasses, of the Telescope, of the Microscope,
of the Camera Obscura, and the mathematical explanation of these and
other phenomena, as given by Kepler and others. I might also have
noticed the progress of knowledge respecting the Eye and Vision. We
have seen that Alhazen described the structure of the eye. The
operation of the parts was gradually made out. Baptista Porta
compares the eye to his _Camera Obscura_ (_Magia Naturalis_, 1579).
Scheiner, in his _Oculus_, published 1652, completed the Theory of
the Eye. And Kepler discussed some of the questions even now often
agitated; as the causes and conditions of our seeing objects single
with two eyes, and erect with inverted images.]




CHAPTER III.

DISCOVERY OF THE LAW OF DISPERSION BY REFRACTION.


EARLY attempts were made to account for the colors of the rainbow,
and various other phenomena in which colors are seen to arise from
transient and unsubstantial combinations of media. Thus Aristotle
explains the colors of the rainbow by supposing[9\9] that it is
light seen through a dark medium: "Now," says he, "the bright seen
through the dark appears red, as, for instance, the fire of green
wood seen through the smoke, and the sun through mist. Also[10\9]
the weaker is the light, or the visual power, and the nearer the
color approaches to the black; becoming first red, then green, then
purple. But[11\9] the {59} vision is strongest in the outer circle,
because the periphery is greater;--thus we shall have a gradation
from red, through green, to purple, in passing from the outer to the
inner circle." This account would hardly have deserved much notice,
if it had not been for a strange attempt to revive it, or something
very like it, in modern times. The same doctrine is found in the
work of De Dominis.[12\9] According to him, light is white: but if
we mix with the light something dark, the colors arise,--first red,
then green, then blue or violet. He applies this to explain the
colors of the rainbow,[13\9] by means of the consideration that, of
the rays which come to the eye from the globes of water, some go
through a larger thickness of the globe than others, whence he
obtains the gradation of colors just described.

[Note 9\9: _Meteor._ iii. 3, p. 373.]

[Note 10\9: Ib. p. 374.]

[Note 11\9: Ib. p. 375.]

[Note 12\9: Cap. iii. p. 9. See also Göthe, _Farbenl._ vol. ii.
p. 251.]

[Note 13\9: Göthe, p. 263.]

Descartes came far nearer the true philosophy of the iridal colors.
He found that a similar series of colors was produced by refraction
of light bounded by shade, through a prism;[14\9] and he rightly
inferred that neither the curvature of the surface of the drops of
water, nor the reflection, nor the repetition of refraction, were
necessary to the generation of such colors. In further examining the
course of the rays, he approaches very near to the true conception
of the case; and we are led to believe that he might have
anticipated Newton in his discovery of the unequal refrangibility of
different colors, if it had been possible for him to reason any
otherwise than in the terms and notions of his preconceived
hypotheses. The conclusion which he draws is,[15\9] that "the
particles of the subtile matter which transmit the action of light,
endeavor to rotate with so great a force and impetus, that they
cannot move in a straight line (whence comes refraction): and that
those particles which endeavor to revolve much more strongly produce
a red color, those which endeavor to move only a little more
strongly produce yellow." Here we have a clear perception that
colors and unequal refraction are connected, though the cause of
refraction is expressed by a gratuitous hypothesis. And we may add,
that he applies this notion rightly, so far as he explains
himself,[16\9] to account for the colors of the rainbow.

[Note 14\9: _Meteor._ Sect. viii. p. 190.]

[Note 15\9: Sect. vii. p. 192.]

[Note 16\9: _Meteor._ Sect. ix.]

It appears to me that Newton and others have done Descartes
injustice, in ascribing to De Dominis the true theory of the
rainbow. There are two main points of this theory, namely, the
showing that a _bright_ circular band, of a certain definite
diameter, arises from the {60} great intensity of the light returned
at a certain angle; and the referring the different _colors_ to the
_different quantity of the refraction_; and both these steps appear
indubitably to be the discoveries of Descartes. And he informs us
that these discoveries were not made without some exertion of
thought. "At first," he says,[17\9] "I doubted whether the iridal
colors were produced in the same way as those in the prism; but, at
last, taking my pen, and carefully calculating the course of the
rays which fell on each part of the drop, I found that many more
come at an angle of forty-one degrees, than either at a greater or a
less angle. So that there is a bright bow terminated by a shade; and
hence the colors are the same as those produced through a prism."

[Note 17\9: Sect. ix. p. 193.]

The subject was left nearly in the same state, in the work of
Grimaldi, _Physico-Mathesis, de Lumine, Coloribus et Iride_,
published at Bologna in 1665. There is in this work a constant
reference to numerous experiments, and a systematic exposition of
the science in an improved state. The author's calculations
concerning the rainbow are put in the same form as those of
Descartes; but he is further from seizing the true principle on
which its coloration depends. He rightly groups together a number of
experiments in which colors arise from refraction;[18\9] and
explains them by saying that the color is brighter where the light
is denser: and the light is denser on the side from which the
refraction turns the ray, because the increments of refraction are
greater in the rays that are more inclined.[19\9] This way of
treating the question might be made to give a sort of explanation of
most of the facts, but is much more erroneous than a developement of
Descartes's view would have been.

[Note 18\9: Prop. 35, p. 254.]

[Note 19\9: Ib. p. 256.]

At length, in 1672, Newton gave[20\9] the true explanation of the
facts; namely, that light consists of rays of different colors and
different refrangibility. This now appears to us so obvious a mode
of interpreting the phenomena, that we can hardly understand how
they can be conceived in any other manner; but yet the impression
which this discovery made, both upon Newton and upon his
contemporaries, shows how remote it was from the then accepted
opinions. There appears to have been a general persuasion that the
coloration was produced, not by any peculiarity in the law of
refraction itself but by some collateral circumstance,--some
dispersion or variation of density of the light, in addition to the
refraction. Newton's discovery consisted in {61} teaching distinctly
that the law of refraction was to be applied, not to the beam of
light in general, but to the colors in particular.

[Note 20\9: _Phil. Trans._ t. vii. p. 3075.]

When Newton produced a bright spot on the wall of his chamber, by
admitting the sun's light through a small hole in his
window-shutter, and making it pass through a prism, he expected the
image to be round; which, of course, it would have been, if the
colors had been produced by an equal dispersion in all directions;
but to his surprise he saw the image, or _spectrum_, five times as
long as it was broad. He found that no consideration of the
different thickness of the glass, the possible unevenness of its
surface, or the different angles of rays proceeding from the two
sides of the sun, could be the cause of this shape. He found, also,
that the rays did not go from the prism to the image in curves; he
was then convinced that the different colors were refracted
separately, and at different angles; and he confirmed this opinion
by transmitting and refracting the rays of each color separately.

The experiments are so easy and common, and Newton's interpretation
of them so simple and evident, that we might have expected it to
receive general assent; indeed, as we have shown, Descartes had
already been led very near the same point. In fact, Newton's
opinions were not long in obtaining general acceptance; but they met
with enough of cavil and misapprehension to annoy extremely the
discoverer, whose clear views and quiet temper made him impatient
alike of stupidity and of contentiousness.

We need not dwell long on the early objections which were made to
Newton's doctrine. A Jesuit, of the name of Ignatius Pardies,
professor at Clermont, at first attempted to account for the
elongation of the image by the difference of the angles made by the
rays from the two edges of the sun, which would produce a difference
in the amount of refraction of the two borders; but when Newton
pointed out the calculations which showed the insufficiency of this
explanation, he withdrew his opposition. Another more pertinacious
opponent appeared in Francis Linus, a physician of Liege; who
maintained, that having tried the experiment, he found the sun's
image, when the sky was clear, to be round and not oblong; and he
ascribed the elongation noticed by Newton, to the effect of clouds.
Newton for some time refused to reply to this contradiction of his
assertions, though obstinately persisted in; and his answer was at
last sent, just about the time of Linus's death, in 1675. But
Gascoigne, a friend of Linus, still maintained that he and others
had seen what the Dutch physician had described; and Newton, who was
pleased with the candor of {62} Gascoigne's letter, suggested that
the Dutch experimenters might have taken one of the images reflected
from the surfaces of the prism, of which there are several, instead
of the proper refracted one. By the aid of this hint, Lucas of Liege
repeated Newton's experiments, and obtained Newton's result, except
that he never could obtain a spectrum whose length was more than
three and a half times its breadth. Newton, on his side, persisted
in asserting that the image would be five times as long as it was
broad, if the experiment were properly made. It is curious that he
should have been so confident of this, as to conceive himself
certain that such would be the result in all cases. We now know that
the dispersion, and consequently the length, of the spectrum, is
very different for different kinds of glass, and it is very probable
that the Dutch prism was really less dispersive than the English
one.[21\9] The erroneous assumption which Newton made in this
instance, he held by to the last; and was thus prevented from making
the discovery of which we have next to speak.

[Note 21\9: Brewster's _Newton_, p. 50.]

Newton was attacked by persons of more importance than those we have
yet mentioned; namely, Hooke and Huyghens. These philosophers,
however, did not object so much to the laws of refraction of
different colors, as to some expressions used by Newton, which, they
conceived, conveyed false notions respecting the composition and
nature of light. Newton had asserted that all the different colors
are of distinct kinds, and that, by their composition, they form
white light. This is true of colors as far as their analysis and
composition by refraction are concerned; but Hooke maintained that
all natural colors are produced by various combinations of two
primary ones, red and violet;[22\9] and Huyghens held a similar
doctrine, taking, however, yellow and blue for his basis. Newton
answers, that such compositions as they speak of are not
compositions of simple colors in his sense of the expressions. These
writers also had both of them adopted an opinion that light
consisted in vibrations; and objected to Newton that his language
was erroneous, as involving the hypothesis that light was a body.
Newton appears to have had a horror of the word _hypothesis_, and
protests against its being supposed that his "theory" rests on such
a foundation.

[Note 22\9: Brewster's _Newton_, p. 54. _Phil. Trans._ viii. 5084,
6086.]

The doctrine of the unequal refrangibility of different rays is
clearly exemplified in the effects of lenses, which produce images
more or {63} less bordered with color, in consequence of this
property. The improvement of telescopes was, in Newton's time, the
great practical motive for aiming at the improvement of theoretical
optics. Newton's theory showed why telescopes were imperfect,
namely, in consequence of the different refraction of different
colors, which produces a _chromatic_ aberration: and the theory was
confirmed by the circumstances of such imperfections. The false
opinion of which we have already spoken, that the dispersion must be
the same when the refraction is the same, led him to believe that
the imperfection was insurmountable,--that _achromatic_ refraction
could not be obtained: and this view made him turn his attention to
the construction of reflecting instead of refracting telescopes. But
the rectification of Newton's error was a further confirmation of
the general truth of his principles in other respects; and since
that time, the soundness of the Newtonian law of refraction has
hardly been questioned among physical philosophers.

It has, however, in modern times, been very vehemently controverted in
a quarter from which we might not readily have expected a detailed
discussion on such a subject. The celebrated Göthe has written a work
on _The Doctrine of Colors_, (_Farbenlehre_; Tübingen, 1810,) one main
purpose of which is, to represent Newton's opinions, and the work in
which they are formally published, (his _Opticks_,) as utterly false
and mistaken, and capable of being assented to only by the most blind
and obstinate prejudice. Those who are acquainted with the extent to
which such an opinion, promulgated by Göthe, was likely to be widely
adopted in Germany, will not be surprised that similar language is
used by other writers of that nation. Thus Schelling[23\9] says:
"Newton's _Opticks_ is the greatest proof of the possibility of a
whole structure of fallacies, which, in all its parts, is founded upon
observation and experiment." Göthe, however, does not concede even so
much to Newton's work. He goes over a large portion of it, page by
page, quarrelling with the experiments, diagrams, reasoning, and
language, without intermission; and holds that it is not reconcileable
with the most simple facts. He declares,[24\9] that the first time he
looked through a prism, he saw the white walls of the room still look
white, "and though alone, I pronounced, as by an instinct, that the
Newtonian doctrine is false." We need not here point out how
inconsistent with the Newtonian doctrine it was, to expect, as Göthe
expected, that the wall should be all over colored various colors.
{64}

[Note 23\9: _Vorlesungen_, p. 270.]

[Note 24\9: _Farbenlehre_, vol. ii. p. 678.]

Göthe not only adopted and strenuously maintained the opinion that
the Newtonian theory was false, but he framed a system of his own to
explain the phenomena of color. As a matter of curiosity, it may be
worth our while to state the nature of this system; although
undoubtedly it forms no part of the _progress_ of physical science.
Göthe's views are, in fact, little different from those of Aristotle
and Antonio de Dominis, though more completely and systematically
developed. According to him, colors arise when we see through a dim
medium ("ein trübes mittel"). Light in itself is colorless; but if
it be seen through a somewhat dim medium, it appears yellow; if the
dimness of the medium increases, or if its depth be augmented, we
see the light gradually assume a yellow-red color, which finally is
heightened to a ruby-red. On the other hand, if darkness is seen
through a dim medium which is illuminated by a light falling on it,
a blue color is seen, which becomes clearer and paler, the more the
dimness of the medium increases, and darker and fuller, as the
medium becomes more transparent; and when we come to "the smallest
degree of the purest dimness," we see the most perfect violet.[25\9]
In addition to this "doctrine of the dim medium," we have a second
principle asserted concerning refraction. In a vast variety of
cases, images are accompanied by "accessory images," as when we see
bright objects in a looking-glass.[26\9] Now, when an image is
displaced by refraction, the displacement is not complete, clear and
sharp, but incomplete, so that there is an accessory image along
with the principal one.[27\9] From these principles, the colors
produced by refraction in the image of a bright object on a dark
ground, are at once derivable. The accessory image is
semitransparent;[28\9] and hence that border of it which is pushed
forwards, is drawn from the dark over the bright, and there the
yellow appears; on the other hand, where the clear border laps over
the dark ground, the blue is seen;[29\9] and hence we easily see
that the image must appear red and yellow at one end, and blue and
violet at the other.

[Note 25\9: _Farbenlehre_, § 150, p. 151.]

[Note 26\9: Ib. § 223.]

[Note 27\9: Ib. § 227.]

[Note 28\9: Ib. § 238.]

[Note 29\9: Ib. § 239.]

We need not explain this system further, or attempt to show how
vague and loose, as well as baseless, are the notions and modes of
conception which it introduces. Perhaps it is not difficult to point
out the peculiarities in Göthe's intellectual character which led to
his singularly unphilosophical views on this subject. One important
{65} circumstance is, that he appears, like many persons in whom the
poetical imagination is very active, to have been destitute of the
talent and the habit of geometrical thought. In all probability, he
never apprehended clearly and steadily those relations of position
on which the Newtonian doctrine depends. Another cause of his
inability to accept the doctrine probably was, that he had conceived
the "composition" of colors in some way altogether different from
that which Newton understands by composition. What Göthe expected to
see, we cannot clearly collect; but we know, from his own statement,
that his intention of experimenting with a prism arose from his
speculations on the roles of coloring in pictures; and we can easily
see that any notion of the composition of colors which such
researches would suggest, would require to be laid aside, before he
could understand Newton's theory of the composition of light.

Other objections to Newton's theory, of a kind very different, have
been recently made by that eminent master of optical science, Sir
David Brewster. He contests Newton's opinion, that the colored rays
into which light is separated by refraction are altogether simple
and homogeneous, and incapable of being further analysed and
modified. For he finds that by passing such rays through colored
media (as blue glass for instance), they are not only absorbed and
transmitted in very various degrees, but that some of them have
their color altered; which effect he conceives as a further analysis
of the rays, one component color being absorbed and the other
transmitted.[30\9] And on this subject we can only say, as we have
before said, that Newton has incontestably and completely
established his doctrine, so far as analysis and decomposition _by
refraction_ are concerned; but that with regard to any other
analysis, which absorbing media or other agents may produce, we have
no right from his experiments to assert, that the colors of the
spectrum are incapable of _such_ decomposition. The whole subject of
the colors of objects, both opake and transparent, is still in
obscurity. Newton's conjectures concerning the causes of the colors
of natural bodies, appear to help us little; and his opinions on
that subject are to be separated altogether from the important step
which he made in optical science, by the establishment of the true
doctrine of refractive dispersion.

[Note 30\9: This latter fact has, however, been denied by other
experimenters.]

[2nd Ed.] [After a careful re-consideration of Sir D. Brewster's
asserted analysis of the solar light into three colors by means of
{66} absorbing media, I cannot consider that he has established his
point as an exception to Newton's doctrine. In the first place, the
analysis of light into _three_ colors appears to be quite arbitrary,
granting all his experimental facts. I do not see why, using other
media, he might not just as well have obtained other elementary
colors. In the next place, this cannot be called an _analysis_ in
the same sense as Newton's analysis, except the relation between the
two is shown. Is it meant that Newton's experiments prove nothing?
Or is Newton's conclusion allowed to be true of light which has not
been analysed by absorption? And where are we to find such light,
since the atmosphere absorbs? But, I must add, in the third place,
that with a very sincere admiration of Sir D. Brewster's skill as an
experimenter, I think his experiment requires, not only limitation,
but confirmation by other experimenters. Mr. Airy repeated the
experiments with about thirty different absorbing substances, and
could not satisfy himself that in any case they changed the color of
a ray of given refractive power. These experiments were described by
him at a meeting of the Cambridge Philosophical Society.]

We now proceed to the corrections which the next generation
introduced into the details of this doctrine.




CHAPTER IV.

DISCOVERY OF ACHROMATISM.


THE discovery that the laws of refractive dispersion of different
substances were such as to allow of combinations which neutralised
the dispersion without neutralizing the refraction, is one which has
hitherto been of more value to art than to science. The property has
no definite bearing, which has yet been satisfactorily explained,
upon the _theory_ of light; but it is of the greatest importance in
its application to the construction of telescopes; and it excited
the more notice, in consequence of the prejudices and difficulties
which for a time retarded the discovery.

Newton conceived that he had proved by experiment,[31\9] that light
{67} is white after refraction, when the emergent rays are parallel
to the incident, and in no other case. If this were so, the
production of colorless images by refracting media would be
impossible; and such, in deference to Newton's great authority, was
for some time the general persuasion. Euler[32\9] observed, that a
combination of lenses which does not color the image must be
possible, since we have an example of such a combination in the
human eye; and he investigated mathematically the conditions
requisite for such a result. Klingenstierna,[33\9] a Swedish
mathematician, also showed that Newton's rule could not be
universally true. Finally, John Dollond,[34\9] in 1757, repeated
Newton's experiment, and obtained an opposite result. He found that
when an object was seen through two prisms, one of glass and one of
water, of such angles that it did not appear displaced by
refraction, it was colored. Hence it followed that, without being
colored, the rays might be made to undergo refraction; and that
thus, substituting lenses for prisms, a combination might be formed,
which should produce an image without coloring it, and make the
construction of an _achromatic_ telescope possible.

[Note 31\9: _Opticks_, B. i. p. ii. Prop. 3.]

[Note 32\9: _Ac. Berlin._ 1747.]

[Note 33\9: _Swedish Trans._ 1754.]

[Note 34\9: _Phil. Trans._ 1758.]

Euler at first hesitated to confide in Dollond's experiments; but he
was assured of their correctness by Clairaut, who had throughout
paid great attention to the subject; and those two great
mathematicians, as well as D'Alembert, proceeded to investigate
mathematical formulæ which might be useful in the application of the
discovery. The remainder of the deductions, which were founded upon
the laws of dispersion of various refractive substances, belongs
rather to the history of art than of science. Dollond used at first,
for his achromatic object-glass, a lens of crown-glass, and one of
flint-glass. He afterwards employed two lenses of the former
substance, including between them one of the latter, adjusting the
curvatures of his lenses in such a way as to correct the
imperfections arising from the spherical form of the glasses, as
well as the fault of color. Afterwards, Blair used fluid media along
with glass lenses, in order to produce improved object-glasses. This
has more recently been done in another form by Mr. Barlow. The
inductive laws of refraction being established, their results have
been deduced by various mathematicians, as Sir J. Herschel and
Professor Airy among ourselves, who have simplified and extended the
investigation of the formulæ which determine the best combination of
lenses in the object-glasses and eye-glasses of {68} telescopes,
both with reference to spherical and to _chromatic_ aberrations.

According to Dollond's discovery, the colored spectra produced by
prisms of two substances, as flint-glass and crown-glass, would be
of the same length when the refraction was different. But a question
then occurred: When the whole distance from the red to the violet in
one spectrum was the same as the whole distance in the other, were
the intermediate colors, yellow, green, &c., in corresponding places
in the two? This point also could not be determined any otherwise
than by experiment. It appeared that such a correspondence did not
exist; and, therefore, when the extreme colors were corrected by
combinations of the different media, there still remained an
uncorrected residue of color arising from the rest of the spectrum.
This defect was a consequence of the property, that the spectra
belonging to different media were not divided in the _same ratio_ by
the same colors, and was hence termed the _irrationality_ of the
spectrum. By using three prisms, or three lenses, three colors may
be made to coincide instead of two, and the effects of this
irrationality greatly diminished.

For the reasons already mentioned, we do not pursue this subject
further,[35\9] but turn to those optical facts which finally led to
a great and comprehensive theory.

[Note 35\9: The discovery of the _fixed lines_ in the spectrum, by
Wollaston and Fraunhofer, has more recently supplied the means of
determining, with extreme accuracy, the corresponding portions of
the spectrum in different refracting substances.]

[2nd Ed.] [Mr. Chester More Hall, of More Hall, in Essex, is said to
have been led by the study of the human eye, which he conceived to
be achromatic, to construct achromatic telescopes as early as 1729.
Mr. Hall, however, kept his invention a secret. David Gregory, in
his _Catoptrics_ (1713), had suggested that it would perhaps be an
improvement of telescopes, if, in imitation of the human eye, the
object-glass were composed of different media. _Encyc. Brit._ art.
_Optics_.

It is said that Clairaut first discovered the irrationality of the
colored spaces in the spectrum. In consequence of this
irrationality, it follows that when two refracting media are so
combined as to correct each other's extreme dispersion, (the
separation of the red and violet rays,) this first step of
correction still leaves a residue of {69} coloration arising from
the unequal dispersion of the intermediate rays (the green, &c.).
These _outstanding_ colors, as they were termed by Professor
Robison, form the residual, or _secondary_ spectrum.

Dr. Blair, by very ingenious devices, succeeded in producing an
object-glass, corrected by a fluid lens, in which this aberration of
color was completely corrected, and which performed wonderfully well.

The dispersion produced by a prism may be corrected by another prism
of the _same substance_ and of a different angle. In this case also
there is an irrationality in the colored spaces, which prevents the
correction of color from being complete; and hence, a new residuary
spectrum, which has been called the _tertiary_ spectrum, by Sir
David Brewster, who first noticed it.

I have omitted, in the notice of discoveries respecting the
spectrum, many remarkable trains of experimental research, and
especially the investigations respecting the power of various media
to absorb the light of different parts of the spectrum, prosecuted
by Sir David Brewster with extraordinary skill and sagacity. The
observations are referred to in chapter iii. Sir John Herschel,
Prof. Miller, Mr. Daniel, Dr. Faraday, and Mr. Talbot, have also
contributed to this part of our knowledge.]




CHAPTER V.

DISCOVERY OF THE LAWS OF DOUBLE REFRACTION.


THE laws of refraction which we have hitherto described, were simple
and uniform, and had a symmetrical reference to the surface of the
refracting medium. It appeared strange to men, when their attention
was drawn to a class of phenomena in which this symmetry was
wanting, and in which a refraction took place which was not even in
the plane of incidence. The subject was not unworthy the notice and
admiration it attracted; for the prosecution of it ended in the
discovery of the general laws of light. The phenomena of which I now
speak, are those exhibited by various kinds of crystalline bodies;
but observed for a long time in one kind only, namely, the
rhombohedral calc-spar; or, as it was usually termed, from the
country which supplied the largest and clearest crystals, _Iceland
spar_. These {70} rhombohedral crystals are usually very smooth and
transparent, and often of considerable size; and it was observed, on
looking through them, that all objects appeared double. The
phenomena, even as early as 1669, had been considered so curious,
that Erasmus Bartholin published a work upon them at
Copenhagen,[36\9] (_Experimenta Crystalli Islandici_, Hafniæ, 1669.)
He analysed the phenomena into their laws, so far as to discover
that one of the two images was produced by refraction after the
usual rule, and the other by an unusual refraction. This latter
refraction Bartholin found to vary in different positions; to be
regulated by a line parallel to the sides of the rhombohedron; and
to be greatest in the direction of a line bisecting two of the
angles of the rhombic face of the crystal.

[Note 36\9: Priestley's _Optics_, p. 550.]

These rules were exact as far as they went; and when we consider how
geometrically complex the law is, which really regulates the unusual
or extraordinary refraction;--that Newton altogether mistook it, and
that it was not verified till the experiments of Haüy and Wollaston
in our own time;--we might expect that it would not be soon or
easily detected. But Huyghens possessed a key to the secret, in the
theory, which he had devised, of the propagation of light by
undulations, and which he conceived with perfect distinctness and
correctness, so far as its application to these phenomena is
concerned. Hence he was enabled to lay down the law of the phenomena
(the only part of his discovery which we have here to consider),
with a precision and success which excited deserved admiration, when
the subject, at a much later period, regained its due share of
attention. His Treatise was written[37\9] in 1678, but not published
till 1690.

[Note 37\9: See his _Traité de la Lumière_. Preface.]

The laws of the _ordinary_ and the _extraordinary_ refraction in
Iceland spar are related to each other; they are, in fact, similar
constructions, made, in the one case, by means of an imaginary
sphere, in the other, by means of a spheroid; the spheroid being of
such oblateness as to suit the rhombohedral form of the crystal, and
the axis of the spheroid being the axis of symmetry of the crystal.
Huyghens followed this general conception into particular positions
and conditions; and thus obtained rules, which he compared with
observation, for cutting the crystal and transmitting the rays in
various manners. "I have examined in detail," says he,[38] "the
properties of the {71} extraordinary refraction of this crystal, to
see if each phenomenon which is deduced from theory, would agree
with what is really observed. And this being so, it is no slight
proof of the truth of our suppositions and principles; but what I am
going to add here confirms them still more wonderfully; that is, the
different modes of cutting this crystal, in which the surfaces
produced give rise to refractions exactly such as they ought to be,
and as I had foreseen them, according to the preceding theory."

[Note 38\9: See Maseres's _Tracts on Optics_, p. 250; or Huyghens,
_Tr. sur la Lum._ ch. v. Art. 43.]

Statements of this kind, coming from a philosopher like Huyghens,
were entitled to great confidence; Newton, however, appears not to
have noticed, or to have disregarded them. In his _Opticks_, he
gives a rule for the extraordinary refraction of Iceland spar which
is altogether erroneous, without assigning any reason for rejecting
the law published by Huyghens; and, so far as appears, without
having made any experiments of his own. The Huyghenian doctrine of
double refraction fell, along with his theory of undulations, into
temporary neglect, of which we shall have hereafter to speak. But in
1788, Haüy showed that Huyghens's rule agreed much better than
Newton's with the phenomena: and in 1802, Wollaston, applying a
method of his own for measuring refraction, came to the same result.
"He made," says Young,[39\9] "a number of accurate experiments with
an apparatus singularly well calculated to examine the phenomena,
but could find no general principle to connect them, until the work
of Huyghens was pointed out to him." In 1808, the subject of double
refraction was proposed as a prize-question by the French Institute;
and Malus, whose Memoir obtained the prize, says, "I began by
observing and measuring a long series of phenomena on natural and
artificial faces of Iceland spar. Then, testing by means of these
observations the different laws proposed up to the present time by
physical writers, I was struck with the admirable agreement of the
law of Huyghens with the phenomena, and I was soon convinced that it
is really the law of nature." Pursuing the consequences of the law,
he found that it satisfied phenomena which Huyghens himself had not
observed. From this time, then, the truth of the Huyghenian law was
universally allowed, and soon afterwards, the theory by which it had
been suggested was generally received.

[Note 39\9: _Quart. Rev._ 1809, Nov. p. 338.]

The property of double refraction had been first studied only in
Iceland spar, in which it is very obvious. The same property
belongs, {72} though less conspicuously, to many other kinds of
crystals. Huyghens had noticed the same fact in rock-crystal;[40\9]
and Malus found it to belong to a large list of bodies besides; for
instance, arragonite, sulphate of lime, of baryta, of strontia, of
iron; carbonate of lead; zircon, corundum, cymophane, emerald,
euclase, felspar, mesotype, peridote, sulphur, and mellite. Attempts
were made, with imperfect success, to reduce all these to the law
which had been established for Iceland spar. In the first instance,
Malus took for granted that the extraordinary refraction depended
always upon an oblate spheroid; but M. Biot[41\9] pointed out a
distinction between two classes of crystals in which this spheroid
was oblong and oblate respectively, and these he called _attractive_
and _repulsive_ crystals. With this correction, the law could be
extended to a considerable number of cases; but it was afterwards
proved by Sir D. Brewster's discoveries, that even in this form, it
belonged only to substances of which the crystallization has
relation to a single axis of symmetry, as the rhombohedron, or the
square pyramid. In other cases, as the rhombic prism, in which the
form, considered with reference to its crystalline symmetry, is
_biaxal_, the law is much more complicated. In that case, the sphere
and the spheroid, which are used in the construction for uniaxal
crystals, transform themselves into the two successful convolutions
of a single continuous curve surface; neither of the two rays
follows the law of ordinary refraction; and the formula which
determines their position is very complex. It is, however, capable
of being tested by measures of the refractions of crystals cut in a
peculiar manner for the purpose, and this was done by MM. Fresnel
and Arago. But this complex law of double refraction was only
discovered through the aid of the theory of a luminiferous ether,
and therefore we must now return to the other facts which led to
such a theory.

[Note 40\9: _ Traité de la Lumière_, ch. v. Art. 20]

[Note 41\9: Biot, _Traité de Phys._ iii. 330.]




CHAPTER VI.

DISCOVERY OF THE LAWS OF POLARIZATION.


IF the Extraordinary Refraction of Iceland spar had appeared
strange, another phenomenon was soon noticed in the same {73}
substance, which appeared stranger still, and which in the sequel
was found to be no less important. I speak of the facts which were
afterwards described under the term _Polarization_. Huyghens was the
discoverer of this class of facts. At the end of the treatise which
we have already quoted, he says,[42\9] "Before I quit the subject of
this crystal, I will add one other marvellous phenomenon, which I
have discovered since writing the above; for though hitherto I have
not been able to find out its cause, I will not, on that account,
omit pointing it out, that I may give occasion to others to examine
it." He then states the phenomena; which are, that when two
rhombohedrons of Iceland spar are in parallel positions, a ray
doubly refracted by the first, is not further divided when it falls
on the second: the ordinarily refracted ray is ordinarily refracted
_only_, and the extraordinary ray is only extraordinarily refracted
by the second crystal, neither ray being doubly refracted. The same
is still the case, if the two crystals have their _principal planes_
parallel, though they themselves are not parallel. But if the
principal plane of the second crystal be perpendicular to that of
the first, the reverse of what has been described takes place; the
ordinarily refracted ray of the first crystal suffers, at the
second, extraordinary refraction _only_, and the extraordinary ray
of the first suffers ordinary refraction only at the second. Thus,
in each of these positions, the double refraction of each ray at the
second crystal is reduced to single refraction, though in a
different manner in the two cases. But in any other position of the
crystals, each ray, produced by the first, is doubly refracted by
the second, so as to produce four rays.

[Note 42\9: _Tr. Opt._ p. 252.]

A step in the right conception of these phenomena was made by
Newton, in the second edition of his _Opticks_ (1717). He
represented them as resulting from this;--that the rays of light
have "sides," and that they undergo the ordinary or extraordinary
refraction, according as these sides are parallel to the principal
plane of the crystal, or at right angles to it (Query 26). In this
way, it is clear, that those rays which, in the first crystal, had
been selected for extraordinary refraction, because their sides were
perpendicular to the principal plane, would all suffer extraordinary
refraction at the second crystal for the same reason, if its
principal plane were parallel to that of the first; and would all
suffer ordinary refraction, if the principal plane of the second
crystal were perpendicular to that of the first, and {74}
consequently parallel to the sides of the refracted ray. This view
of the subject includes some of the leading features of the case,
but still leaves several considerable difficulties.

No material advance was made in the subject till it was taken up by
Malus,[43\9] along with the other circumstances of double refraction,
about a hundred years afterwards. He verified what had been observed
by Huyghens and Newton, on the subject of the variations which light
thus exhibits; but he discovered that this modification, in virtue of
which light undergoes the ordinary, or the extraordinary, refraction,
according to the position of the plane of the crystal, may be
impressed upon it many other ways. One part of this discovery was made
accidentally.[44\9] In 1808, Malus happened to be observing the light
of the setting sun, reflected from the windows of the Luxembourg,
through a rhombohedron of Iceland spar; and he observed that in
turning round the crystal, the two images varied in their intensity.
Neither of the images completely vanished, because the light from the
windows was not properly modified, or, to use the term which Malus
soon adopted, was not completely _polarized_. The complete
polarization of light by reflection from glass, or any other
transparent substance, was found to take place at a certain definite
angle, different for each substance. It was found also that in all
crystals in which double refraction occurred, the separation of the
refracted rays was accompanied by polarization; the two rays, the
ordinary and the extraordinary, being always polarized _oppositely_,
that is, in planes at right angles to each other. The term _poles_,
used by Malus, conveyed nearly the same notion as the term _sides_
which had been employed by Newton, with the additional conception of a
property which appeared or disappeared according as the _poles_ of the
particles were or were not in a certain direction; a property thus
resembling the _polarity_ of magnetic bodies. When a spot of polarized
light is looked at through a transparent crystal of Iceland spar, each
of the two images produced by the double refraction varies in
brightness as the crystal is turned round. If, for the sake of
example, we suppose the crystal to be turned round in the direction of
the points of the compass, N, E, S, W, and if one image be brightest
when the crystal marks N and S, it will disappear when the crystal
marks E and W: and on the contrary, the second image will vanish when
the crystal marks N and S, {75} and will be brightest when the crystal
marks E and W. The first of these images is polarized _in the plane_
NS passing through the ray, and the second _in the plane_ EW,
perpendicular to the other. And these rays are _oppositely_ polarized.
It was further found that whether the ray were polarized by reflection
from glass, or from water, or by double refraction, the modification
of light so produced, or the nature of the polarization, was identical
in all these cases;--that the alternatives of ordinary and
extraordinary refraction and non-refraction, were the same, by
whatever crystal they were tested, or in whatever manner the
polarization had been impressed upon the light; in short, that the
property, when once acquired, was independent of everything except the
sides or _poles_ of the ray; and thus, in 1811, the term
"polarization" was introduced.[45\9]

[Note 43\9: Malus, _Th. de la Doub. Réf._ p. 296.]

[Note 44\9: Arago, art. _Polarization_, Supp. _Enc. Brit._]

[Note 45\9: _Mém. Inst._ 1810.]

This being the state of the subject, it became an obvious question,
by what other means, and according to what laws, this property was
communicated. It was found that some crystals, instead of giving, by
double refraction, two images oppositely polarized, give a single
polarized image. This property was discovered in the agate by Sir D.
Brewster, and in tourmaline by M. Biot and Dr. Seebeck. The latter
mineral became, in consequence, a very convenient part of the
apparatus used in such observations. Various peculiarities bearing
upon this subject, were detected by different experimenters. It was
in a short time discovered, that light might be polarized by
refraction, as well as by reflection, at the surface of
uncrystallized bodies, as glass; the plane of polarization being
perpendicular to the plane of refraction; further, that when a
portion of a ray of light was polarized by reflection, a
corresponding portion was polarized by transmission, the planes of
the two polarizations being at right angles to each other. It was
found also that the polarization which was incomplete with a single
plate, either by reflection or refraction, might be made more and
more complete by increasing the number of plates.

Among an accumulation of phenomena like this, it is our business to
inquire what general laws were discovered. To make such discoveries
without possessing the general theory of the facts, required no
ordinary sagacity and good fortune. Yet several laws were detected
at this stage of the subject. Malus, in 1811, obtained the important
generalization that, whenever we obtain, by any means, a polarized
ray of light, we produce also another ray, polarized in a contrary
{76} direction; thus when reflection gives a polarized ray, the
companion-ray is refracted polarized oppositely, along with a
quantity of unpolarized light. And we must particularly notice _Sir
D. Brewster's rule_ for the _polarizing angle_ of different bodies.

Malus[46\9] had said that the angle of reflection from transparent
bodies which most completely polarizes the reflected ray, does not
follow any discoverable rule with regard to the order of refractive
or dispersive powers of the substances. Yet the rule was in reality
very simple. In 1815, Sir D. Brewster stated[47\9] as the law, which
in all cases determines this angle, that "the index of refraction is
the tangent of the angle of polarization." It follows from this,
that the polarization takes place when the reflected and refracted
rays are at right angles to each other. This simple and elegant rule
has been fully confirmed by all subsequent observations, as by those
of MM. Biot and Seebeck; and must be considered one of the happiest
and most important discoveries of the laws of phenomena in Optics.

[Note 46\9: _Mém. Inst._ 1810.]

[Note 47\9: _Phil. Trans._ 1815.]

The rule for polarization by one reflection being thus discovered,
tentative formulæ were proposed by Sir D. Brewster and M. Biot, for
the cases in which several reflections or refractions take place.
Fresnel also in 1817 and 1818, traced the effect of reflection in
modifying the direction of polarization, which Malus had done
inaccurately in 1810. But the complexity of the subject made all
such attempts extremely precarious, till the theory of the phenomena
was understood, a period which now comes under notice. The laws
which we have spoken of were important materials for the
establishment of the theory; but in the mean time, its progress at
first had been more forwarded by some other classes of facts, of a
different kind, and of a longer standing notoriety, to which we must
now turn our attention.




CHAPTER VII.

DISCOVERY OF THE LAWS OF THE COLOURS OF THIN PLATES.


THE facts which we have now to consider are remarkable, inasmuch as
the colours are produced merely by the smallness of dimensions of
the bodies employed. The light is not analysed by any peculiar {77}
property of the substances, but dissected by the minuteness of their
parts. On this account, these phenomena give very important
indications of the real structure of light; and at an early period,
suggested views which are, in a great measure, just.

Hooke appears to be the first person who made any progress in
discovering the laws of the colors of thin plates. In his
_Micrographia_, printed by the Royal Society in 1664, he describes,
in a detailed and systematic manner, several phenomena of this kind,
which he calls "fantastical colors." He examined them in _Muscovy
glass_ or mica, a transparent mineral which is capable of being
split into the exceedingly thin films which are requisite for such
colors; he noticed them also in the fissures of the same substance,
in bubbles blown of water, rosin, gum, glass; in the films on the
surface of tempered steel; between two plane pieces of glass; and in
other cases. He perceived also,[48\9] that the production of each
color required a plate of determinate thickness, and he employed
this circumstance as one of the grounds of his theory of light.

[Note 48\9: _Micrographia_, p. 53.]

Newton took up the subject where Hooke had left it; and followed it
out with his accustomed skill and clearness, in his _Discourse on
Light and Colors_, communicated to the Royal Society in 1675. He
determined, what Hooke had not ascertained, the thickness of the
film which was requisite for the production of each color; and in
this way explained, in a complete and admirable manner, the colored
rings which occur when two lenses are pressed together, and the
_scale of color_ which the rings follow; a step of the more
consequence, as the same scale occurs in many other optical
phenomena.

It is not our business here to state the hypothesis with regard to
the properties of light which Newton founded on these facts;--the
"fits of easy transmission and reflection." We shall see hereafter
that his attempted induction was imperfect; and his endeavor to
account, by means of the laws of thin plates, for the colors of
natural bodies, is altogether unsatisfactory. But notwithstanding
these failures in the speculations on this subject, he did make in
it some very important steps; for he clearly ascertained that when
the thickness of the plate was about 1⁄178000th of an inch, or three
times, five times, seven times that magnitude, there was a bright
color produced; but blackness, when the thickness was exactly
intermediate between those magnitudes. He found, also, that the
thicknesses which gave red and {78} violet[49\9] were as fourteen to
nine; and the intermediate colors of course corresponded to
intermediate thicknesses, and therefore, in his apparatus,
consisting of two lenses pressed together, appeared as rings of
intermediate sizes. His mode of confirming the rule, by throwing
upon this apparatus differently colored homogeneous light, is
striking and elegant. "It was very pleasant," he says, "to see the
rings gradually swell and contract as the color of the light was
changed."

[Note 49\9: _Opticks_, p. 184.]

It is not necessary to enter further into the detail of these
phenomena, or to notice the rings seen by transmission, and other
circumstances. The important step made by Newton in this matter was,
the showing that the rays of light, in these experiments, as they
pass onwards go periodically through certain cycles of modification,
each period occupying nearly the small fraction of an inch mentioned
above; and this interval being different for different colors.
Although Newton did not correctly disentangle the conditions under
which this periodical character is manifestly disclosed, the
discovery that, under some circumstances, such a periodical
character does exist, was likely to influence, and did influence,
materially and beneficially, the subsequent progress of Optics
towards a connected theory.

We must now trace this progress; but before we proceed to this task,
we will briefly notice a number of optical phenomena which had been
collected, and which waited for the touch of sound theory to
introduce among them that rule and order which mere observation had
sought for in vain.




CHAPTER VIII.

ATTEMPTS TO DISCOVER THE LAWS OF OTHER PHENOMENA.


THE phenomena which result from optical combinations, even of a
comparatively simple nature, are extremely complex. The theory which
is now known accounts for these results with the most curious
exactness, and points out the laws which pervade the apparent
confusion; but without this key to the appearances, it was scarcely
possible that any rule or order should be detected. The undertaking
was of {79} the same kind as it would have been, to discover all the
inequalities of the moon's motion without the aid of the doctrine of
gravity. We will enumerate some of the phenomena which thus employed
and perplexed the cultivators of optics.

The fringes of shadows were one of the most curious and noted of
such classes of facts. These were first remarked by Grimaldi[50\9]
(1665), and referred by him to a property of light which he called
_Diffraction_. When shadows are made in a dark room, by light
admitted through a very small hole, these appearances are very
conspicuous and beautiful. Hooke, in 1672, communicated similar
observations to the Royal Society, as "a new property of light not
mentioned by any optical writer before;" by which we see that he had
not heard of Grimaldi's experiments. Newton, in his _Opticks_,
treats of the same phenomena, which he ascribes to the _inflexion_
of the rays of light. He asks (Qu. 3), "Are not the rays of light,
in passing by the edges and sides of bodies, bent several times
backward and forward with a motion like that of an eel? And do not
the three fringes of colored light in shadows arise from three such
bendings?" It is remarkable that Newton should not have noticed,
that it is impossible, in this way, to account for the facts, or
even to express their laws; since the light which produces the
fringes must, on this theory, be propagated, even after it leaves
the neighborhood of the opake body, in curves, and not in straight
lines. Accordingly, all who have taken up Newton's notion of
inflexion, have inevitably failed in giving anything like an
intelligible and coherent character to these phenomena. This is, for
example, the case with Mr. (now Lord) Brougham's attempts in the
_Philosophical Transactions_ for 1796. The same may be said of other
experimenters, as Mairan[51\9] and Du Four,[52\9] who attempted to
explain the facts by supposing an atmosphere about the opake body.
Several authors, as Maraldi,[53\9] and Comparetti,[54\9] repeated or
varied these experiments in different ways.

[Note 50\9: _Physico-Mathesis, de Lumine, Coloribus et Iride._
Bologna, 1665.]

[Note 51\9: _Ac. Par._ 1738.]

[Note 52\9: _Mémoires Présentés_, vol. v.]

[Note 53\9: _Ac. Par._ 1723.]

[Note 54\9: _Observationes Opticæ de Luce Inflexâ et Coloribus._
Padua, 1787.]

Newton had noticed certain rings of color produced by a glass
speculum, which he called "colors of thick plates," and which he
attempted to connect with the colors of thin plates. His reasoning
is by no means satisfactory; but it was of use, by pointing out this
as a case in which his "fits" (the small periods, or cycles in the
rays of light, of {80} which we have spoken) continued to occur for
a considerable length of the ray. But other persons, attempting to
repeat his experiments, confounded with them extraneous phenomena of
other kinds; as the Duc de Chaulnes, who spread muslin before his
mirror,[55\9] and Dr. Herschel, who scattered hair-powder before
his.[56\9] The colors produced by the muslin were those belonging to
shadows of _gratings_, afterwards examined more successfully by
Fraunhofer, when in possession of the theory. We may mention here
also the colors which appear on finely-striated surfaces, and on
mother-of-pearl, feathers, and similar substances. These had been
examined by various persons (as Boyle, Mazeas, Lord Brougham), but
could still, at this period, be only looked upon as insulated and
lawless facts.

[Note 55\9: _Ac. Par._ 1755.]

[Note 56\9: _Phil. Trans._ 1807.]




CHAPTER IX.

DISCOVERY OF THE LAWS OF PHENOMENA OF DIPOLARIZED LIGHT.


BESIDES the above-mentioned perplexing cases of colors produced by
common light, cases of _periodical colors produced by polarized
light_ began to be discovered, and soon became numerous. In August,
1811, M. Arago communicated to the Institute of France an account of
colors seen by passing polarized light through mica, and
_analysing_[57\9] it with a prism of Iceland spar. It is remarkable
that the light which produced the colors in this case was the light
polarized by the sky, a cause of polarization not previously known.
The effect which the mica thus produced was termed
_depolarization_;--not a very happy term, since the effect is not
the destruction of the polarization, but the combination of a new
polarizing influence with the former. The word _dipolarization_,
which has since been proposed, is a much more appropriate
expression. Several other curious phenomena of the same kind were
observed in quartz, and in flint-glass. M. Arago was not able to
reduce these phenomena to laws, but he had a full conviction of
their value, and ventures to class them with the great steps in {81}
this part of optics. "To Bartholin we owe the knowledge of double
refraction; to Huyghens, that of the accompanying polarization; to
Malus, polarization by reflection; to Arago, depolarization." Sir D.
Brewster was at the same time engaged in a similar train of
research; and made discoveries of the same nature, which, though not
published till some time after those of Arago, were obtained without
a knowledge of what had been done by him. Sir D. Brewster's
_Treatise on New Philosophical Instruments_, published in 1813,
contains many curious experiments on the "depolarizing" properties
of minerals. Both these observers noticed the changes of color which
are produced by changes in the position of the ray, and the
alternations of color in the two oppositely polarized images; and
Sir D. Brewster discovered that, in topaz, the phenomena had a
certain reference to lines which he called the _neutral_ and
_depolarizing_ axes. M. Biot had endeavored to reduce the phenomena
to a law; and had succeeded so far, that he found that in the plates
of sulphate of lime, the place of the tint, estimated in Newton's
_scale_ (see _ante_, chap. vii.), was as the square of the sine of
the inclination. But the laws of these phenomena became much more
obvious when they were observed by Sir D. Brewster with a larger
field of view.[58\9] He found that the colors of topaz, under the
circumstances now described, exhibited themselves in the form of
elliptical rings, crossed by a black bar, "the most brilliant class
of phenomena," as he justly says, "in the whole range of optics." In
1814, also, Wollaston observed the circular rings with a black
cross, produced by similar means in calc-spar; and M. Biot, in 1815,
made the same observation. The rings in several of these cases were
carefully measured by M. Biot and Sir D. Brewster, and a great mass
of similar phenomena was discovered. These were added to by various
persons, as M. Seebeck, and Sir John Herschel.

[Note 57\9: The prism of Iceland spar produces the colors by
separating the transmitted rays according to the laws of double
refraction. Hence it is said to _analyse_ the light.]

[Note 58\9: _Phil. Trans._ 1814.]

Sir D. Brewster, in 1818, discovered a general relation between the
crystalline form and the optical properties, which gave an
incalculable impulse and a new clearness to these researches. He
found that there was a correspondence between the degree of symmetry
of the optical phenomena and the crystalline form; those crystals
which are uniaxal in the crystallographical sense, are also uniaxal
in their optical properties, and give circular rings; those which
are of other forms are, generally speaking, biaxal; they give oval
and knotted _isochromatic_ lines, with two _poles_. He also
discovered a rule for the tint at each point {82} in such cases; and
thus explained, so far as an empirical law of phenomena went, the
curious and various forms of the colored curves. This law, when
simplified by M. Biot,[59\9] made the tint proportional to the
product of the distances of the point from the two poles. In the
following year, Sir J. Herschel confirmed this law by showing, from
actual measurement, that the curve of the isochromatic lines in
these cases was the curve termed the _lemniscata_, which has, for
each point, the product of the distances from two fixed poles equal
to a constant quantity.[60\9] He also reduced to rule some other
apparent anomalies in phenomena of the same class.

[Note 59\9: _Mém. Inst._ 1818, p. 192.]

[Note 60\9: _Phil. Trans._ 1819.]

M. Biot, too, gave a rule for the directions of the planes of
polarization of the two rays produced by double refraction in biaxal
crystals, a circumstance which has a close bearing upon the
phenomena of dipolarization. His rule was, that the one plane of
polarization bisects the dihedral angle formed by the two planes
which pass through the optic axes, and that the other is
perpendicular to such a plane. When, however, Fresnel had discovered
from the theory the true laws of double refraction, it appeared that
the above rule is inaccurate, although in a degree which observation
could hardly detect without the aid of theory.[61\9]

[Note 61\9:  Fresnel, _Mém. Inst._ 1827, p. 162.]

There were still other classes of optical phenomena which attracted
notice; especially those which are exhibited by plates of quartz cut
perpendicular to the axis. M. Arago had observed, in 1811, that this
substance produced a _twist_ of the plane of polarization to the right
or left hand, the amount of this twist being different for different
colors; a result which was afterwards traced to a modification of
light different both from common and from polarized light, and
subsequently known as _circular polarization_. Sir J. Herschel had
the good fortune and sagacity to discover that this peculiar kind of
polarization in quartz was connected with an equally peculiar
modification of crystallization, the _plagihedral_ faces which are
seen, on some crystals, obliquely disposed, and, as it were,
following each other round the crystal from left to right, or from
right to left. Sir J. Herschel found that the _right-handed_ or
_left-handed_ character of the circular polarization corresponded,
in all cases, to that of the crystal.

In 1815, M. Biot, in his researches on the subject of circular
polarization, was led to the unexpected and curious discovery, that
this {83} property which seemed to require for its very conception a
crystalline structure in the body, belonged nevertheless to several
fluids, and in different directions for different fluids. Oil of
turpentine, and an essential oil of laurel, gave the plane of
polarization a rotation to the left hand; oil of citron, syrup of
sugar, and a solution of camphor, gave a rotation to the right hand.
Soon after, the like discovery was made independently by Dr.
Seebeck, of Berlin.

It will easily be supposed that all those brilliant phenomena could
not be observed, and the laws of many of the phenomena discovered,
without attempts on the part of philosophers to combine them all
under the dominion of some wide and profound theory. Endeavors to
ascend from such knowledge as we have spoken of, to the general
theory of light, were, in fact, made at every stage of the subject,
and with a success which at last won almost all suffrages. We are
now arrived at the point at which we are called upon to trace the
history of this theory; to pass from the laws of phenomena to their
causes;--from Formal to Physical Optics. The undulatory theory of
light, the only discovery which can stand by the side of the theory
of universal gravitation, as a doctrine belonging to the same order,
for its generality, its fertility, and its certainty, may properly
be treated of with that ceremony which we have hitherto bestowed
only on the great advances of astronomy; and I shall therefore now
proceed to speak of the Prelude to this epoch, the Epoch itself, and
its Sequel, according to the form of the preceding Book which treats
of astronomy.

[2nd Ed.] [I ought to have stated, in the beginning of this chapter,
that Malus discovered the depolarization of _white light_ in 1811.
He found that a pencil of light which, being polarized, refused to
be reflected by a surface properly placed, recovered its power of
being reflected after being transmitted through certain crystals and
other transparent bodies. Malus intended to pursue this subject,
when his researches were terminated by his death, Feb. 7, 1812. M.
Arago, about the same time, announced his important discovery of the
depolarization of _colors_ by crystals.

I may add, to what is above said of M. Biot's discoveries respecting
the circular polarizing power of fluids, that he pursued his
researches so as to bring into view some most curious relations
among the elements of bodies. It appeared that certain substances,
as sugar of canes, had a right-handed effect, and certain other
substances, as gum, a left-handed effect; and that the molecular
value of this effect was not altered by dilution. It appeared also
that a certain element of the {84} substance of fruits, which had
been supposed to be gum, and which is changed into sugar by the
operation of acids, is not gum, and has a very energetic
right-handed effect. This substance M. Biot called _dextrine_, and
he has since traced its effects into many highly curious and
important results.**]



{{85}}
PHYSICAL OPTICS.




CHAPTER X.

PRELUDE TO THE EPOCH OF YOUNG AND FRESNEL.


BY _Physical_ Optics we mean, as has already been stated, the
theories which explain optical phenomena on mechanical principles.
No such explanation could be given till true mechanical principles
had been obtained; and, accordingly, we must date the commencement
of the essays towards physical optics from Descartes, the founder of
the modern mechanical philosophy. His hypothesis concerning light
is, that it consists of small particles emitted by the luminous
body. He compares these particles to balls, and endeavors to
explain, by means of this comparison, the laws of reflection and
refraction.[62\9] In order to account for the production of colors
by refraction, he ascribes to these balls an alternating rotatory
motion.[63\9] This form of the _emission theory_, was, like most of
the physical speculations of its author, hasty and gratuitous; but
was extensively accepted, like the rest of the Cartesian doctrines,
in consequence of the love which men have for sweeping and simple
dogmas, and deductive reasonings from them. In a short time,
however, the rival optical _theory of undulations_ made its
appearance. Hooke in his _Micrographia_ (1664) propounds it, upon
occasion of his observations, already noticed, (chap. **vii.,) on the
colors of thin plates. He there asserts[64\9] light to consist in a
"quick, short, vibrating motion," and that it is propagated in a
homogeneous medium, in such a way that "every pulse or vibration of
the luminous body will generate a sphere, which will continually
increase and grow bigger, just after the same manner (though
indefinitely swifter) as the waves or rings on the surface of water
do swell into bigger and bigger circles about a point in it."[65\9]
He applies this to the explanation of refraction, {86} by supposing
that the rays in a denser medium move more easily, and hence that
the pulses become oblique; a far less satisfactory and consistent
hypothesis than that of Huyghens, of which we shall next have to
speak. But Hooke has the merit of having also combined with his
theory, though somewhat obscurely, the _Principle of Interferences_,
in the application which he makes of it to the colors of thin
plates. Thus[66\9] he supposes the light to be reflected at the
first surface of such plates; and he adds, "after two refractions
and one reflection (from the second surface) there is propagated a
kind of fainter ray," which comes behind the other reflected pulse;
"so that hereby (the surfaces AB and EF being so near together that
the eye cannot discriminate them from one), this compound or
duplicated pulse does produce on the retina the sensation of a
yellow." The reason for the production of this particular color, in
the case of which he here speaks, depends on his views concerning
the kind of pulses appropriate to each color; and, for the same
reason, when the thickness is different, he finds that the result
will be a red or a green. This is a very remarkable anticipation of
the explanation ultimately given of these colors; and we may observe
that if Hooke could have measured the thickness of his thin plates,
he could hardly have avoided making considerable progress in the
doctrine of interferences.

[Note 62\9: _Diopt._ c. ii. 4.]

[Note 63\9: _Meteor._ c. viii. 6.]

[Note 64\9: _Micrographia_, p. 56.]

[Note 65\9: _Micrographia_, p. 57.]

[Note 66\9: _Micrographia_, p. 66.]

But the person who is generally, and with justice, looked upon as
the great author of the undulatory theory, at the period now under
notice, is Huyghens, whose _Traité de la Lumière_, containing a
developement of his theory, was written in 1678, though not
published till 1690. In this work he maintained, as Hooke had done,
that light consists in undulations, and expands itself spherically,
nearly in the same manner as sound does; and he referred to the
observations of Römer on Jupiter's satellites, both to prove that
this difference takes place successively, and to show its exceeding
swiftness. In order to trace the effect of an undulation, Huyghens
considers that every point of a wave diffuses its motion in all
directions; and hence he draws the conclusion, so long looked upon
as the turning-point of the combat between the rival theories, that
the light will not be _diffused_ beyond the rectilinear space, when
it passes through an aperture; "for," says he,[67\9] "although the
_partial_ waves, produced by the particles comprised in the
aperture, do diffuse themselves beyond the rectilinear space, these
waves do not _concur_ anywhere except in front of the {87}
aperture." He rightly considers this observation as of the most
essential value. "This," he says, "was not known by those who began
to consider the waves of light, among whom are Mr. Hooke in his
_Micrography_, and Father Pardies; who, in a treatise of which he
showed me a part, and which he did not live to finish, had
undertaken to prove, by these waves, the effects of reflection and
refraction. But the principal foundation, which consists in the
remark I have just made, was wanting in his demonstrations."

[Note 67\9: _Tracts on Optics_, p. 209.]

By the help of this view, Huyghens gave a perfectly satisfactory and
correct explanation of the laws of reflection and refraction; and he
also applied the same theory, as we have seen, to the double
refraction of Iceland spar with great sagacity and success. He
conceived that in this crystal, besides the spherical waves, there
might be others of a spheroidal form, the axis of the spheroid being
symmetrically disposed with regard to the faces of the rhombohedron,
for to these faces the optical phenomena are symmetrically related.
He found[68\9] that the position of the refracted ray, determined by
such spheroidal undulations, would give an oblique refraction, which
would coincide in its laws with the refraction observed in Iceland
spar; and, as we have stated, this coincidence was long after fully
confirmed by other observers.

[Note 68\9: _Tracts on Optics_, 237.]

Since Huyghens, at this early period, expounded the undulatory
theory with so much distinctness, and applied it with so much skill,
it may be asked why we do not hold him up as the great Author of the
induction of undulations of light;--the person who marks the epoch
of the theory? To this we reply, that though Huyghens discovered
strong presumptions in favor of the undulatory theory, it was not
_established_ till a later era, when the fringes of shadows, rightly
understood, made the waves visible, and when the hypothesis which
had been assumed to account for double refraction, was found to
contain also an explanation of polarization. It is _then_ that this
theory of light assumes its commanding form; and the persons who
gave it this form, we must make the great names of our narrative;
without, however, denying the genius and merit of Huyghens, who is,
undoubtedly, the leading character in the prelude to the discovery.

The undulatory theory, from this time to our own, was unfortunate in
its career. It was by no means destitute of defenders, but these
were not experimenters; and none of them thought of applying it to
{88} Grimaldi's experiments on fringes, of which we have spoken a
little while ago. And the great authority of the period, Newton,
adopted the opposite hypothesis, that of emission, and gave it a
currency among his followers which kept down the sounder theory for
above a century.

Newton's first disposition appears to have been by no means averse
to the assumption of an ether as the vehicle of luminiferous
undulations. When Hooke brought against his prismatic analysis of
light some objections, founded on his own hypothetical notions,
Newton, in his reply, said,[69\9] "The hypothesis has a much greater
affinity with his own hypothesis than he seems to be aware of; the
vibrations of the ether being as useful and necessary in this as in
his." This was in 1672; and we might produce, from Newton's writing,
passages of the same kind, of a much later date. Indeed it would
seem that, to the last, Newton considered the assumption of an ether
as highly probable, and its vibrations important parts of the
phenomena of light; but he also introduced into his system the
hypothesis of emission, and having followed this hypothesis into
mathematical detail, while he has left all that concerns the ether
in the form of queries and conjectures, the emission theory has
naturally been treated as the leading part of his optical doctrines.

[Note 69\9: _Phil. Trans._ vii. 5087.]

The principal propositions of the _Principia_ which bear upon the
question of optical theory are those of the fourteenth Section of
the first Book,[70\9] in which the law of the sines in refraction is
proved on the hypothesis that the particles of bodies act on light
only at very small distances; and the proposition of the eighth
Section of the second Book;[71\9] in which it is pretended to be
demonstrated that the motion propagated in a fluid must diverge when
it has passed through an aperture. The former proposition shows that
the law of refraction, an optical truth which mainly affected the
choice of a theory, (for about reflection there is no difficulty on
any mechanical hypothesis,) follows from the theory of emission: the
latter proposition was intended to prove the inadmissibility of the
rival hypothesis, that of undulations. As to the former point,--the
hypothetical explanation of refraction, on the assumptions there
made,--the conclusion is quite satisfactory; but the reasoning in
the latter case, (respecting the propagation of undulations,) is
certainly inconclusive and vague; and something better might the
more reasonably have been expected, since Huyghens had at least {89}
endeavored to prove the opposite proposition. But supposing we leave
these properties, the rectilinear course, the reflection, and the
refraction of light, as problems in which neither theory has a
decided advantage, what is the next material point? The colors of
thin plates. Now, how does Newton's theory explain these? By a new
and special supposition;--that of _fits of easy transmission and
reflection_: a supposition which, though it truly expresses these
facts, is not borne out by any other phenomena. But, passing over
this, when we come to the peculiar laws of polarization in Iceland
spar, how does Newton's meet this? Again by a special and new
supposition;--that the rays of light have _sides_. Thus we find no
fresh evidence in favor of the emission hypothesis springing out of
the fresh demands made upon it. It may be urged, in reply, that the
same is true of the undulatory theory; and it must be allowed that,
at the time of which we now speak, its superiority in this respect
was not manifested; though Hooke, as we have seen, had caught a
glimpse of the explanation, which this theory supplies, of the
colors of thin plates.

[Note 70\9:  _Principia_, Prop. 94, _et seq._]

[Note 71\9: Ib. Prop. 42.]

At a later period, Newton certainly seems to have been strongly
disinclined to believe light to consist in undulations merely. "Are
not," he says, in Question twenty-eight of the _Opticks_, "all
hypotheses erroneous, in which light is supposed to consist in
pression or motion propagated through a fluid medium?" The arguments
which most weighed with him to produce this conviction, appear to
have been the one already mentioned,--that, on the undulatory
hypothesis, undulations passing through an aperture would be
diffused; and again,--his conviction, that the properties of light,
developed in various optical phenomena, "depend not upon new
modifications, but upon the original and unchangeable properties of
the rays." (Question twenty-seven.)

But yet, even in this state of his views, he was very far from
abandoning the machinery of vibrations altogether. He is disposed to
use such machinery to produce his "fits of easy transmission." In
his seventeenth Query, he says,[72\9] "when a ray of light falls
upon the surface of any pellucid body, and is there refracted or
reflected; may not waves of vibrations or tremors be thereby excited
in the refracting or reflecting medium at the point of incidence? .
. . . and do not these vibrations overtake the rays of light, and by
overtaking them successively, do they not put them into the fits of
easy reflection and easy {90} transmission described above?" Several
of the other queries imply the same persuasion, of the necessity for
the assumption of an ether and its vibrations. And it might have
been asked, whether any good reason could be given for the
hypothesis of an ether as a _part_ of the mechanism of light, which
would not be equally valid in favor of this being the _whole_ of the
mechanism, especially if it could be shown that nothing more was
wanted to produce the results.

[Note 72\9: _Opticks_, p. 322.]

The emission theory was, however, embraced in the most strenuous
manner by the disciples of Newton. That propositions existed in the
_Principia_ which proceeded on this hypothesis, was, with many of
these persons, ground enough for adopting the doctrine; and it had
also the advantage of being more ready of conception, for though the
propagation of a wave is not very difficult to conceive, at least by
a mathematician, the motion of a particle is still easier.

On the other hand, the undulation theory was maintained by no less a
person than Euler; and the war between the two opinions was carried
on with great earnestness. The arguments on one side and on the
other soon became trite and familiar, for no person explained any
new class of facts by either theory. Thus it was urged by Euler
against the system of emission,[73\9]--that the perpetual emanation
of light from the sun must have diminished the mass;--that the
stream of matter thus constantly flowing must affect the motions of
the planets and comets; that the rays must disturb each other;--that
the passage of light through transparent bodies is, on this system,
inconceivable: all such arguments were answered by representations
of the exceeding minuteness and velocity of the matter of light. On
the other hand, there was urged against the theory of waves, the
favorite Newtonian argument, that on this theory the light passing
through an aperture ought to be diffused, as sound is. It is curious
that Euler does not make to this argument the reply which Huyghens
had made before. The fact really was, that he was not aware of the
true ground of the difference of the result in the cases of sound
and light; namely, that any ordinary aperture bears an immense ratio
to the length of an undulation of light, but does not bear a very
great ratio to the length of an undulation of sound. The
demonstrable consequence of this difference is, that light darts
through such an orifice in straight rays, while sound is diffused in
all directions. Euler, not perceiving this difference, rested his
answer mainly upon a circumstance by no means {91} unimportant, that
the partitions usually employed are not impermeable to sound, as
opake bodies are to light. He observes that the sound does not all
come through the aperture; for we hear, though the aperture be
stopped. These were the main original points of attack and defence,
and they continued nearly the same for the whole of the last
century; the same difficulties were over and over again proposed,
and the same solutions given, much in the manner of the disputations
of the schoolmen of the middle ages.

[Note 73\9: Fischer, iv. 449.]

The struggle being thus apparently balanced, the scale was naturally
turned by the general ascendancy of the Newtonian doctrines: and the
emission theory was the one most generally adopted. It was still
more firmly established, in consequence of the turn generally taken
by the scientific activity of the latter half of the eighteenth
century: for while nothing was added to our knowledge of optical
laws, the chemical effects of light were studied to a considerable
extent by various inquirers;[74\9] and the opinions at which these
persons arrived, they found that they could express most readily, in
consistency with the reigning chemical views, by assuming the
materiality of light. It is, however, clear, that no reasonings of
the inevitably vague and doubtful character which belong to these
portions of chemistry, ought to be allowed to interfere with the
steady and regular progress of induction and generalization, founded
on relations of space and number, by which procedure the mechanical
sciences are formed. We reject, therefore, all these chemical
speculations, as belonging to other subjects; and consider the
history of optical theory as a blank, till we arrive at some very
different events, of which we have now to speak. {92}

[Note 74\9: As Scheele, Selle, Lavoisier, De Luc, Richter,
Leonhardi, Gren, Girtanner, Link, Hagen, Voigt, De la Metherie,
Scherer, Dizé, Brugnatelli. See Fischer, vii. p. 20.]




CHAPTER XI.

EPOCH OF YOUNG AND FRESNEL.


_Sect._ 1.--_Introduction._

THE man whose name must occupy the most distinguished place in the
history of Physical Optics, in consequence of what he did in
reviving and establishing the undulatory theory of light, is Dr.
Thomas Young. He was born in 1773, at Milverton in Somersetshire, of
Quaker parents; and after distinguishing himself during youth by the
variety and accuracy of his attainments, he settled in London as a
physician in 1801; but continued to give much of his attention to
general science. His optical theory, for a long time, made few
proselytes; and several years afterwards, Auguste Fresnel, an
eminent French mathematician, an engineer officer, took up similar
views, proved their truth, and traced their consequences, by a
series of labors almost independent of those of Dr. Young. It was
not till the theory was thus re-echoed from another land, that it
was able to take any strong hold on the attention of the countrymen
of its earlier promulgator.

The theory of undulations, like that of universal gravitation, may
be divided into several successive steps of generalization. In both
cases, all these steps were made by the same persons; but there is
this difference:--all the parts of the law of universal gravitation
were worked out in one burst of inspiration by its author, and
published at one time;--in the doctrine of light, on the other hand,
the different steps of the advance were made and published at
separate times, with intervals between. We see the theory in a
narrower form, and in detached portions, before the widest
generalizations and principles of unity are reached; we see the
authors struggling with the difficulties before we see them
successful. They appear to us as men like ourselves, liable to
perplexity and failure, instead of coming before us, as Newton does
in the history of Physical Astronomy, as the irresistible and almost
supernatural hero of a philosophical romance. {93}

The main subdivisions of the great advance in physical optics, of
which we have now to give an account, are the following:--

1. The explanation of the _periodical colors_ of thin plates, thick
plates, fringed shadows, striated surfaces, and other phenomena of
the same kind, by means of the doctrine of the _interference_ of
undulations.

2. The explanation of the phenomena of _double refraction_ by the
propagation of undulations in a medium of which the optical
_elasticity_ is different in different directions.

3. The conception of _polarization_ as the result of the vibrations
being _transverse_; and the consequent explanation of the production
of polarization, and the necessary connexion between polarization
and double refraction, on mechanical principles.

4. The explanation of the phenomena of _dipolarization_, by means of
the interference of the _resolved parts_ of the vibrations after
double refraction.

The history of each of these discoveries will be given separately to
a certain extent; by which means the force of proof arising from
their combination will be more apparent.


_Sect._ 2.--_Explanation of the Periodical Colors of Thin Plates and
Shadows by the Undulatory Theory._

THE explanation of periodical colors by the principle of
interference of vibrations, was the first step which Young made in
his confirmation of the undulatory theory. In a paper on Sound and
Light, dated Emmanuel College, Cambridge, 9th July, 1799, and read
before the Royal Society in January following, he appears to incline
strongly to the Huyghenian theory; not however offering any new
facts or calculations in its favor, but pointing out the great
difficulties of the Newtonian hypothesis. But in a paper read before
the Royal Society, November 12, 1801, he says, "A further
consideration of the colors of thin plates has converted that
prepossession which I before entertained for the undulatory theory
of light, into a very strong conviction of its truth and efficiency;
a conviction which has since been most strikingly confirmed by an
analysis of the colors of _striated surfaces_." He here states the
general principle of interferences in the form of a proposition.
(Prop. viii.) "When two undulations from different origins coincide
either perfectly or very nearly in direction, their joint effect is
a combination of the motions belonging to them." He explains, by the
help of this proposition, the colors which were observed in
Coventry's {94} micrometers, in which instrument lines were drawn on
glass at a distance of 1⁄500th of an inch. The interference of the
undulations of the rays reflected from the two sides of these fine
lines, produced periodical colors. In the same manner, he accounts
for the colors of thin plates, by the interference of the light
partially reflected from the two surfaces of the plates. We have
already seen that Hooke had long before suggested the same
explanation; and Young says at the end of his paper, "It was not
till I had satisfied myself respecting all these phenomena, that I
found in Hooke's _Micrographia_ a passage which might have led me
earlier to a similar opinion." He also quotes from Newton many
passages which assume the existence of an ether; of which, as we
have already seen, Newton suggests the necessity in these very
phenomena, though he would apply it in combination with the emission
of material light. In July, 1802, Young explained, on the same
principle, some facts in indistinct vision, and other similar
appearances. And in 1803,[75\9] he speaks more positively still. "In
making," he says, "some experiments on the fringes of colors
accompanying shadows, I have found so simple and so demonstrative a
proof of the general law of interference of two portions of light,
which I have already endeavored to establish, that I think it right
to lay before the Royal Society a short statement of the facts which
appear to me to be thus decisive." The two papers just mentioned
certainly ought to have convinced all scientific men of the truth of
the doctrine thus urged; for the number and exactness of the
explanations is very remarkable. They include the colored fringes
which are seen with the shadows of fibres; the colors produced by a
dew between two pieces of glass, which, according to the theory,
should appear when the thickness of the plate is _six_ times that of
thin plates, and which do so; the changes resulting from the
employment of other fluids than water; the effect of inclining the
plates; also the fringes and bands which accompany shadows, the
phenomena observed by Grimaldi, Newton, Maraldi, and others, and
hitherto never at all reduced to rule. Young observes, very justly,
"whatever may be thought of the theory, we have got a simple and
general law" of the phenomena. He moreover calculated the length of
an undulation from the measurements of fringes of shadows, as he had
done before from the colors of thin plates; and found a very close
accordance of the results of the various cases with one another. {95}

[Note 75\9: _Phil. Trans._ Memoir, read Nov. 24.]

There is one difficulty, and one inaccuracy, in Young's views at
this period, which it may be proper to note. The difficulty was,
that he found it necessary to suppose that light, when reflected at
a rarer medium, is retarded by half an undulation. This assumption,
though often urged at a later period as an argument against the
theory, was fully justified as the mechanical principles of the
subject were unfolded; and the necessity of it was clear to Young
from the first. On the strength of this, says he, "I ventured to
predict, that if the reflections were of the same kind, made at the
surfaces of a thin plate, of a density intermediate between the
densities of the mediums surrounding it, the central spot would be
white; and I have now the pleasure of stating, that I have fully
verified this prediction by interposing a drop of oil of sassafras
between a prism of flint-glass and a lens of crown-glass."

The inaccuracy of his calculations consisted in his considering the
external fringe of shadows to be produced by the interference of a
ray _reflected_ from the _edge_ of the object, with a ray which
passes clear of it; instead of supposing _all the parts_ of the wave
of light to corroborate or interfere with one another. The
mathematical treatment of the question on the latter hypothesis was
by no means easy. Young was a mathematician of considerable power in
the solution of the problems which came before him: though his
methods possessed none of the analytical elegance which, in his
time, had become general in France. But it does not appear that he
ever solved the problem of undulations as applied to fringes, with
its true conditions. He did, however, rectify his conceptions of the
nature of the interference; and we may add, that the numerical error
of the consequences of the defective hypothesis is not such as to
prevent their confirming the undulatory theory.[76\9]

[Note 76\9: I may mention, in addition to the applications which
Young made of the principle of interferences, his _Eriometer_, an
instrument invented for the purpose of measuring the thickness of
the fibres of wood; and the explanation of the supernumerary bands
of the rainbow. These explanations involve calculations founded on
the length of an undulation of light, and were confirmed by
experiment, as far as experiment went.]

But though this theory was thus so powerfully recommended by
experiment and calculation, it met with little favor in the
scientific world. Perhaps this will be in some measure accounted
for, when we come, in the next chapter, to speak of the mode of its
reception by {96} the supposed judges of science and letters. Its
author went on laboring at the completion and application of the
theory in other parts of the subject; but his extraordinary success
in unravelling the complex phenomena of which we have been speaking,
appears to have excited none of the notice and admiration which
properly belonged to it, till Fresnel's Memoir _On Diffraction_ was
delivered to the Institute, in October, 1815.

MM. Arago and Poinsot were commissioned to make a report upon this
Memoir; and the former of these philosophers threw himself upon the
subject with a zeal and intelligence which peculiarly belonged to
him. He verified the laws announced by Fresnel: "laws," he says,
"which appear to be destined to make an epoch in science." He then
cast a rapid glance at the history of the subject, and recognized,
at once, the place which Young occupied in it. Grimaldi, Newton,
Maraldi, he states, had observed the facts, and tried in vain to
reduce them to rule or cause. "Such[77\9] was the state of our
knowledge on this difficult question, when Dr. Thomas Young made the
very remarkable experiment which is described in the _Philosophical
Transactions_ for 1803;" namely, that to obliterate all the bands
within the shadow, we need only stop the ray which is going to
graze, or has grazed, one border of the object. To this, Arago added
the important observation, that the same obliteration takes place,
if we stop the ray, with a transparent plate; except the plate be
very thin, in which case the bands are displaced, and not
extinguished. "Fresnel," says he, "guessed the effect which a thin
plate would produce, when I had told him of the effect of a thick
glass." Fresnel himself declares[78\9] that he was not, at the time,
aware of Young's previous labors. After stating nearly the same
reasonings concerning fringes which Young had put forward in 1801,
he adds, "it is therefore the meeting, the actual crossing of the
rays, which produces the fringes. This consequence, which is only,
so to speak, the translation of the phenomena, seems to me entirely
opposed to the hypothesis of emission, and confirms the system which
makes light consist in the vibrations of a peculiar fluid." And thus
the Principle of Interferences, and the theory of undulations, so
far as that principle depends upon the theory, was a second time
established by Fresnel in France, fourteen years after it had been
discovered, fully proved, and repeatedly published by Young in
England. {97}

[Note 77\9: _An. Chim._ 1815, Febr.]

[Note 78\9: Ib. tom. xvii. p. 402.]

In this Memoir of Fresnel's, he takes very nearly the same course as
Young had done; considering the interference of the direct light
with that reflected at the edge, as the cause of the external
fringes; and he observes, that in this reflection it is necessary to
suppose half an undulation lost: but a few years later, he
considered the propagation of undulations in a more true and general
manner, and obtained the solution of this difficulty of the
half-undulation. His more complete Memoir on _Diffraction_ was
delivered to the Institute of France, July 29, 1818; and had the
prize awarded it in 1819:[79\9] but by the delays which at that
period occurred in the publication of the _Parisian Academical
Transactions_, it was not published[80\9] till 1826, when the theory
was no longer generally doubtful or unknown in the scientific world.
In this Memoir, Fresnel observes, that we must consider the effect
of _every portion_ of a wave of light upon a distant point, and
must, on this principle, find the illumination produced by any
number of such waves together. Hence, in general, the process of
integration is requisite; and though the integrals which here offer
themselves are of a new and difficult kind, he succeeded in making
the calculation for the cases in which he experimented. His _Table
of the Correspondences of Theory and Observation_,[81\9] is very
remarkable for the closeness of the agreement; the errors being
generally less than one hundredth of the whole, in the distances of
the black bands. He justly adds, "A more striking agreement could
not be expected between experiment and theory. If we compare the
smallness of the differences with the extent of the breadths
measured; and if we remark the great variations which _a_ and _b_
(the distance of the object from the luminous point and from the
screen) have received in the different observations, we shall find
it difficult not to regard the integral which has led us to these
results as the faithful expression of the law of the phenomena."

[Note 79\9: _Ann. Chim._ May, 1819.]

[Note 80\9: _Mém. Inst._ for 1821-2.]

[Note 81\9: _Mém. Inst._ p. 420-424.]

A mathematical theory, applied, with this success, to a variety of
cases of very different kinds, could not now fail to take strong
hold of the attention of mathematicians; and accordingly, from this
time, the undulatory doctrine of diffraction has been generally
assented to, and the mathematical difficulties which it involves,
have been duly studied and struggled with.

Among the remarkable applications of the undulatory doctrine to
diffraction, we may notice those of Joseph Fraunhofer, a {98}
mathematical optician of Munich. He made a great number of
experiments on the shadows produced by small holes, and groups of
small holes, very near each other. These were published[82\9] in his
_New Modifications of Light_, in 1823. The greater part of this
Memoir is employed in tracing the laws of phenomena of the extremely
complex and splendid appearances which he obtained; but at the
conclusion he observes, "It is remarkable that the laws of the
reciprocal influence and of the diffraction of the rays, can be
deduced from the principles of the undulatory theory: knowing the
conditions, we may, by means of an extremely simple equation,
determine the extent of a luminous wave for each of the different
colors; and in every case, the calculation corresponds with
observation." This mention of "an extremely simple equation,"
appears to imply that he employed only Young's and Fresnel's earlier
mode of calculating interferences, by considering two portions of
light, and not the method of integration. Both from the late period
at which they were published, and from the absence of mathematical
details, Fraunhofer's labors had not any strong influence on the
establishment of the undulatory theory; although they are excellent
verifications of it, both from the goodness of the observations, and
the complexity and beauty of the phenomena.

[Note 82\9: In Schumacher's _Astronomische Abhandlungen_, in French;
earlier in German.]

We have now to consider the progress of the undulatory theory in
another of its departments, according to the division already stated.


_Sect._ 3.--_Explanation of Double Refraction by the Undulatory
Theory._

WE have traced the history of the undulatory theory applied to
diffraction, into the period when Young came to have Fresnel for his
fellow-laborer. But in the mean time, Young had considered the
theory in its reference to other phenomena, and especially to those
of _double refraction_.

In this case, indeed, Huyghens's explanation of the facts of Iceland
spar, by means of spheroidal undulations, was so complete, and had
been so fully confirmed by the measurements of Haüy and Wollaston,
that little remained to be done, except to connect the Huyghenian
hypothesis with the mechanical views belonging to the theory, and to
extend his law to other cases. The former part of this task Young
executed, by remarking that we may conceive the _elasticity_ of the
{99} crystal, on which the velocity of propagation of the
luminiferous undulation depends, to be different, in the direction
of the crystallographic axis, and in the direction of the planes at
right angles to this axis; and from such a difference, he deduces
the existence of spheroidal undulations. This suggestion appeared in
the _Quarterly Review_ for November, 1809, in a critique upon an
attempt of Laplace to account for the same phenomena. Laplace had
proposed to reduce the double refraction of such crystals as Iceland
spar, to his favorite machinery of forces which are sensible at
small distances only. The peculiar forces which produce the effect
in this case, he conceives to emanate from the crystallographic
axis: so that the velocity of light within the crystal will depend
only on the situation of the ray with respect to this axis. But the
establishment of this condition is, as Young observes, the main
difficulty of the problem. How are we to conceive refracting forces,
independent of the surface of the refracting medium, and regulated
only by a certain internal line? Moreover, the law of force which
Laplace was obliged to assume, namely, that it varied as the square
of the sine of the angle which the ray made with the axis, could
hardly be reconciled with mechanical principles. In the critique
just mentioned, Young appears to feel that the undulatory theory,
and perhaps he himself, had not received justice at the hands of men
of science; he complains that a person so eminent in the world of
science as Laplace then was, should employ his influence in
propagating error, and should disregard the extraordinary
confirmations which the Huyghenian theory had recently received.

The extension of this view, of the different elasticity of crystals
in different directions, to other than uniaxal crystals, was a more
complex and difficult problem. The general notion was perhaps
obvious, after what Young had done; but its application and
verification involved mathematical calculations of great generality,
and required also very exact experiments. In fact, this application
was not made till Fresnel, a pupil of the Polytechnic School,
brought the resources of the modern analysis to bear upon the
problem;--till the phenomena of dipolarized light presented the
properties of biaxal crystals in a vast variety of forms;--and till
the theory received its grand impulse by the combination of the
explanation of polarization with the explanation of double
refraction. To the history of this last-mentioned great step we now
proceed. {100}


_Sect._ 4.--_Explanation of Polarization by the Undulatory Theory._

EVEN while the only phenomena of _polarization_ which were known were
those which affect the two images in Iceland spar, the difficulty
which these facts seemed at first to throw in the way of the
undulatory theory was felt and acknowledged by Young. Malus's
discovery of polarization by reflection increased the difficulty,
and this Young did not attempt to conceal. In his review of the
papers containing this discovery[83\9] he says, "The discovery
related in these papers appears to us to be by far the most
important and interesting which has been made in France concerning
the properties of light, at least since the time of Huyghens; and it
is so much the more deserving of notice, as it greatly influences
the general balance of evidence in the comparison of the undulatory
and projectile theories of the nature of light." He then proceeds to
point out the main features in this comparison, claiming justly a
great advantage for the theory of undulations on the two points we
have been considering, the phenomena of diffraction and of double
refraction. And he adds, with reference to the embarrassment
introduced by polarization, that we are not to expect the course of
scientific discovery to run smooth and uninterrupted; but that we
are to lay our account with partial obscurity and seeming
contradiction, which we may hope that time and enlarged research
will dissipate. And thus he steadfastly held, with no blind
prejudice, but with unshaken confidence, his great philosophical
trust, the fortunes of the undulatory theory. It is here, after the
difficulties of polarization had come into view, and before their
solution had been discovered, that we may place the darkest time of
the history of the theory; and at this period Young was alone in the
field.

[Note 83\9: _Quart. Rev._ May, 1810.]

It does not appear that the light dawned upon him for some years. In
the mean time, Young found that his theory would explain dipolarized
colors; and he had the satisfaction to see Fresnel re-discover, and
M. Arago adopt, his views on diffraction. He became engaged in
friendly intercourse with the latter philosopher, who visited him in
England in 1816. On January the 12th, 1817, in writing to this
gentleman, among other remarks on the subject of optics, he says, "I
have also been reflecting on the possibility of giving an imperfect
explanation of the affection of light which constitutes
polarization, {101} without departing from the genuine doctrine of
undulation." He then proceeds to suggest the possibility of "a
_transverse_ vibration, propagated in the direction of the radius,
the motions of the particles being in a certain constant direction
with respect to that radius; and this," he adds, "is
_polarization_." From his further explanation of his views, it
appears that he conceived the motions of the particles to be oblique
to the direction of the ray, and not perpendicular, as the theory
was afterwards framed; but still, here was the essential condition
for the explanation of the facts of polarization,--the transverse
nature of the vibrations. This idea at once made it possible to
conceive how the rays of light could have _sides_; for the direction
in which the vibration was transverse to the ray, might be marked by
peculiar properties. And after the idea was once started, it was
comparatively easy for men like Young and Fresnel to pursue and
modify it till it assumed its true and distinct form.

We may judge of the difficulty of taking firmly hold of the
conception of transverse vibrations of the ether, as those which
constitute light, by observing how long the great philosophers of
whom we are speaking lingered within reach of it, before they
ventured to grasp it. Fresnel says, in 1821, "When M. Arago and I
had remarked (in 1816) that two rays polarized at right angles
always give the same quantity of light by their union, I thought
this might be explained by supposing the vibrations to be
transverse, and to be at right angles when the rays are polarized at
right angles. But this supposition was so contrary to the received
ideas on the nature of the vibrations of elastic fluids," that
Fresnel hesitated to adopt it till he could reconcile it better to
his mechanical notions. "Mr. Young, more bold in his conjectures,
and less confiding in the views of geometers, published it before
me, though perhaps he thought it after me." And M. Arago was
afterwards wont to relate[84\9] that when he and Fresnel had
obtained their joint experimental results of the non-interference of
oppositely-polarized pencils, and when Fresnel pointed out that
transverse vibrations were the only possible translation of this
fact into the undulatory theory, he himself protested that he had
not courage to publish such a conception; and accordingly, the
second part of the Memoir was published in Fresnel's name alone.
What renders this more remarkable is, that it occurred when M. Arago
had in his possession the very letter of Young, in which he proposed
the same suggestion. {102}

[Note 84\9: I take the liberty of stating this from personal
knowledge.]

Young's first published statement of the doctrine of transverse
vibrations was given in the explanation of the phenomena of
dipolarization, of which we shall have to speak in the next Section.
But the primary and immense value of this conception, as a step in
the progress of the undulatory theory, was the connexion which it
established between polarization and double refraction; for it held
forth a promise of accounting for polarization, if any conditions
could be found which might determine what was the direction of the
transverse vibrations. The analysis of these conditions is, in a
great measure, the work of Fresnel; a task performed with profound
philosophical sagacity and great mathematical skill.

Since the double refraction of uniaxal crystals could be explained
by undulations of the form of a spheroid, it was perhaps not
difficult to conjecture that the undulations of biaxal crystals
would be accounted for by undulations of the form of an ellipsoid,
which differs from the spheroid in having its three axes unequal,
instead of two only; and consequently has that very relation to the
other, in respect of symmetry, which the crystalline and optical
phenomena have. Or, again, instead of supposing two different
degrees of elasticity in different directions, we may suppose three
such different degrees in directions at right angles to each other.
This kind of generalization was tolerably obvious to a practised
mathematician.

But what shall call into play all these elasticities at once, and
produce waves governed by each of them? And what shall explain the
different polarization of the rays which these separate waves carry
with them? These were difficult questions, to the solution of which
mathematical calculation had hitherto been unable to offer any aid.

It was here that the conception of transverse vibrations came in,
like a beam of sunlight, to disclose the possibility of a mechanical
connexion of all these facts. If transverse vibrations, travelling
through a uniform medium, come to a medium not uniform, but
constituted so that the elasticity shall be different in different
directions, in the manner we have described, what will be the course
and condition of the waves in the second medium? Will the effects of
such waves agree with the phenomena of doubly-refracted light in
biaxal crystals? Here was a problem, striking to the mathematician
for its generality and difficulty, and of deep interest to the
physical philosopher, because the fate of a great theory depended
upon its solution.

The solution, obtained by great mathematical skill, was laid before
the French Institute by Fresnel in November, 1821, and was carried
{103} further in two Memoirs presented in 1822. Its import is very
curious. The undulations which, coming from a distant centre, fall
upon such a medium as we have described, are, it appears from the
principles of mechanics, propagated in a manner quite different from
anything which had been anticipated. The "surface of the waves"
(that is, the surface which would bound undulations diverging from a
point), is a very complex, yet symmetrical curve surface; which, in
the case of uniaxal crystals, resolves itself into a sphere and a
spheroid; but which, in general, forms a continuous double envelope
of the central point to which it belongs, intersecting itself and
returning into itself. The directions of the rays are determined by
this curve surface in biaxal crystals, as in uniaxal crystals they
are determined by the sphere and the spheroid; and the result is,
that in biaxal crystals, _both_ rays suffer _extraordinary_
refraction according to determinate laws. And the positions of the
planes of polarization of the two rays follow from the same
investigation; the plane of polarization in every case being
supposed to be that which is perpendicular to the transverse
vibrations. Now it appeared that the polarization of the two rays,
as determined by Fresnel's theory, would be in directions, not
indeed exactly accordant with the law deduced by M. Biot from
experiment, but deviating so little from those directions, that
there could be small doubt that the empirical formula was wrong, and
the theoretical one right.

The theory was further confirmed by an experiment showing that, in a
biaxal crystal (topaz), neither of the rays was refracted according
to the ordinary law, though it had hitherto been supposed that one
of them was so; a natural inaccuracy, since the error was
small.[85\9] Thus this beautiful theory corrected, while it
explained, the best of the observations which had previously been
made; and offered itself to mathematicians with an almost
irresistible power of conviction. The explanation of laws so strange
and diverse as those of double refraction and polarization, by the
same general and symmetrical theory, could not result from anything
but the truth of the theory.

[Note 85\9: _An. Ch._ xxviii. p. 264.]

"Long," says Fresnel,[86\9] "before I had conceived this theory, I
had convinced myself by a pure contemplation of the facts, that it
was not possible to discover the true explanation of double
refraction, without explaining, at the same time, the phenomena of
polarization, which always goes along with it; and accordingly, it
was after having found {104} what mode of vibration constituted
polarization, that I caught sight of the mechanical causes of double
refraction."

[Note 86\9: _Sur la Double Réf., Mém. Inst._ 1826, p. 174.]

Having thus got possession of the principle of the mechanism of
polarization, Fresnel proceeded to apply it to the other cases of
polarized light, with a rapidity and sagacity which reminds us of
the spirit in which Newton traced out the consequences of the
principle of universal gravitation. In the execution of his task,
indeed, Fresnel was forced upon several precarious assumptions,
which make, even yet, a wide difference between the theory of
gravitation and that of light. But the mode in which these were
confirmed by experiment, compels us to admire the happy apparent
boldness of the calculator.

The subject of _polarization by reflection_ was one of those which
seemed most untractable; but, by means of various artifices and
conjectures, it was broken up and subdued. Fresnel began with the
simplest case, the reflection of light polarized in the plane of
reflection; which he solved by means of the laws of collision of
elastic bodies. He then took the reflection of light polarized
perpendicularly to this plane; and here, adding to the general
mechanical principles a hypothetical assumption, that the
communication of the resolved motion parallel to the refracting
surface, takes place according to the laws of elastic bodies, he
obtains his formula. These results were capable of comparison with
experiment; and the comparison, when made by M. Arago, confirmed the
formulæ. They accounted, too, for Sir D. Brewster's law concerning
the polarizing angle (see Chap. vi.); and this could not but be
looked upon as a striking evidence of their having some real
foundation. Another artifice which MM. Fresnel and Arago employed,
in order to trace the effect of reflection upon common light, was to
use a ray polarized in a plane making half a right angle with the
plane of reflection; for the quantities of the oppositely[87\9]
polarized light in such an incident ray are equal, as they are in
common light; but the relative quantities of the oppositely
polarized light in the reflected ray are indicated by the new plane
of polarization; and thus these relative quantities become known for
the case of common light. The results thus obtained were also
confirmed by facts; and in this manner, all that was doubtful in the
process of Fresnel's reasoning, seemed to be authorized by its
application to real cases. {105}

[Note 87\9: It will be recollected all along, that _oppositely_
polarized rays are those which are polarized in two planes
_perpendicular_ to each other. See above, chap. vi.]

These investigations were published[88\9] in 1821. In succeeding
years, Fresnel undertook to extend the application of his formulæ to
a case in which they ceased to have a meaning, or, in the language
of mathematicians, became _imaginary_; namely, to the case of
internal reflection at the surface of a transparent body. It may
seem strange to those who are not mathematicians, but it is
undoubtedly true, that in many cases in which the solution of a
problem directs impossible arithmetical or algebraical operations to
be performed, these directions may be so interpreted as to point out
a true solution of the question. Such an interpretation Fresnel
attempted[89\9] in the case of which we now speak; and the result at
which he arrived was, that the reflection of light through a rhomb
of glass of a certain form (since called _Fresnel's rhomb_, would
produce a polarization of a kind altogether different from those
which his theory had previously considered, namely, that kind which
we have spoken of as _circular polarization_. The complete
confirmation of this curious and unexpected result by trial, is
another of the extraordinary triumphs which have distinguished the
history of the theory at every step since the commencement of
Fresnel's labors.

[Note 88\9: _An. Chim._ t. xvii.]

[Note 89\9: _Bullet. des Sc._ Feb. 1823.]

But anything further which has been done in this way, may be treated
of more properly in relating the verification of the theory. And we
have still to speak of the most numerous and varied class of facts
to which rival theories of light were applied, and of the
establishment of the undulatory doctrine in reference to that
department; I mean the phenomena of depolarized, or rather, as I
have already said, _di_polarized light.


_Sect._ 5.--_Explanation of Dipolarization by the Undulatory Theory._

WHEN Arago, in 1811, had discovered the colors produced by polarized
light passing through certain crystals,[90\9] it was natural that
attempts should be made to reduce them to theory. M. Biot, animated
by the success of Malus in detecting the laws of double refraction,
and Young, knowing the resources of his own theory, were the first
persons to enter upon this undertaking. M. Biot's theory, though in
the end displaced by its rival, is well worth notice in the history
of the subject. It was what he called the doctrine of _moveable
polarization_. He conceived that when the molecules of light pass
through {106} thin crystalline plates, the plane of polarization
undergoes an oscillation which carries it backwards and forwards
through a certain angle, namely, twice the angle contained between
the original plane of polarization and the principal section of the
crystal. The intervals which this oscillation occupies are lengths
of the path of the ray, very minute, and different for different
colors, like Newton's fits of easy transmission; on which model,
indeed, the new theory was evidently framed.[91\9] The colors
produced in the phenomena of dipolarization really do depend, in a
periodical manner, on the length of the path of the light through
the crystal, and a theory such as M. Biot's was capable of being
modified, and was modified, so as to include the leading features of
the facts as then known; but many of its conditions being founded on
special circumstances in the experiments, and not on the real
conditions of nature, there were in it several incongruities, as
well as the general defect of its being an arbitrary and unconnected
hypothesis.

[Note 90\9: See chap. ix.]

[Note 91\9: See MM. Arago and Biot's Memoirs, _Mém. Inst._ for 1811;
the whole volume for 1812 is a Memoir of M. Biot's (published 1814);
also _Mém. Inst._ for 1817; M. Biot's Mem. read in 1818, published
in 1819 and for 1818.]

Young's mode of accounting for the brilliant phenomena of
dipolarization appeared in the _Quarterly Review_ for 1814. After
noticing the discoveries of MM. Arago, Brewster, and Biot, he adds,
"We have no doubt that the surprise of these gentlemen will be as
great as our own satisfaction in finding that they are perfectly
reducible, like other causes of recurrent colors, to the general
laws of the interference of light which have been established in
this country;" giving a reference to his former statements. The
results are then explained by the interference of the ordinary and
extraordinary ray. But, as M. Arago properly observes, in his
account of this matter,[92\9] "It must, however, be added that Dr.
Young had not explained either in what circumstances the
interference of the rays can take place, nor why we see no colors
unless the crystallized plates are exposed to light previously
polarized." The explanation of these circumstances depends on the
laws of interference of polarized light which MM. Arago and Fresnel
established in 1816. They then proved, by direct experiment, that
when polarized light was treated so as to bring into view the most
marked phenomena of interference, namely, the bands of shadows;
pencils of light which have a common origin, and which are polarized
in the parallel planes, interfere completely, while those which are
{107} polarized in _opposite_ (that is, perpendicular,) planes do
not interfere at all.[93\9] Taking these principles into the
account, Fresnel explained very completely, by means of the
interference of undulations, all the circumstances of colors
produced by crystallized plates; showing the necessity of the
_polarization_ in the first instance; the _dipolarizing_ effect of
the crystal; and the office of the _analysing plate_, by which
certain portions of each of the two rays in the crystal are made to
interfere and produce color. This he did, as he says,[94\9] without
being aware, till Arago told him, that Young had, to some extent,
anticipated him.

[Note 92\9: _Enc. Brit._ Supp. art. _Polarization._]

[Note 93\9: _Ann. Chim._ tom. x.]

[Note 94\9: Ib. tom. xvii. p. 402.]

When we look at the history of the emission-theory of light, we see
exactly what we may consider as the natural course of things in the
career of a false theory. Such a theory may, to a certain extent,
explain the phenomena which it was at first contrived to meet; but
every new class of facts requires a new supposition,--an addition to
the machinery; and as observation goes on, these incoherent
appendages accumulate, till they overwhelm and upset the original
frame-work. Such was the history of the hypothesis of solid
epicycles; such has been the history of the hypothesis of the
material emission of light. In its simple form, it explained
reflection and refraction; but the colors of thin plates added to it
the hypothesis of fits of easy transmission and reflection; the
phenomena of diffraction further invested the particles with complex
hypothetical laws of attraction and repulsion; polarization gave
them sides; double refraction subjected them to peculiar forces
emanating from the axes of crystals; finally, dipolarization loaded
them with the complex and unconnected contrivance of moveable
polarization; and even when all this had been assumed, additional
mechanism was wanting. There is here no unexpected success, no happy
coincidence, no convergence of principles from remote quarters; the
philosopher builds the machine, but its parts do not fit; they hold
together only while he presses them: this is not the character of
truth.

In the undulatory theory, on the other hand, all tends to unity and
simplicity. We explain reflection and refraction by undulations;
when we come to thin plates, the requisite "fits" are already
involved in our fundamental hypothesis, for they are the length of
an undulation; the phenomena of diffraction also require such
intervals; and the intervals thus required agree exactly with the
others in magnitude, {108} so that no new property is needed.
Polarization for a moment checks us; but not long; for the direction
of our vibrations is hitherto arbitrary;--we allow polarization to
decide it. Having done this for the sake of polarization, we find
that it also answers an entirely different purpose, that of giving
the law of double refraction. Truth may give rise to such a
coincidence; falsehood cannot. But the phenomena become more
numerous, more various, more strange; no matter: the Theory is equal
to them all. It makes not a single new physical hypothesis; but out
of its original stock of principles it educes the counterpart of all
that observation shows. It accounts for, explains, simplifies, the
most entangled cases; corrects known laws and facts; predicts and
discloses unknown ones; becomes the guide of its former teacher,
Observation; and, enlightened by mechanical conceptions, acquires an
insight which pierces through shape and color to force and cause.

We thus reach the philosophical _moral_ of this history, so
important in reference to our purpose; and here we shall close the
account of the discovery and promulgation of the undulatory theory.
Any further steps in its development and extension, may with
propriety be noticed in the ensuing chapters, respecting its
reception and verification.

[2nd Ed.] [In the _Philosophy of the Inductive Sciences_, B. xi. ch.
iii. Sect. 11, I have spoken of the _Consilience of Inductions_ as
one of the characters of scientific truth. We have several striking
instances of such consilience in the history of the undulatory
theory. The phenomena of fringes of shadows and colored bands in
crystals _jump together_ in the Theory of Vibrations. The phenomena
of polarization and double refraction _jump together_ in the Theory
of Crystalline Vibrations. The phenomena of polarization and of the
interference of polarized rays _jump together_ in the Theory of
Transverse Vibrations.

The proof of what is above said of the undulatory theory is
contained in the previous history. This theory has "accounted for,
explained, and simplified the most entangled cases;" as the cases of
fringes of shadows; shadows of gratings; colored bands in biaxal
crystals, and in quartz. There are no optical phenomena more
entangled than these. It has "corrected experimental laws," as in
the case of M. Biot's law of the direction of polarization in biaxal
crystals. It has done this, "without making any new physical
hypothesis;" for the transverse direction of vibrations, the
different optical elasticities of crystals in different directions,
and (if it be adopted) the hypothesis of finite {109} intervals of
the particles (see chap. x. and hereafter, chap. xiii.), are only
limitations of what was indefinite in the earlier form of the
hypothesis. And so far as the properties of visible radiant light
are concerned, I do not think it at all too much to say, as M.
Schwerd has said, that "the undulation theory accounts for the
phenomena as completely as the theory of gravitation does for the
facts of the solar system."

This we might say, even if some facts were not yet fully explained;
for there were till very lately, if there are not still, such
unexplained facts with regard to the theory of gravitation,
presented to us by the solar system. With regard to the undulatory
theory, these exceptions are, I think, disappearing quite as rapidly
and as completely as in the case of gravitation. It is to be
observed that no presumption against the theory can with any show of
reason be collected from the cases in which classes of phenomena
remain unexplained, the theory having never been applied to them by
any mathematician capable of tracing its results correctly. The
history of the theory of gravitation may show us abundantly how
necessary it is to bear in mind this caution; and the results of the
undulatory theory cannot be traced without great mathematical skill
and great labor, any more than those of gravitation.

This remark applies to such cases as that of the _transverse fringes
of grooved surfaces_. The general phenomena of these cases are
perfectly explained by the theory. But there is an interruption in
the light in an oblique direction, which has not yet been explained;
but looking at what has been done in other cases, it is impossible
to doubt that this phenomenon depends upon the results of certain
integrations, and would be explained if these were rightly performed.

The phenomena of _crystallized surfaces_, and especially their
effects upon the plane of polarization, were examined by Sir D.
Brewster, and laws of the phenomena made out by him with his usual
skill and sagacity. For a time these were unexplained by the theory.
But recently Mr. Mac Cullagh has traced the consequences of the
theory in this case,[95\9] and obtained a law which represents with
much exactness, Sir D. Brewster's observation.

[Note 95\9: Prof. Lloyd's _Report, Brit. Assoc._ 1834, p. 374.]

The phenomena which Sir D. Brewster, in 1837, called a _new property
of light_, (certain appearances of the spectrum when the pupil of
the eye is half covered with a thin glass or crystal,) have been
explained by Mr. Airy in the _Phil. Trans._ for 1840.

Mr. Airy's explanation of the phenomena termed by Sir D. {110}
Brewster a _new property of light_, is completed in the
_Philosophical Magazine_ for November, 1846. It is there shown that
a dependence of the breadth of the bands upon the aperture of the
pupil, which had been supposed to result from the theory, and which
does not appear in the experiment, did really result from certain
limited conditions of the hypothesis, which conditions do not belong
to the experiment; and that when the problem is solved without those
limitations, the discrepance of theory and observation vanishes; so
that, as Mr. Airy says, "this very remarkable experiment, which long
appeared inexplicable, seems destined to give one of the strongest
confirmations to the Undulatory Theory."

I may remark also that there is no force in the objection which has
been urged against the admirers of the undulatory theory, that by
the fulness of their assent to it, they discourage further
researches which may contradict or confirm it. We must, in this
point of view also, look at the course of the theory of gravitation
and its results. The acceptance of that theory did not prevent
mathematicians and observers from attending to the apparent
exceptions, but on the contrary, stimulated them to calculate and to
observe with additional zeal, and still does so. The acceleration of
the Moon, the mutual disturbances of Jupiter and Saturn, the motions
of Jupiter's Satellites, the effect of the Earth's oblateness on the
Moon's motion, the motions of the Moon about her own centre, and
many other phenomena, were studied with the greater attention,
_because_ the general theory was deemed so convincing: and the same
cause makes the remaining exceptions objects of intense interest to
astronomers and mathematicians. The mathematicians and optical
experimenters who accept the undulatory theory, will of course
follow out their conviction in the same manner. Accordingly, this
has been done and is still doing, as in Mr. Airy's mathematical
investigation of the effect of an annular aperture; Mr. Earnshaw's,
of the effect of a triangular aperture; Mr. Talbot's explanation of
the effect of interposing a film of mica between a part of the pupil
and the pure spectrum, so nearly approaching to the phenomena which
have been spoken of as a new Polarity of Light; besides other labors
of eminent mathematicians, elsewhere mentioned in these pages.

The phenomena of the _absorption_ of light have no especial bearing
upon the undulatory theory. There is not much difficulty in
explaining the _possibility_ of absorption upon the theory. When the
light is absorbed, it ceases to belong to the theory. {111}

For, as I have said, the theory professes only to explain the
phenomena of _radiant visible_ light. We know very well that light
has other bearings and properties. It produces chemical effects. The
optical polarity of crystals is connected with the chemical polarity
of their constitution. The natural colors of bodies, too, are
connected with their chemical constitution. Light is also connected
with heat. The undulatory theory does not undertake to explain these
properties and their connexion. If it did, it would be a Theory of
Heat and of Chemical Composition, as well as a Theory of Light.

Dr. Faraday's recent experiments have shown that the magnetic
polarity is directly connected with that optical polarity by which
the plane of polarization is affected. When the lines of magnetic
force pass through certain transparent bodies, they communicate to
them a certain kind of circular polarizing power; yet different from
the circular polarizing power of quartz, and certain fluids
mentioned in chapter ix.

Perhaps I may be allowed to refer to this discovery as a further
illustration of the views I have offered in the _Philosophy of the
Inductive Sciences_ respecting the _Connexion of Co-existent
Polarities_. (B. v. Chap. ii.)]




CHAPTER XII.

SEQUEL TO THE EPOCH OF YOUNG AND FRESNEL. RECEPTION OF THE
UNDULATORY THEORY.


WHEN Young, in 1800, published his assertion of the Principle of
Interferences, as the true theory of optical phenomena, the
condition of England was not very favorable to a fair appreciation
of the value of the new opinion. The men of science were strongly
pre-occupied in favor of the doctrine of emission, not only from a
national interest in Newton's glory, and a natural reverence for his
authority, but also from deference towards the geometers of France,
who were looked up to as our masters in the application of
mathematics to physics, and who were understood to be Newtonians in
this as in other subjects. A general tendency to an atomic
philosophy, which had begun to appear from the time of Newton,
operated powerfully; and {112} the hypothesis of emission was so
easily conceived, that, when recommended by high authority, it
easily became popular; while the hypothesis of luminiferous
undulations, unavoidably difficult to comprehend, even by the aid of
steady thought, was neglected, and all but forgotten.

Yet the reception which Young's opinions met with was more harsh
than he might have expected, even taking into account all these
considerations. But there was in England no visible body of men,
fitted by their knowledge and character to pronounce judgment on
such a question, or to give the proper impulse and bias to public
opinion. The Royal Society, for instance, had not, for a long time,
by custom or institution, possessed or aimed at such functions. The
writers of "Reviews" alone, self-constituted and secret tribunals,
claimed this kind of authority. Among these publications, by far the
most distinguished about this period was the _Edinburgh Review_;
and, including among its contributors men of eminent science and
great talents, employing also a robust and poignant style of writing
(often certainly in a very unfair manner), it naturally exercised
great influence. On abstruse doctrines, intelligible to few persons,
more than on other subjects, the opinions and feelings expressed in
a Review must be those of the individual reviewer. The criticism on
some of Young's early papers on optics was written by Mr.
(afterwards Lord) Brougham, who, as we have seen, had experimented
on diffraction, following the Newtonian view, that of inflexion. Mr.
Brougham was perhaps at this time young enough[96\9] to be somewhat
intoxicated with the appearance of judicial authority in matters of
science, which his office of anonymous reviewer gave him: and even
in middle-life, he was sometimes considered to be prone to indulge
himself in severe and sarcastic expressions. In January, 1803, was
published[97\9] his critique on Dr. Young's Bakerian Lecture, _On
the Theory of Light and Colors_, in which lecture the doctrine of
undulations and the law of interferences was maintained. This
critique was an uninterrupted strain of blame and rebuke. "This
paper," the reviewer said, "contains nothing which deserves the name
either of experiment or discovery." He charged the writer with
"dangerous relaxations of the principles of physical logic." "We
wish," he cried, "to recall philosophers to the strict and severe
methods of investigation," describing them as those pointed out by
Bacon, Newton, and the like. Finally, Dr. Young's speculations {113}
were spoken of as a hypothesis, which is a mere work of fancy; and
the critic added, "we cannot conclude our review without entreating
the attention of the Royal Society, which has admitted of late so
many hasty and unsubstantial papers into its _Transactions_;" which
habit he urged them to reform. The same aversion to the undulatory
theory appears soon after in another article by the same reviewer,
on the subject of Wollaston's measures of the refraction of Iceland
spar; he says, "We are much disappointed to find that so acute and
ingenious an experimentalist should have adopted the wild optical
theory of vibrations." The reviewer showed ignorance as well as
prejudice in the course of his remarks; and Young drew up an answer,
which was ably written, but being published separately had little
circulation. We can hardly doubt that these Edinburgh reviews had
their effect in confirming the general disposition to reject the
undulatory theory.

[Note 96\9: His age was twenty-four.]

[Note 97\9: _Edin. Review_, vol. i. p. 450.]

We may add, however, that Young's mode of presenting his opinions
was not the most likely to win them favor; for his mathematical
reasonings placed them out of the reach of popular readers, while
the want of symmetry and system in his symbolical calculations,
deprived them of attractiveness for the mathematician. He himself
gave a very just criticism of his own style of writing, in speaking
on another of his works:[98\9] "The mathematical reasoning, for want
of mathematical symbols, was not understood, even by tolerable
mathematicians. From a dislike of the affectation of algebraical
formality which he had observed in some foreign authors, he was led
into something like an affectation of simplicity, which was equally
inconvenient to a scientific reader."

[Note 98\9: See _Life of Young_, p. 54.]

Young appears to have been aware of his own deficiency in the power
of drawing public favor, or even notice, to his discoveries. In
1802, Davy writes to a friend, "Have you seen the theory of my
colleague, Dr. Young, on the undulations of an ethereal medium as
the cause of light? It is not likely to be a popular hypothesis,
after what has been said by Newton concerning it. He would be very
much flattered if you could offer any observations upon it, _whether
for or against it_." Young naturally felt confident in his power of
refuting objections, and wanted only the opportunity of a public
combat.

Dr. Brewster, who was, at this period, enriching optical knowledge
with so vast a train of new phenomena and laws, shared the general
aversion to the undulatory theory, which, indeed, he hardly overcame
{114} thirty years later. Dr. Wollaston was a person whose character
led him to look long at the laws of phenomena, before he attempted
to determine their causes; and it does not appear that he had
decided the claims of the rival theories in his own mind. Herschel
(I now speak of the son) had at first the general mathematical
prejudice in favor of the emission doctrine. Even when he had
himself studied and extended the laws of dipolarized phenomena, he
translated them into the language of the theory of moveable
polarization. In 1819, he refers to, and corrects, this theory; and
says, it is now "relieved from every difficulty, and entitled to
rank with the fits of easy transmission and reflection as a general
and simple physical law;" a just judgment, but one which now conveys
less of praise than he then intended. At a later period, he remarked
that we cannot be certain that if the theory of emission had been as
much cultivated as that of undulation, it might not have been as
successful; an opinion which was certainly untenable after the fair
trial of the two theories in the case of diffraction, and
extravagant after Fresnel's beautiful explanation of double
refraction and polarization. Even in 1827, in a _Treatise on Light_,
published in the _Encyclopædia Metropolitana_, he gives a section to
the calculations of the Newtonian theory; and appears to consider
the rivalry of the theories as still subsisting. But yet he there
speaks with a proper appreciation of the advantages of the new
doctrine. After tracing the prelude to it, he says, "But the
unpursued speculations of Newton, and the opinions of Hooke, however
distinct, must not be put in competition, and, indeed, ought
scarcely to be mentioned, with the elegant, simple, and
comprehensive theory of Young,--a theory which, if not founded in
nature, is certainly one of the happiest fictions that the genius of
man ever invented to grasp together natural phenomena, which, at
their first discovery, seemed in irreconcileable opposition to it.
It is, in fact, in all its applications and details, one succession
of _felicities_; insomuch, that we may almost be induced to say, if
it be not true, it deserves to be so."

In France, Young's theory was little noticed or known, except
perhaps by M. Arago, till it was revived by Fresnel. And though
Fresnel's assertion of the undulatory theory was not so rudely
received as Young's had been, it met with no small opposition from
the older mathematicians, and made its way slowly to the notice and
comprehension of men of science. M. Arago would perhaps have at once
adopted the conception of transverse vibrations, when it was
suggested by his fellow-laborer, Fresnel, if it had not been that he
was a member of the {115} Institute, and had to bear the brunt of
the war, in the frequent discussions on the undulatory theory; to
which theory Laplace, and other leading members, were so vehemently
opposed, that they would not even listen with toleration to the
arguments in its favor. I do not know how far influences of this
kind might operate in producing the delays which took place in the
publication of Fresnel's papers. We have seen that he arrived at the
conception of transverse vibrations in 1816, as the true key to the
understanding of polarization. In 1817 and 1818, in a memoir read to
the Institute, he analysed and explained the perplexing phenomena of
quartz, which he ascribed to a _circular polarization_. This memoir
had not been printed, nor any extract from it inserted in the
scientific journals, in 1822, when he confirmed his views by further
experiments.[99\9] His remarkable memoir, which solved the
extraordinary and capital problem of the connexion of double
refraction and crystallization, though written in 1821, was not
published till 1827. He appears by this time to have sought other
channels of publication. In 1822, he gave,[100\9] in the _Annales de
Chimie et de Physique_, an explanation of refraction on the
principles of the undulatory theory; alleging, as the reason for
doing so, that the theory was still little known. And in succeeding
years there appeared in the same work, his theory of reflection. His
memoir on this subject (_Mémoire sur la Loi des Modifications que la
Réflexion imprime à la Lumière Polarisée_,) was read to the Academy
of Sciences in **1823. But the original paper was mislaid, and, for a
time, supposed to be lost; it has since been recovered among the
papers of M. Fourier, and printed in the eleventh volume of the
Memoirs of the Academy.[101\9] Some of the speculations to which he
refers, as communicated to the Academy, have never yet
appeared.[102\9]

[Note 99\9: Hersch. _Light_, p. 539.]

[Note 100\9: _Ann. de Chim._ 1822, tom. xxi. p. 235.]

[Note 101\9: Lloyd. _Report on Optics_, p. 363. (Fourth Rep. of
Brit. Ass.)]

[Note 102\9: Ib. p. 316, _note._]

Still Fresnel's labors were, from the first, duly appreciated by
some of the most eminent of his countrymen. His _Memoir on
Diffraction_ was, as we have seen, crowned in 1819: and, in 1822, a
Report upon his _Memoir on Double Refraction_ was drawn up by a
commission consisting of MM. Ampère, Fourier, and Arago. In this
report[103\9] Fresnel's theory is spoken of as confirmed by the most
delicate tests. The reporters add, respecting his "theoretical ideas
on the particular kind of undulations which, according to him,
constitute light," that "it would be impossible for them to
pronounce at present a decided {116} judgment," but that "they have
not thought it right to delay any longer making known a work of
which the difficulty is attested by the fruitless efforts of the
most skilful philosophers, and in which are exhibited in the same
brilliant degree, the talent for experiment and the spirit of
invention."

[Note 103\9: _Ann. Chim._ tom. xx. p. 343.]

In the meantime, however, a controversy between the theory of
undulations and the theory of moveable polarization which M. Biot
had proposed with a view of accounting for the colors produced by
dipolarizing crystals, had occurred among the French men of science.
It is clear that in some main features the two theories coincide;
the intervals of interference in the one theory being represented by
the intervals of the oscillations in the other. But these intervals
in M. Biot's explanations were arbitrary hypotheses, suggested by
these very facts themselves; in Fresnel's theory, they were
essential parts of the general scheme. M. Biot, indeed, does not
appear to have been averse from a coalition; for he allowed[104\9]
to Fresnel that "the theory of undulations took the phenomena at a
higher point and carried them further." And M. Biot could hardly
have dissented from M. Arago's account of the matter, that Fresnel's
views "_linked together_"[105\9] the oscillations of moveable
polarization. But Fresnel, whose hypothesis was all of one piece,
could give up no part of it, although he allowed the usefulness of
M. Biot's formulæ. Yet M. Biot's speculations fell in better with
the views of the leading mathematicians of Paris. We may consider as
evidence of the favor with which they were looked upon, the large
space they occupy in the volumes of the Academy for 1811, 1812,
1817, and 1818. In 1812, the entire volume is filled with a memoir
of M. Biot's on the subject of moveable polarization. This doctrine
also had some advantage in coming early before the world in a
didactic form, in his _Traité de Physique_, which was published in
1816, and was the most complete treatise on general physics which
had appeared up to that time. In this and others of this author's
writings, he expresses facts so entirely in the terms of his own
hypothesis, that it is difficult to separate the two. In the sequel
M. Arago was the most prominent of M. Biot's opponents; and in his
report upon Fresnel's memoir on the colors of crystalline plates, he
exposed the weaknesses of the theory of moveable polarization with
some severity. The details of this controversy need not occupy us;
but we may observe that this may be considered as the last struggle
{117} in favor of the theory of emission among mathematicians of
eminence. After this crisis of the war, the theory of moveable
polarization lost its ground; and the explanations of the undulatory
theory, and the calculations belonging to it, being published in the
_Annales de Chimie et de Physique_, of which M. Arago was one of the
conductors, soon diffused it over Europe.

[Note 104\9: _Ann. Chim._ tom. xvii. p. 251.]

[Note 105\9: "Nouait".]

It was probably in consequence of the delays to which we have
referred, in the publication of Fresnel's memoirs, that as late as
December, 1826, the Imperial Academy at St Petersburg proposed, as
one of their prize-questions for the two following years, this,--"To
deliver the optical system of waves from all the objections which
have (as it appears) with justice been urged against it, and to
apply it to the polarization and double refraction of light." In the
programme to this announcement, Fresnel's researches on the subject
are not alluded to, though his memoir on diffraction is noticed;
they were, therefore, probably not known to the Russian Academy.

Young was always looked upon as a person of marvellous variety of
attainments and extent of knowledge; but during his life he hardly
held that elevated place among great discoverers which posterity
will probably assign him. In 1802, he was constituted Foreign
Secretary of the Royal Society, an office which he held during life;
in 1827 he was elected one of the eight Foreign Members of the
Institute of France; perhaps the greatest honor which men of science
usually receive. The fortune of his life in some other respects was
of a mingled complexion. His profession of a physician occupied,
sufficiently to fetter, without rewarding him; while he was Lecturer
at the Royal Institution, he was, in his lectures, too profound to
be popular; and his office of Superintendent of the _Nautical
Almanac_ subjected him to much minute labor, and many petulant
attacks of pamphleteers. On the other hand, he had a leading part in
the discovery of the long-sought key to the Egyptian hieroglyphics;
and thus the age which was marked by two great discoveries, one in
science and one in literature, owed them both in a great measure to
him. Dr. Young died in 1829, when he had scarcely completed his
fifty-sixth year. Fresnel was snatched from science still more
prematurely, dying, in 1827, at the early age of thirty-nine.

We need not say that both these great philosophers possessed, in an
eminent degree, the leading characteristics of the discoverer's
mind, perfect clearness of view, rich fertility of invention, and
intense love of knowledge. We cannot read without great interest a
letter of {118} Fresnel to Young,[106\9] in November, 1824: "For a
long time that sensibility, or that vanity, which people call love
of glory, is much blunted in me. I labor much less to catch the
suffrages of the public, than to obtain an inward approval which has
always been the sweetest reward of my efforts. Without doubt I have
often wanted the spur of vanity to excite me to pursue my researches
in moments of disgust and discouragement. But all the compliments
which I have received from MM. Arago, De Laplace, or Biot, never
gave me so much pleasure as the discovery of a theoretical truth, or
the confirmation of a calculation by experiment."

[Note 106\9: I was able to give this, and some other extracts, from
the then unedited correspondence of Young and Fresnel, by the
kindness of (the Dean of Ely) Professor Peacock, of Trinity College,
Cambridge, whose Life of Dr. Young has since been published.]

Though Young and Fresnel were in years the contemporaries of many
who are now alive, we must consider ourselves as standing towards
them in the relation of posterity. The Epoch of Induction in Optics
is past; we have now to trace the Verification and Application of
the true theory.




CHAPTER XIII.

CONFIRMATION AND EXTENSION OF THE UNDULATORY THEORY.


AFTER the undulatory theory had been developed in all its main
features, by its great authors, Young and Fresnel, although it bore
marks of truth that could hardly be fallacious, there was still
here, as in the case of other great theories, a period in which
difficulties were to be removed, objections answered, men's minds
familiarized to the new conceptions thus presented to them; and in
which, also, it might reasonably be expected that the theory would
be extended to facts not at first included in its domain. This
period is, indeed, that in which we are living; and we might,
perhaps with propriety, avoid the task of speaking of our living
contemporaries. But it would be unjust to the theory not to notice
some of the remarkable events, characteristic of such a period,
which have already occurred; and this may be done very simply. {119}

In the case of this great theory, as in that of gravitation, by far
the most remarkable of these confirmatory researches were conducted
by the authors of the discovery, especially Fresnel. And in looking
at what he conceived and executed for this purpose, we are, it
appears to me, strongly reminded of Newton, by the wonderful
inventiveness and sagacity with which he devised experiments, and
applied to them mathematical reasonings.

1. _Double Refraction of Compressed Glass._--One of these
confirmatory experiments was the production of double refraction by
the compression of glass. Fresnel observes,[107\9] that though Sir
D. Brewster had shown that glass under compression produced colors
resembling those which are given by doubly-refracting crystals,
"very skilful physicists had not considered those experiments as a
sufficient proof of the bifurcation of the light." In the hypothesis
of moveable polarization, it is added, there is no apparent
connexion between these phenomena of coloration and double
refraction; but on Young's theory, that the colors arise from two
rays which have traversed the crystal with different velocities, it
appears almost unavoidable to admit also a difference of path in the
two rays.

[Note 107\9: _Ann. de Chim._ 1822, tom. xx. p. 377.]

"Though," he says, "I had long since adopted this opinion, it did
not appear to me so completely demonstrated, that it was right to
neglect an experimental verification of it;" and therefore, in 1819,
he proceeded to satisfy himself of the fact, by the phenomena of
diffraction. The trial left no doubt on the subject; but he still
thought it would be interesting actually to produce two images in
glass by compression; and by a highly-ingenious combination,
calculated to exaggerate the effect of the double refraction, which
is very feeble, even when the compression is most intense, he
obtained two distinct images. This evidence of the dependence of
dipolarizing structure upon a doubly-refracting state of particles,
thus excogitated out of the general theory, and verified by trial,
may well be considered, as he says, "as a new occasion of proving
the infallibility of the principle of interferences."

2. _Circular Polarization._--Fresnel then turned his attention to
another set of experiments, related to this indeed, but by a tie so
recondite, that nothing less than his clearness and acuteness of
view could have detected any connexion. The optical properties of
quartz had been perceived to be peculiar, from the period of the
discovery {120} of dipolarized colors by MM. Arago and Biot. At the
end of the Notice just quoted, Fresnel says,[108\9] "As soon as my
occupations permit me, I propose to employ a pile of prisms similar
to that which I have described, in order to study the double
refraction of the rays which traverse crystals of quartz in the
direction of the axis." He then ventures, without hesitation, to
describe beforehand what the phenomena will be. In the _Bulletin des
Sciences_[109\9] for December, 1822, it is stated that experiment
had confirmed what he had thus announced.

[Note 108\9: _Ann. de Chim._ 1822, tom. xx. p. 382.]

[Note 109\9: Ib. _Ann. de Chim._ 1822, tom. xx. p. 191.]

The phenomena are those which have since been spoken of as _circular
polarization_; and the term first occurs in this notice.[110\9] They
are very remarkable, both by their resemblances to, and their
differences from, the phenomena of _plane-polarized_ light. And the
manner in which Fresnel was led to this anticipation of the facts is
still more remarkable than the facts themselves. Having ascertained
by observation that two differently-polarized rays, totally
reflected at the internal surface of glass, suffer different
_retardations_ of their undulations, he applied the formulæ which he
had obtained for the polarizing effect of reflection to this case.
But in this case the formulæ expressed an impossibility; yet as
algebraical formulæ, even in such cases, have often some meaning, "I
interpreted," he says,[111\9] "in the manner which appeared to me
most natural and most probable, what the analysis indicated by this
imaginary form;" and by such an interpretation he collected the law
of the difference of undulation of the two rays. He was thus able to
predict that by two internal reflections in a _rhomb_, or
parallelopiped of glass, of a certain form and position, a polarized
ray would acquire a circular undulation of its particles; and this
constitution of the ray, it appeared, by reasoning further, would
show itself by its possessing peculiar properties, partly the same
as those of polarized light, and partly different. This
extraordinary anticipation was exactly confirmed; and thus the
apparently bold and strange guess of the author was fully justified,
or at least assented to, even by the most cautious philosophers. "As
I cannot appreciate the mathematical evidence for the nature of
circular polarization," says Prof. Airy,[112\9] "I shall mention the
experimental evidence on which I receive it." The conception has
since been universally adopted.

[Note 110\9: Ib. p. 194.]

[Note 111\9: _Bullet. des Sc._ 1823, p. 33.]

[Note 112\9: _Camb. Trans._ vol. iv. p. 81, 1831.]

But Fresnel, having thus obtained circularly-polarized rays, saw
{121} that he could account for the phenomena of quartz, already
observed by M. Arago, as we have noticed in Chap. ix., by supposing
two circularly-polarized rays to pass, with different velocities,
along the axis. The curious succession of colors, following each
other in right-handed or left-handed circular order, of which we
have already spoken, might thus be hypothetically explained.

But was this hypothesis of two circularly-polarized rays, travelling
along the axis of such crystals, to be received, merely because it
accounted for the phenomena? Fresnel's ingenuity again enabled him
to avoid such a defect in theorizing. If there were two such rays,
they might be visibly separated[113\9] by the same artifice, of a
pile of prisms properly achromatized, which he had used for
compressed glass. The result was, that he did obtain a visible
separation of the rays; and this result has since been confirmed by
others, for instance. Professor Airy.[114\9] The rays were found to
be in all respects identical with the circularly-polarized rays
produced by the internal reflections in Fresnel's rhomb. This kind
of double refraction gave a hypothetical explanation of the laws
which M. Biot had obtained for the phenomena of this class; for
example,[115\9] the rule, that the deviation of the plane of
polarization of the emergent ray is inversely as the square of the
length of an undulation for each kind of rays. And thus the
phenomena produced by light passing along the axis of quartz were
reduced into complete conformity with the theory.

[Note 113\9: _Bull. des Sc._ 1822, p. 193.]

[Note 114\9: _Cambridge Trans._ iv. p. 80.]

[Note 115\9: _Bull. des Sc._ 1822, p. 197.]

[2nd Ed.] [I believe, however, Fresnel did not deduce the phenomenon
from the mathematical formula, without the previous suggestion of
experiment. He _observed_ appearances which implied a difference of
retardation in the two differently-polarized rays at total
reflection; as Sir D. Brewster observed in reflection of metals
phenomena having a like character. The general fact being observed,
Fresnel used the theory to discover the law of this retardation, and
to determine a construction in which, one ray being a quarter of an
undulation retarded more than the other, circular polarization would
be produced. And this anticipation was verified by the construction
of his _rhomb_.

As a still more curious verification of this law, another of
Fresnel's experiments may be mentioned. He found the proper angles
for a circularly-polarizing glass rhomb on the supposition that
there were {122} _four_ internal reflections instead of two; two of
the four taking place when the surface of the glass was dry, and two
when it was wet. The rhomb was made; and when all the points of
reflection were dry, the light was not circularly polarized; when
two points were wet, the light was circularly polarized; and when
all four were wet, it was not circularly polarized.]

3. _Elliptical Polarization in Quartz._--We now come to one of the
few additions to Fresnel's theory which have been shown to be
necessary. He had accounted fully for the colors produced by the
rays which travel _along the axis_ of quartz crystals; and thus, for
the colors and changes of the central spot which is produced when
polarized light passes through a transverse plate of such crystals.
But this central spot is surrounded by rings of colors. How is the
theory to be extended to these?

This extension has been successfully made by Professor Airy.[116\9]
His hypothesis is, that as rays passing along the axis of a quartz
crystal are circularly polarized, rays which are oblique to the axis
are elliptically polarized, the amount of ellipticity depending, in
some unknown manner, upon the obliquity; and that each ray is
separated by double refraction into two rays polarized elliptically;
the one right-handed, the other left-handed. By means of these
suppositions, he not only was enabled to account for the simple
phenomena of single plates of quartz; but for many most complex and
intricate appearances which arise from the superposition of two
plates, and which at first sight might appear to defy all attempts
to reduce them to law and symmetry; such as spirals, curves
approaching to a square form, curves broken in four places. "I can
hardly imagine," he says,[117\9] very naturally, "that any other
supposition would represent the phenomena to such extreme accuracy.
I am not so much struck with the accounting for the continued
dilatation of circles, and the general representation of the forms
of spirals, as with the explanations of the minute deviations from
symmetry; as when circles become almost square, and crosses are
inclined to the plane of polarization. And I believe that any one
who shall follow my investigation, and imitate my experiments, will
be surprised at their perfect agreement."

[Note 116\9: _Camb. Trans._, iv. p. 83, &c.]

[Note 117\9: _Camb. Trans._, iv. p. 122.]

4. _Differential Equations of Elliptical Polarization._--Although
circular and elliptical polarization can be clearly conceived, and
their existence, it would seem, irresistibly established by the
phenomena, it {123} is extremely difficult to conceive any
arrangement of the particles of bodies by which such motions can
mechanically be produced; and this difficulty is the greater,
because some fluids and some gases impress a circular polarization
upon light; in which cases we cannot imagine any definite
arrangement of the particles, such as might form the mechanism
requisite for the purpose. Accordingly, it does not appear that any
one has been able to suggest even a plausible hypothesis on that
subject. Yet, even here, something has been done. Professor Mac
Cullagh, of Dublin, has discovered that by slightly modifying the
_analytical expressions_ resulting from the common case of the
propagation of light, we may obtain other expressions which would
give rise to such motions as produce circular and elliptical
polarization. And though we cannot as yet assign the mechanical
interpretation of the language of analysis thus generalized, this
generalization brings together and explains by one common numerical
supposition, two distinct classes of facts;--a circumstance which,
in all cases, entitles an hypothesis to a very favorable
consideration.

Mr. Mac Cullagh's assumption consists in adding to the two equations
of motion which are expressed by means of second differentials, two
other terms involving third differentials in a simple and
symmetrical manner. In doing this, he introduces a coefficient, of
which the magnitude determines both the amount of rotation of the
polarization of a ray passing along the axis, as observed and
measured by Biot, and the ellipticity of the polarization of a ray
which is oblique to the axis, according to Mr. Airy's theory, of
which ellipticity that philosopher also had obtained certain
measures. The agreement between the two sets of measures[118\9] thus
brought into connexion is such as very strikingly to confirm Mr. Mac
Cullagh's hypothesis. It appears probable, too, that the
confirmation of this hypothesis involves, although in an obscure and
oracular form, a confirmation of the undulatory theory, which is the
starting-point of this curious speculation.

[Note 118\9: _Royal I. A. Trans._ 1836.]

5. _Elliptical Polarization of Metals._--The effect of metals upon
the light which they reflect, was known from the first to be
different from that which transparent bodies produce. Sir David
Brewster, who has recently examined this subject very fully,[119\9]
has described the modification thus produced, as _elliptic
polarization_. In employing this term, "he seems to have been led,"
it has been observed,[120\9] "by a {124} desire to avoid as much as
possible all reference to theory. The laws which he has obtained,
however, belong to elliptically-polarized light in the sense in
which the term was introduced by Fresnel." And the identity of the
light produced by metallic reflection with the
elliptically-polarized light of the wave-theory, is placed beyond
all doubt, by an observation of Professor Airy, that the rings of
uniaxal crystals, produced by Fresnel's elliptically-polarized
light, are exactly the same as those produced by Brewster's metallic
light.

[Note 119\9: _Phil. Trans._ 1830.]

[Note 120\9: Lloyd, _Report on Optics_, p. 372. (Brit. Assoc.)]

6. _Newton's Rings by Polarized Light._--Other modifications of the
phenomena of thin plates by the use of polarized light, supplied
other striking confirmations of the theory. These were in one case
the more remarkable, since the result was foreseen by means of a
rigorous application of the conception of the vibratory motion of
light, and confirmed by experiment. Professor Airy, of Cambridge,
was led by his reasonings to see, that if Newton's rings are
produced between a lens and a plate of metal, by polarized light,
then, up to the polarizing angle, the central spot will be black,
and instantly beyond this, it will be white. In a note,[121\9] in
which he announced this, he says, "This I anticipated from Fresnel's
expressions; it is confirmatory of them, and defies emission." He
also predicted that when the rings were produced between two
substances of very different refractive powers, the centre would
twice pass from black to white and from white to black, by
increasing the angle; which anticipation was fulfilled by using a
diamond for the higher refraction.[122\9]

[Note 121\9: Addressed to myself, dated May 28, 1831. I ought,
however, to notice, that this experiment had been made by M. Arago,
fifteen years earlier, and published: though not then recollected by
Mr. Airy.]

[Note 122\9: _Camb. Trans._ vol. ii. p. 409.]

7. _Conical Refraction._--In the same manner. Professor Hamilton of
Dublin pointed out that according to the Fresnelian doctrine of double
refraction, there is a certain direction of a crystal in which a
single ray of light will be refracted so as to form a _conical
pencil_. For the direction of the refracted ray is determined by a
plane which touches the wave surface, the rule being that the ray must
pass from the centre of the surface to the point of contact; and
though in general this contact gives a single point only, it so
happens, from the peculiar inflected form of the wave surface, which
has what is called _a cusp_, that in one particular position, the
plane can touch the surface in an entire circle. Thus the general rule
which assigns the path of {125} the refracted ray, would, in this
case, guide it from the centre of the surface to every point in the
circumference of the circle, and thus make it a cone. This very
curious and unexpected result, which Professor Hamilton thus obtained
from the theory, his friend Professor Lloyd verified as an
experimental fact. We may notice, also, that Professor Lloyd found the
light of the conical pencil to be polarized according to a law of an
unusual kind; but one which was easily seen to be in complete
accordance with the theory.

8. _Fringes of Shadows._--The phenomena of the _fringes of shadows_
of small holes and groups of holes, which had been the subject of
experiment by Fraunhofer, were at a later period carefully observed
in a vast variety of cases by M. Schwerd of Spires, and published in
a separate work,[123\9] _Beugungs-erscheinungen_ (Phenomena of
Inflection), 1836. In this Treatise, the author has with great
industry and skill calculated the integrals which, as we have seen,
are requisite in order to trace the consequences of the theory; and
the accordance which he finds between these and the varied and
brilliant results of observation is throughout exact. "I shall,"
says he, in the preface,[124\9] "prove by the present Treatise, that
all inflection-phenomena, through openings of any form, size, and
arrangement, are not only explained by the undulation-theory, but
that they can be represented by analytical expressions, determining
the intensity of the light in any point whatever." And he justly
adds, that the undulation-theory accounts for the phenomena of
light, as completely as the theory of gravitation does for the facts
of the solar system.

[Note 123\9: _Die Beugungs-erscheinungen, aus dem Fundamental-gesetz
der Undulations-Theorie analytisch entwickelt und in Bildern
dargestellt_, von F. M. Schwerd. Mannheim, 1835.]

[Note 124\9: Dated Speyer, Aug. 1835.]

9. _Objections to the Theory._--We have hitherto mentioned only
cases in which the undulatory theory was either entirely successful
in explaining the facts, or at least hypothetically consistent with
them and with itself. But other objections were started, and some
difficulties were long considered as very embarrassing. Objections
were made to the theory by some English experimenters, as Mr.
Potter, Mr. Barton, and others. These appeared in scientific
journals, and were afterwards answered in similar publications. The
objections depended partly on the measure of the _intensity_ of
light in the different points of the phenomena (a datum which it is
very difficult to obtain with accuracy {126} by experiment), and
partly on misconceptions of the theory; and I believe there are none
of them which would now be insisted on.

We may mention, also, another difficulty, which it was the habit of
the opponents of the theory to urge as a reproach against it, long
after it had been satisfactorily explained: I mean the
_half-undulation_ which Young and Fresnel had found it necessary, in
some cases, to assume as gained or lost by one of the rays. Though
they and their followers could not analyse the mechanism of
reflection with sufficient exactness to trace out all the
circumstances, it was not difficult to see, upon Fresnel's
principles, that reflection from the interior and exterior surface
of glass must be of opposite kinds, which might be expressed by
supposing one of these rays to lose half an undulation. And thus
there came into view a justification of the step which had
originally been taken upon empirical grounds alone.

10. _Dispersion, on the Undulatory Theory._--A difficulty of another
kind occasioned a more serious and protracted embarrassment to the
cultivators of this theory. This was the apparent impossibility of
accounting, on the theory, for the prismatic dispersion of color.
For it had been shown by Newton that the amount of refraction is
different for every color; and the amount of refraction depends on
the velocity with which light is propagated. Yet the theory
suggested no reason why the velocity should be different for
different colors: for, by mathematical calculation, vibrations of
all degrees of rapidity (in which alone colors differ) are
propagated with the same speed. Nor does analogy lead us to expect
this variety. There is no such difference between quick and slow
waves of air. The sounds of the deepest and the highest bells of a
peal are heard at any distance in the same order. Here, therefore,
the theory was at fault.

But this defect was far from being a fatal one. For though the
theory did not explain, it did not contradict, dispersion. The
suppositions on which the calculations had been conducted, and the
analogy of sound, were obviously in no small degree precarious. The
velocity of propagation might differ for different rates of
undulation, in virtue of many causes which would not affect the
general theoretical results.

Many such hypothetical causes were suggested by various eminent
mathematicians, as solutions of this conspicuous difficulty. But
without dwelling upon these conjectures, it may suffice to notice
that hypothesis upon which the attention of mathematicians was soon
concentrated. This was the _hypothesis of finite intervals_ between
the {127} particles of the ether. The length of one of those
undulations which produce light, is a very small quantity, its mean
value being 1⁄50,000th of an inch; but in the previous
investigations of the consequences of the theory, it had been
assumed that the distance from each other, of the particles of the
ether, which, by their attractions or repulsions, caused the
undulations to be propagated, is indefinitely less than this small
quantity;--so that its amount might be neglected in the cases in
which the length of the undulation was one of the quantities which
determined the result. But this assumption was made arbitrarily, as
a step of simplification, and because it was imagined that, in this
way, a nearer approach was made to the case of a continuous fluid
ether, which the supposition of distinct particles imperfectly
represented. It was still free for mathematicians to proceed upon
the opposite assumption, of particles of which the distances were
finite, either as a mathematical basis of calculation, or as a
physical hypothesis; and it remained to be seen if, when this was
done, the velocity of light would still be the same for different
lengths of undulation, that is, for different colors. M. Cauchy,
calculating, upon the most general principles, the motion of such a
collection of particles as would form an elastic medium, obtained
results which included the new extension of the previous hypothesis.
Professor Powell, of Oxford, applied himself to reduce to
calculation, and to compare with experiment, the result of these
researches. And it appeared that, on M. Cauchy's principles, a
variation in the velocity of light is produced by a variation in the
length of the wave, provided that the interval between the molecules
of the ether bears a sensible ratio to the length of an
undulation.[125\9] Professor Powell obtained also, from the general
expressions, a formula expressing the relation between the
refractive index of a ray, and the length of a wave, or the color of
light.[126\9] It then became his task to ascertain whether this
relation obtained experimentally; and he found a very close
agreement between the numbers which resulted from the formula and
those observed by Fraunhofer, for ten different kinds of media,
namely, certain glasses and fluids.[127\9] To these he afterwards
added ten other cases of crystals observed by M. Rudberg.[128\9] Mr.
Kelland, of Cambridge, also calculated, in a manner somewhat
different, the results of the same hypothesis of finite
intervals;[129\9] and, obtaining {128} formulæ not exactly the same
as Professor Powell, found also an agreement between these and
Fraunhofer's observations.

[Note 125\9: _Phil. Mag._ vol. vi. p. 266.]

[Note 126\9: Ib. vol. vii. 1835, p. 266.]

[Note 127\9: _Phil. Trans._ 1835, p. 249.]

[Note 128\9: Ib. 1836, p. 17.]

[Note 129\9: _Camb. Trans._ vol.  vi. p. 153.]

It may be observed, that the refractive indices observed and
employed in these comparisons, were not those determined by the
color of the ray, which is not capable of exact identification, but
those more accurate measures which Fraunhofer was enabled to make,
in consequence of having detected in the spectrum the black lines
which he called B, C, D, E, F, G, H. The agreement between the
theoretical formulæ and the observed numbers is remarkable,
throughout all the series of comparisons of which we have spoken.
Yet we must at present hesitate to pronounce upon the hypothesis of
finite intervals, as proved by these calculations; for though this
hypothesis has given results agreeing so closely with experiment, it
is not yet clear that other hypotheses may not produce an equal
agreement. By the nature of the case, there must be a certain
gradation and continuity in the succession of colors in the
spectrum, and hence, any supposition which will account for the
general fact of the whole dispersion, may possibly account for the
amount of the intermediate dispersions, because these must be
interpolations between the extremes. The result of this hypothetical
calculation, however, shows very satisfactorily that there is not,
in the fact of dispersion, anything which is at all formidable to
the undulatory theory.

11. _Conclusion._--There are several other of the more recondite
points of the theory which may be considered as, at present, too
undecided to allow us to speak historically of the discussions which
they have occasioned.[130\9] For example, it was conceived, for some
time, that the vibrations of polarized light are perpendicular to
the plane of polarization. But this assumption was not an essential
part of the theory; and all the phenomena would equally allow us to
suppose the vibrations to be in the polarization plane; the main
requisite being, that light polarized in planes at right angles to
each other, should also have the vibrations at right angles.
Accordingly, for some time, this point was left undecided by Young
and Fresnel, and, more recently, some mathematicians have come to
the opinion that ether vibrates in the plane of polarization. The
theory of transverse vibrations is equally stable, whichever
supposition may be finally confirmed.

[Note 130\9:  For on account of these, see Professor Lloyd's _Report
on Physical Optics_. (Brit. Assoc. Report, 1834.)]

We may speak, in the same manner, of the suppositions which, from
{129} the time of Young and Fresnel, the cultivators of this theory
have been led to make respecting the mechanical constitution of the
ether, and the forces by which transverse vibrations are produced.
It was natural that various difficulties should arise upon such
points, for transverse vibrations had not previously been made the
subject of mechanical calculation, and the forces which occasion
them must act in a different manner from those which were previously
contemplated. Still, we may venture to say, without entering into
these discussions, that it has appeared, from all the mathematical
reasonings which have been pursued, that there is not, in the
conception of transverse vibrations, anything inconsistent either
with the principles of mechanics, or with the best general views
which we can form, of the forces by which the universe is held
together.

I willingly speak as briefly as the nature of my undertaking allows,
of those points of the undulatory theory which are still under
deliberation among mathematicians. With respect to these, an
intimate acquaintance with mathematics and physics is necessary to
enable any one to understand the steps which are made from day to
day; and still higher philosophical qualifications would be
requisite in order to pronounce a judgment upon them. I shall,
therefore, conclude this survey by remarking the highly promising
condition of this great department of science, in respect to the
character of its cultivators. Nothing less than profound thought and
great mathematical skill can enable any one to deal with this
theory, in any way likely to promote the interests of science. But
there appears, in the horizon of the scientific world, a
considerable class of young mathematicians, who are already bringing
to these investigations the requisite talents and zeal; and who,
having acquired their knowledge of the theory since the time when
its acceptation was doubtful, possess, without effort, that
singleness and decision of view as to its fundamental doctrines,
which it is difficult for those to attain whose minds have had to go
through the hesitation, struggle, and balance of the epoch of the
establishment of the theory. In the hands of this new generation, it
is reasonable to suppose the Analytical Mechanics of light will be
improved as much as the Analytical Mechanics of the solar system was
by the successors of Newton. We have already had to notice many of
this younger race of undulationists. For besides MM. Cauchy,
Poisson, and Ampère, M. Lamé has been more recently following these
researches in France.[131\9] In {130} Belgium, M. Quetelet has given
great attention to them; and, in our own country, Sir William
Hamilton, and Professor Lloyd, of Dublin, have been followed by Mr.
Mac Cullagh. Professor Powell, of Oxford, has continued his
researches with unremitting industry; and, at Cambridge, Professor
Airy, who did much for the establishment and diffusion of the theory
before he was removed to the post of Astronomer Royal, at Greenwich,
has had the satisfaction to see his labors continued by others, even
to the most recent time; for Mr. Kelland,[132\9] whom we have
already mentioned, and Mr. Archibald Smith,[133\9] the two persons
who, in 1834 and 1836, received the highest mathematical honors
which that university can bestow, have both of them published
investigations respecting the undulatory theory.

[Note 131\9: Prof. Lloyd's _Report_, p. 392.]

[Note 132\9: _On the Dispersion of Light, as explained by the
Hypothesis of Finite Intervals._ Camb. Trans. vol. vi. p. 153.]

[Note 133\9: _Investigation of the Equation to Fresnel's Wave
Surface_, ib. p. 85. See also, in the same volume, _Mathematical
Considerations on the Problem of the Rainbow_, showing it to belong
to Physical Optics, by R. Potter, Esq., of Queen's College.]

We may be permitted to add, as a reflection obviously suggested by
these facts, that the cause of the progress of science is
incalculably benefited by the existence of a body of men, trained
and stimulated to the study of the higher mathematics, such as exist
in the British universities, who are thus prepared, when an abstruse
and sublime theory comes before the world with all the characters of
truth, to appreciate its evidence, to take steady hold of its
principles, to pursue its calculations, and thus to convert into a
portion of the permanent treasure and inheritance of the civilized
world, discoveries which might otherwise expire with the great
geniuses who produced them, and be lost for ages, as, in former
times, great scientific discoveries have sometimes been.

The reader who is acquainted with the history of recent optical
discovery, will see that we have omitted much which has justly
excited admiration; as, for example, the phenomena produced by glass
under heat or pressure, noticed by MM. Lobeck, and Biot, and
Brewster, and many most curious properties of particular minerals.
We have omitted, too, all notice of the phenomena and laws of the
absorption of light, which hitherto stand unconnected with the
theory. But in this we have not materially deviated from our main
design; for our end, in what we have done, has been to trace the
advances of Optics {131} towards perfection as a theory; and this
task we have now nearly executed as far as our abilities allow.

We have been desirous of showing that the _type_ of this progress,
in the histories of the two great sciences, Physical Astronomy and
Physical Optics, is the same. In both we have many _Laws of
Phenomena_ detected and accumulated by acute and inventive men; we
have _Preludial_ guesses which touch the true theory, but which
remain for a time imperfect, undeveloped, unconfirmed: finally we
have the _Epoch_ when this true theory, clearly apprehended by great
philosophical geniuses, is recommended by its fully explaining what
it was first meant to explain, and confirmed by its explaining what
it was not meant to explain. We have then its _Progress_ struggling
for a little while with adverse prepossessions and difficulties;
finally overcoming all these, and moving onwards, while its
triumphal procession is joined by all the younger and more vigorous
men of science.

It would, perhaps, be too fanciful to attempt to establish a
parallelism between the prominent persons who figure in these two
histories. If we were to do this, we must consider Huyghens and
Hooke as standing in the place of Copernicus, since, like him, they
announced the true theory, but left it to a future age to give it
development and mechanical confirmation; Malus and Brewster,
grouping them together, correspond to Tycho Brahe and Kepler,
laborious in accumulating observations, inventive and happy in
discovering laws of phenomena; and Young and Fresnel combined, make
up the Newton of optical science.

[2nd Ed.] [In the _Report on Physical Optics_, (_Brit. Ass.
Reports_, 1834,) by Prof. Lloyd, the progress of the mathematical
theory after Fresnel's labors is stated more distinctly than I have
stated it, to the following effect. Ampère, in 1828, proved
Fresnel's mathematical results directly, which Fresnel had only
proved indirectly, and derived from his proof Fresnel's beautiful
geometrical construction. Prof. Mac Cullagh not long after gave a
concise demonstration of the same theorem, and of the other
principal points of Fresnel's theory. He represents the elastic
force by means of an ellipsoid whose axes are inversely proportional
to those of Fresnel's generating ellipsoid, and deduces Fresnel's
construction geometrically. In the third Supplement to his _Essay on
the Theory of Systems of Rays_ (_Trans. R. I. Acad._ vol. xvii.),
Sir W. Hamilton has presented that portion of Fresnel's theory which
relates to the fundamental problem of the determination of the
velocity and polarization of a plane wave, in a very elegant and
analytical form. This he does by means of what he calls the {132}
_characteristic function_ of the optical system to which the problem
belongs. From this function is deduced the _surface of
wave-slowness_ of the medium; and by means of this surface, the
direction of the rays refracted into the medium. From this
construction also Sir W. Hamilton was led to the anticipation of
_conical refraction_, mentioned above.

The investigations of MM. Cauchy and Lamé refer to the laws by which
the particles of the ether act upon each other and upon the
particles of other bodies;--a field of speculation which appears to
me not yet ripe for the final operations of the analyst.

Among the mathematicians who have supplied defects in Fresnel's
reasoning on this subject, I may mention Mr. Tovey, who treated it
in several papers in the _Philosophical Magazine_ (1837-40). Mr.
Tovey's early death must be deemed a loss to mathematical science.

Besides investigating the motion of symmetrical systems of particles
which may be supposed to correspond to biaxal crystals, Mr. Tovey
considered the case of unsymmetrical systems, and found that the
undulations propagated would, in the general case, be elliptical;
and that in a particular case, circular undulations would take
place, such as are propagated along the axis of quartz. It appears
to me, however, that he has not given a definite meaning to those
limitations of his general hypothesis which conduct him to this
result. Perhaps if the hypothetical conditions of this result were
traced into detail, they would be found to reside in a _screw-like_
arrangement of the elementary particles, in some degree such as
crystals of quartz themselves exhibit in their forms, when they have
plagihedral faces at both ends.

Such crystals of quartz are, some like a right-handed and some like
a left-handed screw; and, as Sir John Herschel discovered, the
circular polarization is right-handed or left-handed according as
the plagihedral form is so. In Mr. Tovey's hypothetical
investigation it does not appear upon what part of the hypothesis
this difference of right and left-handed depends. The definition of
this part of the hypothesis is a very desirable step.

When crystals of Quartz are right-handed at one end, they are
right-handed at the other end: but there is a different kind of
plagihedral form, which occurs in some other crystals, for instance,
in Apatite: in these the plagihedral faces are right-handed at the
one extremity and left-handed at the other. For the sake of
distinction, we may call the former _homologous_ plagihedral faces,
since, at both ends, they have the same name; and the latter
_heterologous_ plagihedral faces. {133}

The homologous plagihedral faces of Quartz crystals are accompanied
by homologous circular polarization of the same name. I do not know
that heterologous circular polarization has been observed in any
crystal, but it has been discovered by Dr. Faraday to occur in
glass, &c., when subjected to powerful magnetic action.

Perhaps it was presumptuous in me to attempt to draw such
comparisons, especially with regard to living persons, as I have
done in the preceding pages of this Book. Having published this
passage, however, I shall not now suppress it. But I may observe
that the immense number and variety of the beautiful optical
discoveries which we owe to Sir David Brewster makes the comparison
in his case a very imperfect representation of his triumphs over
nature; and that, besides his place in the history of the Theory of
Optics, he must hold a most eminent position in the history of
Optical Crystallography, whenever the discovery of a True Optical
Theory of Crystals supplies us with the _Epoch_ to which his labors
in this field form so rich a _Prelude_. I cordially assent to the
expression employed by Mr. Airy in the _Phil. Trans._ for 1840, in
which he speaks of Sir David Brewster as "the Father of Modern
Experimental Optics."]



{{135}}
BOOK X.

_SECONDARY MECHANICAL SCIENCES._
(CONTINUED.)

HISTORY
OF
THERMOTICS AND ATMOLOGY.


  Et primum faciunt ignem se vortere in auras
  Aëris; hinc imbrem gigni terramque creari
  Ex imbri; retroque a terrâ cuncta revorti,
  Humorem primum, post aëra deinde calorem;
  Nec cessare hæc inter se mutare, meare,
  De cœlo ad terram de terrâ ad sidera mundi.
          LUCRETIUS, i. 783.

  Water, and Air, and Fire, alternate run
  Their endless circle, multiform, yet one.
  For, moulded by the fervor's latent beams,
  Solids flow loose, and fluids flash to steams,
  And elemental flame, with secret force,
  Pursues through earth, air, sky, its stated course.



{{137}}
INTRODUCTION.

_Of Thermotics and Atmology._


I EMPLOY the term _Thermotics_ to include all the doctrines
respecting Heat, which have hitherto been established on proper
scientific grounds. Our survey of the history of this branch of
science must be more rapid and less detailed than it has been in
those subjects of which we have hitherto treated: for our knowledge
is, in this case, more vague and uncertain than in the others, and
has made less progress towards a general and certain theory. Still,
the narrative is too important and too instructive to be passed over.

The distinction of Formal Thermotics and Physical Thermotics,--of
the discovery of the mere Laws of Phenomena, and the discovery of
their causes,--is applicable here, as in other departments of our
knowledge. But we cannot exhibit, in any prominent manner, the
latter division of the science now before us; since no general
theory of heat has yet been propounded, which affords the means of
calculating the circumstances of the phenomena of conduction,
radiation, expansion, and change of solid, liquid, and gaseous form.
Still, on each of these subjects there have been proposed, and
extensively assented to, certain general views, each of which
explains its appropriate class of phenomena; and, in some cases,
these principles have been clothed in precise and mathematical
conditions, and thus made bases of calculation.

These principles, thus possessing a generality of a limited kind,
connecting several observed laws of phenomena, but yet not
connecting all the observed classes of facts which relate to heat,
will require our separate attention. They may be described as the
Doctrine of Conduction, the Doctrine of Radiation, the Doctrine of
Specific Heat, and the Doctrine of Latent Heat; and these, and
similar doctrines respecting heat, make up the science which we may
call _Thermotics proper_.

But besides these collections of principles which regard heat by
itself, the relations of heat and moisture give rise to another and
important collection of laws and principles, which I shall treat of
in connexion with Thermotics, and shall term _Atmology_, borrowing
{138} the term from the Greek word (ἄτμος,) which signifies _vapor_.
The _Atmosphere_ was so named by the Greeks, as being a sphere of
vapor; and, undoubtedly, the most general and important of the
phenomena which take place in the air, by which the earth is
surrounded, are those in which water, of one _consistence_ or other
(ice, water, or steam,) is concerned. The knowledge which relates to
what takes place in the atmosphere has been called _Meteorology_, in
its collective form: but such knowledge is, in fact, composed of
parts of many different sciences. And it is useful for our purpose
to consider separately those portions of Meteorology which have
reference to the laws of aqueous vapor, and these we may include
under the term Atmology.

The instruments which have been invented for the purpose of
measuring the moisture of the air, that is, the quantity of vapor
which exists in it, have been termed _Hygrometers_; and the
doctrines on which these instruments depend, and to which they lead,
have been called _Hygrometry_; but this term has not been used in
quite so extensive a sense as that which we intend to affix to
_Atmology_.

In treating of Thermotics, we shall first describe the earlier
progress of men's views concerning Conduction, Radiation, and the
like, and shall then speak of the more recent corrections and
extensions, by which they have been brought nearer to theoretical
generality.



{{139}}
THERMOTICS PROPER.




CHAPTER I.

THE DOCTRINES OF CONDUCTION AND RADIATION.

_Section_ 1.--_Introduction of the Doctrine of Conduction._


BY _conduction_ is meant the propagation of heat from one part to
another of a continuous body; or from one body to another in contact
with it; as when one end of a poker stuck in the fire heats the
other end, or when this end heats the hand which takes hold of it.
By _radiation_ is meant the diffusion of heat from the surface of a
body to points not in contact. It is clear in both these cases,
that, in proportion as the hot portion is hotter, it produces a
greater effect in warming the cooler portion; that is, it
_communicates more Heat_ to it, if _Heat_ be the abstract conception
of which this effect is the measure. The simplest rule which can be
proposed is, that the heat thus communicated in a given instant is
proportional to the excess of the heat of the hot body over that of
the contiguous bodies; there are no obvious phenomena which
contradict the supposition that this is the true law; and it was
thence assumed by Newton as the true law for radiation and by other
writers for conduction. This assumption was confirmed approximately,
and afterwards corrected, for the case of Radiation; in its
application to Conduction, it has been made the basis of calculation
up to the present time. We may observe that this statement takes for
granted that we have attained to a measure of heat (or of
_temperature_, as heat thus measured is termed), corresponding to
the law thus assumed; and, in fact, as we shall have occasion to
explain in speaking of the _measures_ of sensible qualities, {140}
the thermometrical scale of heat according to the expansion of
liquids (which is the measure of temperature here adopted), was
constructed with a reference to Newton's law of radiation of heat;
and thus the law is necessarily consistent with the scale.

In any case in which the parts of a body are unequally hot, the
temperature will vary _continuously_ in passing from one part of the
body to another; thus, a long bar of iron, of which one end is kept
red hot, will exhibit a gradual diminution of temperature at
successive points, proceeding to the other end. The law of
temperature of the parts of such a bar might be expressed by the
ordinates of a _curve_ which should run alongside the bar. And, in
order to trace mathematically the consequences of the assumed law,
some of those processes would be necessary, by which mathematicians
are enabled to deal with the properties of curves; as the method of
infinitesimals, or the differential calculus; and the truth or
falsehood of the law would be determined, according to the usual
rules of inductive science, by a comparison of results so deduced
from the principle, with the observed phenomena.

It was easily perceived that this comparison was the task which
physical inquirers had to perform; but the execution of it was
delayed for some time; partly, perhaps, because the mathematical
process presented some difficulties. Even in a case so simple as
that above mentioned, of a linear bar with a stationary temperature
at one end, _partial differentials_ entered; for there were three
variable quantities, the time, as well as the place of each point
and its temperature. And at first, another scruple occurred to M.
Biot when, about 1804, he undertook this problem.[1\10] "A
difficulty," says Laplace,[2\10] in 1809, "presents itself, which
has not yet been solved. The quantities of heat received and
communicated in an instant (by any point of the bar) must be
infinitely small quantities of the same order as the excess of the
heat of a slice of the body over that of the contiguous slice;
therefore the _excess_ of the heat received by any slice over the
heat communicated, is an infinitely small quantity of the second
order; and the accumulation in a finite time (which depends on this
excess) cannot be finite." I conceive that this difficulty arises
entirely from an arbitrary and unnecessary assumption concerning the
relation of the infinitesimal parts of the body. Laplace resolved
the difficulty by further reasoning founded upon the same assumption
which occasioned {141} it; but Fourier, who was the most
distinguished of the cultivators of this mathematical doctrine of
conduction, follows a course of reasoning in which the difficulty
does not present itself. Indeed it is stated by Laplace, in the
Memoir above quoted,[3\10] that Fourier had already obtained the
true fundamental equations by views of his own.

[Note 1\10: Biot, _Traité de Phys._ iv. p. 669.]

[Note 2\10: Laplace, _Mém. Inst._ for 1809, p. 332.]

[Note 3\10: Laplace, _Mém. Inst._ for 1809, p. 538.]

The remaining part of the history of the doctrine of conduction is
principally the history of Fourier's labors. Attention having been
drawn to the subject, as we have mentioned, the French Institute, in
January, 1810, proposed, as their prize question, "To give the
mathematical theory of the laws of the propagation of heat, and to
compare this theory with exact observations." Fourier's Memoir (the
sequel of one delivered in 1807,) was sent in September, 1811; and
the prize (3000 francs) adjudged to it in 1812. In consequence of
the political confusion which prevailed in France, or of other
causes, these important Memoirs were not published by the Academy
till 1824; but extracts had been printed in the _Bulletin des
Sciences_ in 1808, and in the _Annales de Chimie_ in 1816; and
Poisson and M. Cauchy had consulted the manuscript itself.

It is not my purpose to give, in this place,[4\10] an account of the
analytical processes by which Fourier obtained his results. The
skill displayed in these Memoirs is such as to make them an object
of just admiration to mathematicians; but they consist entirely of
deductions from the fundamental principle which I have
noticed,--that the quantity of heat conducted from a hotter to a
colder point is proportional to the excess of heat, modified by the
_conductivity_, or conducting power of each substance. The equations
which flow from this principle assume nearly the same forms as those
which occur in the most general problems of hydrodynamics. Besides
Fourier's solution, Laplace, Poisson, and M. Cauchy have also
exercised their great analytical skill in the management of these
formulæ. We shall briefly speak of the comparison of the results of
these reasonings with experiment, and notice some other consequences
to which they lead. But before we can do this, we must pay some
attention to the subject of radiation. {142}

[Note 4\10: I have given an account of Fourier's mathematical
results in the _Reports of the British Association_ for 1835.]


_Sect._ 2.--_Introduction of the Doctrine of Radiation._

A HOT body, as a mass of incandescent iron, emits heat, as we
perceive by our senses when we approach it; and by this emission of
heat the hot body cools down. The first step in our systematic
knowledge of the subject was made in the _Principia_. "It was in the
destiny of that great work," says Fourier, "to exhibit, or at least
to indicate, the causes of the principal phenomena of the universe."
Newton assumed, as we have already said, that the rate at which a
body cools, that is, parts with its heat to surrounding bodies, is
proportional to its heat; and on this assumption he rested the
verification of his scale of temperatures. It is an easy deduction
from this law, that if times of cooling be taken in arithmetical
progression, the heat will decrease in geometrical progression.
Kraft, and after him Richman, tried to verify this law by direct
experiments on the cooling of vessels of warm water; and from these
experiments, which have since been repeated by others, it appears
that for differences of temperature which do not exceed 50 degrees
(boiling water being 100), this geometrical progression represents,
with tolerable (but not with complete) accuracy, the process of
cooling.

This principle of radiation, like that of conduction, required to be
followed out by mathematical reasoning. But it required also to be
corrected in the first place, for it was easily seen that the rate
of cooling depended, not on the absolute temperature of the body,
but on the excess of its temperature above the surrounding objects
to which it communicated its heat in cooling. And philosophers were
naturally led to endeavor to explain or illustrate this process by
some physical notions. Lambert in 1765 published[5\10] an _Essay on
the Force of Heat_, in which he assimilates the communication of
heat to the flow of a fluid out of one vessel into another by an
excess of pressure; and mathematically deduces the laws of the
process on this ground. But some additional facts suggested a
different view of the subject. It was found that heat is propagated
by radiation according to straight lines, like light; and that it
is, as light is, capable of being reflected by mirrors, and thus
brought to a focus of intenser action. In this manner the radiative
effect of a body could be more precisely traced. A fact, however,
came under notice, which, at first sight, appeared to {143} offer
some difficulty. It appeared that cold was reflected no less than
heat. A mass of ice, when its effect was concentrated on a
thermometer by a system of mirrors, made the thermometer fall, just
as a vessel of hot water placed in a similar situation made it rise.
Was cold, then, to be supposed a real substance, no less than heat?

[Note 5\10: _Act. Helvet._ tom. ii. p. 172.]

The solution of this and similar difficulties was given by Pierre
Prevost, professor at Geneva, whose theory of radiant heat was
proposed about 1790. According to this theory, heat, or _caloric_,
is constantly radiating from every point of the surface of all
bodies in straight lines; and it radiates the more copiously, the
greater is the quantity of heat which the body contains. Hence a
constant exchange of heat is going on among neighboring bodies; and
a body grows hotter or colder, according as it receives more caloric
than it emits, or the contrary. And thus a body is cooled by
rectilinear rays from a cold body, because along these paths it
sends rays of heat in greater abundance than those which return the
same way. This _theory of exchanges_ is simple and satisfactory, and
was soon generally adopted; but we must consider it rather as the
simplest mode of expressing the dependence of the communication of
heat on the excess of temperature, than as a proposition of which
the physical truth is clearly established.

A number of curious researches on the effect of the different kinds
of surface of the heating and of the heated body, were made by
Leslie and others. On these I shall not dwell; only observing that
the relative amount of this radiative and receptive energy may be
expressed by numbers, for each kind of surface; and that we shall
have occasion to speak of it under the term _exterior conductivity_;
it is thus distinguished from _interior conductivity_, which is the
relative rate at which heat is conducted in the interior of
bodies.[6\10]

[Note 6\10: The term employed by Fourier, _conductibility_ or
_conducibility_, suggests expressions altogether absurd, as if the
bodies could be called _conductible_, or _conducible_, with respect
to heat: I have therefore ventured upon a slight alteration of the
word, and have used the abstract term which analogy would suggest,
if we suppose bodies to be _conductive_ in this respect.]


_Sect._ 3.--_Verifications of the Doctrines of Conduction and
Radiation._

THE interior and exterior conductivity of bodies are numbers, which
enter as elements, or _coefficients_, into the mathematical
calculations founded on the doctrines of conduction and radiation.
These {144} coefficients are to be determined for each case by
appropriate experiments: when the experimenters had obtained these
data, as well as the mathematical solutions of the problems, they
could test the truth of their fundamental principles by a comparison
of the theoretical and actual results in properly-selected cases.
This was done for the law of conduction in the simple cases of
metallic bars heated at one end, by M. Biot,[7\10] and the
accordance with experiment was sufficiently close. In the more
complex cases of conduction which Fourier considered, it was less
easy to devise a satisfactory mode of comparison. But some rather
curious relations which he demonstrated to exist among the
temperatures at different points of an _armille_, or ring, afforded
a good criterion of the value of the calculations, and confirmed
their correctness.[8\10]

[Note 7\10: _Tr. de Phys._ iv. 671.]

[Note 8\10: _Mém. Inst._ 1819, p. 192, published 1824.]

We may therefore presume these doctrines of radiation and conduction
to be sufficiently established; and we may consider their
application to any remarkable case to be a portion of the history of
science. We proceed to some such applications.


_Sect._ 4.--_The Geological and Cosmological Application of
Thermotics._

BY far the most important case to which conclusions from these
doctrines have been applied, is that of the globe of the earth, and
of those laws of climate to which the modifications of temperature
give rise; and in this way we are led to inferences concerning other
parts of the universe. If we had any means of observing these
terrestrial and cosmical phenomena to a sufficient extent, they
would be valuable facts on which we might erect our theories; and
they would thus form part, not of the corollaries, but of the
foundations of our doctrine of heat. In such a case, the laws of the
propagation of heat, as discovered from experiments on smaller
bodies, would serve to explain these phenomena of the universe, just
as the laws of motion explain the celestial movements. But since we
are almost entirely without any definite indications of the
condition of the other bodies in the solar system as to heat; and
since, even with regard to the earth, we know only the temperature
of the parts at or very near the surface, our knowledge of the part
which heat plays in the earth and the heavens must be in a great
measure, not a generalization of observed facts, but a deduction
from theoretical principles. Still, such knowledge, whether obtained
{145} from observation or from theory, must possess great interest
and importance. The doctrines of this kind which we have to notice
refer principally to the effect of the sun's heat on the earth, the
laws of climate,--the thermotical condition of the interior of the
earth,--and that of the planetary spaces.

1. _Effect of Solar Heat on the Earth._--That the sun's heat passes
into the interior of the earth in a variable manner, depending upon
the succession of days and nights, summers and winters, is an
obvious consequence of our first notions on this subject. The mode
in which it proceeds into the interior, after descending below the
surface, remained to be gathered, either from the phenomena, or from
reasoning. Both methods were employed.[9\10] Saussure endeavored to
trace its course by digging, in 1785, and thus found that at the
depth of about thirty-one feet, the annual variation of temperature
is about 1⁄12th what it is at the surface. Leslie adopted a better
method, sinking the bulbs of thermometers deep in the earth, while
their stems appeared above the surface. In 1813, '16, and '17, he
observed thus the temperatures at the depths of one, two, four, and
eight feet, at Abbotshall, in Fifeshire. The results showed that the
extreme annual oscillations of the temperature diminish as we
descend. At the depth of one foot, the yearly range of oscillation
was twenty-five degrees (Fahrenheit); at two feet it was twenty
degrees; at four feet it was fifteen degrees; at eight feet it was
only nine degrees and a half. And the time at which the heat was
greatest was later and later in proceeding to the lower points. At
one foot, the maximum and minimum were three weeks after the
solstice of summer and of winter; at two feet, they were four or
five weeks; at four feet, they were two months; and at eight feet,
three months. The mean temperature of all the thermometers was
nearly the same. Similar results were obtained by Ott at Zurich in
1762, and by Herrenschneider at Strasburg in 1821, '2, '3.[10\10]

[Note 9\10: Leslie, art. _Climate_, Supp. _Enc. Brit._ 179.]

[Note 10\10: Pouillet, _Météorol._ t. ii. p. 643.]

These results had already been explained by Fourier's theory of
conduction. He had shown[11\10] that when the surface of a sphere is
affected by a periodical heat, certain alternations of heat travel
uniformly into the interior, but that the extent of the alternation
diminishes in geometrical progression in this descent. This
conclusion applies to the effect of days and years on the
temperature of the earth, and shows that such facts as those
observed by Leslie are both exemplifications of {146} the general
circumstances of the earth, and are perfectly in accordance with the
principles on which Fourier's theory rests.

[Note 11\10: _Mém. Inst._ for 1821 (published 1826), p. 162.]

2. _Climate._--The term _climate_, which means _inclination_, was
applied by the ancients to denote that inclination of the axis of
the terrestrial sphere from which result the inequalities of days in
different latitudes. This inequality is obviously connected also
with a difference of thermotical condition. Places near the poles
are colder, on the whole, than places near the equator. It was a
natural object of curiosity to determine the law of this variation.

Such a determination, however, involves many difficulties, and the
settlement of several preliminary points. How is the temperature of
any place to be estimated? and if we reply, by its _mean_
temperature, how are we to learn this mean? The answers to such
questions require very multiplied observations, exact instruments,
and judicious generalizations; and cannot be given here. But certain
first approximations may be obtained without much difficulty; for
instance, the mean temperature of any place may be taken to be the
temperature of deep springs, which is probably identical with the
temperature of the soil below the reach of the annual oscillations.
Proceeding on such facts, Mayer found that the mean temperature of
any place was nearly proportional to the square of the cosine of the
latitude. This, as a law of phenomena, has since been found to
require considerable correction; and it appears that the mean
temperature does not depend on the latitude alone, but on the
distribution of land and water, and on other causes. M. de Humboldt
has expressed these deviations[12\10] by his map of _isothermal
lines_, and Sir D. Brewster has endeavored to reduce them to a law
by assuming two _poles of maximum cold_.

[Note 12\10: British Assoc. 1833. Prof. Forbes's _Report on
Meteorology_, p. 215.]

The expression which Fourier finds[13\10] for the distribution of
heat in a homogeneous sphere, is not immediately comparable with
Mayer's empirical formula, being obtained on a certain hypothesis,
namely, that the equator is kept constantly at a fixed temperature.
But there is still a general agreement; for, according to the
theory, there is a diminution of heat in proceeding from the equator
to the poles in such a case; the heat is propagated from the equator
and the neighboring parts, and radiates out from the poles into the
surrounding space. And thus, in the case of the earth, the solar
heat enters in the tropical {147} parts, and constantly flows
towards the polar regions, by which it is emitted into the planetary
spaces.

[Note 13\10: Fourier. _Mém. Inst._ tom. v. p. 173.]

Climate is affected by many thermotic influences, besides the
conduction and radiation of the solid mass of the earth. The
atmosphere, for example, produces upon terrestrial temperatures
effects which it is easy to see are very great; but these it is not
yet in the power of calculation to appreciate;[14\10] and it is
clear that they depend upon other properties of air besides its
power to transmit heat. We must therefore dismiss them, at least for
the present.

[Note 14\10: _Mém. Inst._ tom. vii. p. 584]

3. _Temperature of the Interior of the Earth._--The question of the
temperature of the interior of the earth has excited great interest,
in consequence of its bearing on other branches of knowledge. The
various facts which have been supposed to indicate the fluidity of
the central parts of the terrestrial globe, belong, in general, to
geological science; but so far as they require the light of
thermotical calculations in order to be rightly reasoned upon, they
properly come under our notice here.

The principal problem of this kind which has been treated of is
this:--If in the globe of the earth there be a certain original
heat, resulting from its earlier condition, and independent of the
action of the sun, to what results will this give rise? and how far
do the observed temperatures of points below the surface lead us to
such a supposition? It has, for instance, been asserted, that in
many parts of the world the temperature, as observed in mines and
other excavations, increases in descending, at the rate of one degree
(centesimal) in about forty yards. What inference does this justify?

The answer to this question was given by Fourier and by Laplace. The
former mathematician had already considered the problem of the
cooling of a large sphere, in his Memoirs of 1807, 1809, and 1811.
These, however, lay unpublished in the archives of the Institute for
many years. But in 1820, when the accumulation of observations which
indicated an increase of the temperature of the earth as we descend,
had drawn observation to the subject, Fourier gave, in the Bulletin
of the Philomathic Society,[15\10] a summary of his results, as far
as they bore on this point. His conclusion was, that such an
increase of temperature in proceeding towards the centre of the
earth, can arise from nothing but the remains of a primitive
heat;--that the heat which the sun's action would communicate,
would, in its final and {148} permanent state, be uniform in the
same vertical line, as soon as we get beyond the influence of the
superficial oscillations of which we have spoken;--and that, before
the distribution of temperature reaches this limit, it will
decrease, not increase, in descending. It appeared also, by the
calculation, that this remaining existence of the primitive heat in
the interior of the earth's mass, was quite consistent with the
absence of all perceptible traces of it at the surface; and that the
same state of things which produces an increase of one degree of
heat in descending forty yards, does not make the surface a quarter
of a degree hotter than it would otherwise be. Fourier was led also
to some conclusions, though necessarily very vague ones, respecting
the time which the earth must have taken to cool from a supposed
original state of incandescence to its present condition, which time
it appeared must have been very great; and respecting the extent of
the future cooling of the surface, which it was shown must be
insensible. Everything tended to prove that, within the period which
the history of the human race embraces, no discoverable change of
temperature had taken place from the progress of this central
cooling. Laplace further calculated the effect[16\10] which any
contraction of the globe of the earth by cooling would produce on
the length of the day. He had already shown, by astronomical
reasoning, that the day had not become shorter by 1⁄200th of a
second, since the time of Hipparchus; and thus his inferences agreed
with those of Fourier. As far as regards the smallness of the
perceptible effect due to the past changes of the earth's
temperature, there can be no doubt that all the curious conclusions
just stated are deduced in a manner quite satisfactory, from the
fact of a general increase of heat in descending below the surface
of the earth; and thus our principles of speculative science have a
bearing upon the history of the past changes of the universe, and
give us information concerning the state of things in portions of
time otherwise quite out of our reach.

[Note 15\10: _Bullet. des Sc._ 1820, p. 58.]

[Note 16\10: _Conn. des Tems_, 1823.]

4. _Heat of the Planetary Spaces._--In the same manner, this portion
of science is appealed to for information concerning parts of space
which are utterly inaccessible to observation. The doctrine of heat
leads to conclusions concerning the temperatures of the spaces which
surround the earth, and in which the planets of the solar system
revolve. In his Memoir, published in 1827,[17\10] Fourier states
that he conceives it to follow from his principles, that these
planetary spaces {149} are not absolutely cold, but have a "proper
heat" independent of the sun and of the planets. If there were not
such a heat, the cold of the polar regions would be much more
intense than it is, and the alternations of cold and warmth, arising
from the influence of the sun, would be far more extreme and sudden
than we find them. As the cause of this heat in the planetary
spaces, he assigns the radiation of the innumerable stars which are
scattered through the universe.

[Note 17\10: _Mém. Inst._ tom. vii. p. 580.]

Fourier says,[18\10] "We conclude from these various remarks, and
principally from the mathematical examination of the question," that
this is so. I am not aware that the mathematical calculation which
bears peculiarly upon this point has anywhere been published. But it
is worth notice, that Svanberg has been led[19\10] to the opinion of
the same temperature in these spaces which Fourier had adopted (50
centigrade below zero), by an entirely different course of
reasoning, founded on the relation of the atmosphere to heat.

[Note 18\10: _Mém. Inst._ tom. vii. p. 581.]

[Note 19\10: Berzel. _Jahres Bericht_, xi. p. 50.]

In speaking of this subject, I have been led to notice incomplete
and perhaps doubtful applications of the mathematical doctrine of
conduction and radiation. But this may at least serve to show that
Thermotics is a science, which, like Mechanics, is to be established
by experiments on masses capable of manipulation, but which, like
that, has for its most important office the solution of geological
and cosmological problems. I now return to the further progress of
our thermotical knowledge.


_Sect._ 5.--_Correction of Newton's Law of Cooling._

IN speaking of the establishment of Newton's assumption, that the
temperature communicated is proportional to the excess of
temperature, we stated that it was approximately verified, and
afterwards corrected (chap. i., sect. 1.)**. This correction was the
result of the researches of MM. Dulong and Petit in 1817, and the
researches by which they were led to the true law, are an admirable
example both of laborious experiment and sagacious induction. They
experimented through a very great range of temperature (as high as
two hundred and forty degrees centigrade), which was necessary
because the inaccuracy of Newton's law becomes considerable only at
high temperatures. They removed the effect of the surrounding
medium, by making their experiments in a vacuum. They selected with
great {150} judgment the conditions of their experiments and
comparisons, making one quantity vary while the others remained
constant. In this manner they found, that _the quickness of cooling
for a constant excess of temperature, increases in geometrical
progression, when the temperature of the surrounding space increases
in arithmetical progression_; whereas, according to the Newtonian
law, this quickness would not have varied at all. Again, this
variation being left out of the account, it appeared that _the
quickness of cooling, so far as it depends on the excess of
temperature of the hot body, increases as the terms of a geometrical
progression diminished by a constant number, when the temperature of
the hot body increases in arithmetical progression_. These two laws,
with the coefficients requisite for their application to particular
substances, fully determine the conditions of cooling in a vacuum.

Starting from this determination, MM. Dulong and Petit proceeded to
ascertain the effect of the medium, in which the hot body is placed,
upon its rate of cooling; for this effect became a _residual
phenomenon_,[20\10] when the cooling in the vacuum was taken away.
We shall not here follow this train of research; but we may briefly
state, that they were led to such laws as this;--that the rapidity
of cooling due to any gaseous medium in which the body is placed, is
the same, so long as the excess of the body's temperature is the
same, although the temperature itself vary;--that the cooling power
of a gas varies with the elasticity, according to a determined law;
and other similar rules.

[Note 20\10: See _Phil. Ind. Sciences_, B. xiii. c. 7, Sect. iv.]

In reference to the process of their induction, it is worthy of
notice, that they founded their reasonings upon Prevost's law of
exchanges; and that, in this way, the second of their laws above
stated, respecting the quickness of cooling, was a mathematical
consequence of the first. It may be observed also, that their
temperatures are measured by means of the air-thermometer, and that
if they were estimated on another scale, the remarkable simplicity
and symmetry of their results would disappear. This is a strong
argument for believing such a measure of temperature to have a
natural prerogative of simplicity. This belief is confirmed by other
considerations; but these, depending on the laws of _expansion_ by
heat, cannot be here referred to; and we must proceed to finish our
survey of the mathematical theory of heat, as founded on the
phenomena of radiation and conduction, which alone have as yet been
traced up to general principles.

We may observe, before we quit this subject, that this correction of
{151} Newton's law will materially affect the mathematical
calculations on the subject, which were made to depend on that law
both by Fourier, Laplace, and Poisson. Probably, however, the
general features of the results will be the same as on the old
supposition. M. Libri, an Italian mathematician, has undertaken one
of the problems of this kind, that of the armil, with Dulong and
Petit's law for his basis, in a Memoir read to the Institute of
France in 1825, and since published at Florence.[21\10]

[Note 21\10: _Mém. de Math. et de Phys._ 1829.]


_Sect._ 6.--_Other Laws of Phenomena with respect to Radiation._

THE laws of radiation as depending upon the surface of radiating
bodies, and as affecting screens of various kinds interposed between
the hot body and the thermometer, were examined by several
inquirers. I shall not attempt to give an account of the latter
course of research, and of the different laws which luminous and
non-luminous heat have been found to follow in reference to bodies,
whether transparent or opaque, which intercept them. But there are
two or three laws of the phenomena, depending upon the effects of
the surfaces of bodies, which are important.

1. In the first place, the powers of bodies to _emit_ and to
_absorb_ heat, as far as depends upon their surface, appear to be in
the same proportion. If we blacken the surface of a canister of hot
water, it radiates heat more copiously; and in the same measure, it
is more readily heated by radiation.

2. In the next place, as the radiative power increases, the power of
reflection diminishes, and the contrary. A bright metal vessel
reflects much heat; on this very account it does not emit much; and
hence a hot fluid which such a vessel contains, remains hot longer
than it does in an unpolished case.

3. The heat is emitted from every point of the surface of a hot body
in all directions; but by no means in all directions with equal
intensity. The intensity of the heating ray is as the sine of the
angle which it makes with the surface.

The last law is entirely, the two former in a great measure, due to
the researches of Leslie, whose _Experimental Inquiry into the
Nature and Propagation of Heat_, published in 1804, contains a great
number of curious and striking results and speculations. The laws
now just {152} stated bear, in a very important manner, upon the
formation of the theory; and we must now proceed to consider what
appears to have been done in this respect; taking into account, it
must still be borne in mind, only the phenomena of conduction and
radiation.


_Sect._ 7.--_Fourier's Theory of Radiant Heat._

THE above laws of phenomena being established, it was natural that
philosophers should seek to acquire some conception of the physical
action by which they might account, both for these laws, and for the
general fundamental facts of Thermotics; as, for instance, the fact
that all bodies placed in an inclosed space assume, in time, the
temperature of the inclosure. Fourier's explanation of this class of
phenomena must be considered as happy and successful; for he has
shown that the supposition to which we are led by the most simple
and general of the facts, will explain, moreover, the less obvious
laws. It is an obvious and general fact, that bodies which are
included in the space tend to acquire the same temperature. And this
identity of temperature of neighboring bodies requires an
hypothesis, which, it is found, also accounts for Leslie's law of
the sine, in radiation.

This hypothesis is, that the radiation takes place, not from the
surface alone of the hot body, but from all particles situated
within a certain small depth of the surface. It is easy to
see[22\10] that, on this supposition, a ray emitted obliquely from
an internal particle, will be less intense than one sent forth
perpendicular to the surface, because the former will be intercepted
in a greater degree, having a greater length of path within the
body; and Fourier shows, that whatever be the law of this
intercepting power, the result will be, that the radiative intensity
is as the sine of the angle made by the ray with the surface.

[Note 22\10: _Mém. Inst._ t. v. 1821, p. 204.]

But this law is, as I have said, likewise necessary, in order that
neighboring bodies may tend to assume the same temperature: for
instance, in order that a small particle placed within a spherical
shell, should finally assume the temperature of the shell. If the
law of the sines did not obtain, the final temperature of such a
particle would depend upon its place in the inclosure;[23\10] and
within a shell of ice we should have, at certain points, the
temperature of boiling water and of melting iron.

[Note 23\10: _An. Chim._ iv. 1817, p. 129.]

This proposition may at first appear strange and unlikely; but it
may {153} be shown to be a necessary consequence of the assumed
principle, by very simple reasoning, which I shall give in a general
form in a Note.[24\10]

[Note 24\10: The following reasoning may show the connexion of the
law of the sines in radiant heat with the general principle of
ultimate identity of neighboring temperatures. The equilibrium and
identity of temperature between an including shell and an included
body, cannot obtain upon the whole, except it obtain between each
pair of parts of the two surfaces of the body and of the shell; that
is, any part of the one surface, in its exchanges with any part of
the other surface, must give and receive the same quantity of heat.
Now the quantity exchanged, so far as it depends on the receiving
surface, will, by geometry, be proportional to the sine of the
obliquity of that surface: and as, in the exchanges, each may be
considered as receiving, the quantity transferred must be
proportional to the sines of the two obliquities; that is, to that
of the giving as well as of the receiving surface.

Nor is this conclusion disturbed by the consideration, that all the
rays of heat which fall upon a surface are not absorbed, some being
reflected according to the nature of the surface. For, by the other
above-mentioned laws of phenomena, we know that, in the same measure
in which the surface loses the power of admitting, it loses the
power of emitting, heat; and the superficial parts gain, by
absorbing their own radiation, as much as they lose by not absorbing
the incident heat; so that the result of the preceding reasoning
remains unaltered.]

This reasoning is capable of being presented in a manner quite
satisfactory, by the use of mathematical symbols, and proves that
Leslie's law of the sines is rigorously and mathematically true on
Fourier's hypothesis. And thus Fourier's theory of _molecular
extra-radiation_ acquires great consistency.


_Sect._ 8.--_Discovery of the Polarization of Heat._

THE laws of which the discovery is stated in the preceding Sections
of this Chapter, and the explanations given of them by the theories
of conduction and radiation, all tended to make the conception of a
material heat, or _caloric_, communicated by an actual flow and
emission, familiar to men's minds; and, till lately, had led the
greater part of thermotical philosophers to entertain such a view,
as the most probable opinion concerning the nature of heat. But some
steps have recently been made in thermotics, which appear to be
likely to overturn this belief, and to make the doctrine of emission
as untenable with regard to heat, as it had been found to be with
regard to light. I speak of the discovery of the polarization of
heat. It being ascertained that rays of heat are polarized in the
same manner as rays of {154} light, we cannot retain the doctrine
that heat radiates by the emanation of material particles, without
supposing those particles of caloric to have poles; an hypothesis
which probably no one would embrace; for, besides that the ill
fortune which attended that hypothesis in the case of light must
deter speculators from it, the intimate connexion of heat and light
would hardly allow us to suppose polarization in the two cases to be
produced by two different kinds of machinery.

But, without here tracing further the influence which the
polarization of heat must exercise upon the formation of our
theories of heat, we must briefly notice this important discovery,
as a law of phenomena.

The analogies and connexions between light and heat are so strong,
that when the polarization of light had been discovered, men were
naturally led to endeavor to ascertain whether heat possessed any
corresponding property. But partly from the difficulty of obtaining
any considerable effect of heat separated from light, and partly
from the want of a thermometrical apparatus sufficiently delicate,
these attempts led, for some time, to no decisive result. M. Berard
took up the subject in 1813. He used Malus's apparatus, and
conceived that he found heat to be polarized by reflection at the
surface of glass, in the same manner as light, and with the same
circumstances.[25\10] But when Professor Powell, of Oxford, a few
years later (1830), repeated these experiments with a similar
apparatus, he found[26\10] that though the heat which is conveyed
along with light is, of course, polarizable, "simple radiant heat,"
as he terms it, did not offer the smallest difference in the two
rectangular azimuths of the second glass, and thus showed no trace
of polarization.

[Note 25\10: _Ann. Chim._ March, 1813.]

[Note 26\10: _Edin. Journ. of Science_, 1830, vol. ii. p. 303.]

Thus, with the old thermometers, the point remained doubtful. But
soon after this time, MM. Melloni and Nobili invented an apparatus,
depending on certain galvanic laws, of which we shall have to speak
hereafter, which they called a _thermomultiplier_; and which was
much more sensitive to changes of temperature than any
previously-known instrument. Yet even with this instrument, M.
Melloni failed; and did not, at first, detect any perceptible
polarization of heat by the tourmaline;[27\10] nor did M.
Nobili,[28\10] in repeating M. Berard's experiment. But in this
experiment the attempt was made to polarize heat by reflection from
glass, as light is polarized: and the quantity {155} reflected is so
small that the inevitable errors might completely disguise the whole
difference in the two opposite positions. When Prof. Forbes, of
Edinburgh, (in 1834,) employed mica in the like experiments, he
found a very decided polarizing effect; first, when the heat was
transmitted through several films of mica at a certain angle, and
afterwards, when it was reflected from them. In this case, he found
that with non-luminous heat, and even with the heat of water below
the boiling point, the difference of the heating power in the two
positions of opposite polarity (parallel and _crossed_) was
manifest. He also detected by careful experiments,[29\10] the
polarizing effect of tourmaline. This important discovery was soon
confirmed by M. Melloni. Doubts were suggested whether the different
effect in the opposite positions might not be due to other
circumstances; but Professor Forbes easily showed that these
suppositions were inadmissible; and the property of a difference of
_sides_, which at first seemed so strange when ascribed to the rays
of light, also belongs, it seems to be proved, to the rays of heat.
Professor Forbes also found, by interposing a plate of mica to
intercept the ray of heat in an intermediate point, an effect was
produced in certain positions of the mica analogous to what was
called _depolarization_ in the case of light; namely, a partial
destruction of the differences which polarization establishes.

[Note 27\10: _Ann. de Chimie_, vol. lv.]

[Note 28\10: _Bibliothèque Universelle_.]

[Note 29\10: _Ed. R. S. Transactions_, vol. xiv.; and _Phil. Mag._
1835, vol. v. p. 209. Ib. vol. vii. p. 349.]

Before this discovery, M. Melloni had already proved by experiment
that heat is _refracted_ by transparent substances as light is. In
the case of light, the _depolarizing_ effect was afterwards found to
be really, as we have seen, a _dipolarizing_ effect, the ray being
divided into two rays by _double refraction_. We are naturally much
tempted to put the same interpretation upon the dipolarizing effect
in the case of heat; but perhaps the assertion of the analogy
between light and heat to this extent is as yet insecure.

It is the more necessary to be cautious in our attempt to identify
the laws of light and heat, inasmuch as along with all the
resemblances of the two agents, there are very important
differences. The power of transmitting light, _the diaphaneity_ of
bodies, is very distinct from their power of transmitting heat,
which has been called _diathermancy_ by M. Melloni. Thus both a
plate of alum and a plate of rock-salt transmit nearly the whole
light; but while the first stops nearly the whole heat, the second
stops very little of it; and a plate of opake {156} quartz, nearly
impenetrable by light, allows a large portion of the heat to pass.
By passing the rays through various media, the heat may be, as it
were, _sifted_ from the light which accompanies it.

[2nd Ed.] [The diathermancy of bodies is distinct from their
diaphaneity, in so far that the same bodies do not exercise the same
powers of selection and suppression of certain rays on heat and on
light; but it appears to be proved by the investigations of modern
thermotical philosophers (MM. De la Roche, Powell, Melloni, and
Forbes), that there is a close analogy between the absorption of
certain colors by transparent bodies, and the absorption of certain
kinds of heat by diathermanous bodies. Dark sources of heat emit
rays which are analogous to blue and violet rays of light; and
highly luminous sources emit rays which are analogous to red rays.
And by measuring the angle of total reflection for heat of different
kinds, it has been shown that the former kind of calorific rays are
really less refrangible than the latter.[30\10]

[Note 30\10: See Prof. Forbes's _Third Series of Researches on
Heat_, _Edinb. R.S. Trans._ vol. xiv.]

M. Melloni has assumed this analogy as so completely established,
that he has proposed for this part of thermotics the name
_Thermochroology_ (Qu. _Chromothermotics_?); and along with this
term, many others derived from the Greek, and founded on the same
analogy. If it should appear, in the work which he proposes to
publish on this subject, that the doctrines which he has to state
cannot easily be made intelligible without the use of the terms he
suggests, his nomenclature will obtain currency; but so large a mass
of etymological innovations is in general to be avoided in
scientific works.

M. Melloni's discovery of the extraordinary power of _rock-salt_ to
transmit heat, and Professor Forbes's discovery of the extraordinary
power of _mica_ to polarize and depolarize heat, have supplied
thermotical inquirers with two new and most valuable
instruments.[31\10]]

[Note 31\10: For an account of many thermotical researches, which I
have been obliged to pass unnoticed here, see two Reports by Prof.
Powell on the present state of our knowledge respecting Radiant
Heat, in the _Reports of the British Association_ for 1832 and 1840.]

Moreover, besides the laws of conduction and radiation, many other
laws of the phenomena of heat have been discovered by philosophers;
and these must be taken into account in judging any theory of heat.
To these other laws we must now turn our attention. {157}




CHAPTER II.

THE LAWS OF CHANGES OCCASIONED BY HEAT.


_Sect._ 1.--_Expansion by Heat.--The Law of Dalton and Gay-Lussac
for Gases._

ALMOST all bodies expand by heat; solids, as metals, in a small
degree; fluids, as water, oil, alcohol, mercury, in a greater
degree. This was one of the facts first examined by those who
studied the nature of heat, because this property was used for the
measure of heat. In the _Philosophy of the Inductive Sciences_, Book
iv., Chap. iv., I have stated that secondary qualities, such as
Heat, must be measured by their effects: and in Sect. 4 of that
Chapter I have given an account of the successive attempts which
have been made to obtain measures of heat. I have there also spoken
of the results which were obtained by comparing the rate at which
the expansion of different substances went on, under the same
degrees of heat; or as it was called, the different _thermometrical
march_ of each substance. Mercury appears to be the liquid which is
most uniform in its thermometrical march; and it has been taken as
the most common material of our thermometers; but the expansion of
mercury is not proportional to the heat. De Luc was led, by his
experiments, to conclude "that the dilatations of mercury follow an
accelerated march for equal augmentations of heat." Dalton
conjectured that water and mercury both expand as the square of the
_real temperature_ from the point of greatest contraction: the real
temperature being measured so as to lead to such a result. But none
of the rules thus laid down for the expansion of solids and fluids
appear to have led, as yet, to any certain general laws.

With regard to gases, thermotical inquirers have been more
successful. Gases expand by heat; and their expansion is governed by
a law which applies alike to all degrees of heat, and to all gaseous
fluids. The law is this: that _for equal increments of temperature
they expand by the same fraction of their own bulk_; which fraction
is _three-eights_ {158} in proceeding from freezing to boiling
water. This law was discovered by Dalton and M. Gay-Lussac
independently of each other;[32\10] and is usually called by both
their names, _the law of Dalton and Gay-Lussac_. The latter
says,[33\10] "The experiments which I have described, and which have
been made with great care, prove incontestably that oxygen,
hydrogen, azotic acid, nitrous acid, ammoniacal acid, muriatic acid,
sulphurous acid, carbonic acid, gases, expand equally by equal
increments of heat." "Therefore," he adds with a proper inductive
generalization, "the result does not depend upon physical
properties, and I collect that _all gases expand equally by heat_."
He then extends this to vapors, as ether. This must be one of the
most important foundation-stones of any sound theory of heat.

[Note 32\10: _Manch. Mem._ vol. v. 1802; and _Ann. Chim._ xliii.
p. 137.]

[Note 33\10: Ib. p. 272.]

[2nd Ed.] Yet MM. Magnus and Regnault conceive that they have
overthrown this law of Dalton and Gay-Lussac, and shown that the
different gases do not expand alike for the same increment of heat.
Magnus found the ratio to be for atmospheric air, 1∙366; for
hydrogen, 1∙365; for carbonic acid, 1∙369; for sulphurous-acid gas,
1∙385. But these differences are not greater than the differences
obtained for the same substances by different observers; and as this
law is referred to in Laplace's hypothesis, hereafter to be
discussed, I do not treat the law as disproved.

Yet that the rate of expansion of gas in certain circumstances is
different for different substances, must be deemed very probable,
after Dr. Faraday's recent investigations _On the Liquefaction and
Solidification of Bodies generally existing as Gases_,[34\10] by
which it appears that the elasticity of vapors _in contact with
their fluids_ increases at different rates in different substances.
"That the force," he says, "of vapor increases in a geometrical
ratio for equal increments of heat is true for all bodies, but the
ratio is not the same for all. . . . For an increase of pressure
from two to six atmospheres, the following number of degrees require
to be added to the bodies named:--water 69°, sulphureous acid 63°,
cyanogen 64°∙5, ammonia 60°, arseniuretted hydrogen 54°,
sulphuretted hydrogen 56°∙5, muriatic acid 43°, carbonic acid 32°∙5,
nitrous oxide 30°."]

[Note 34\10: _Phil. Trans._ 1845, Pt. 1.]

We have already seen that the opinion that the air-thermometer is a
true measure of heat, is strongly countenanced by the symmetry
which, by using it, we introduce into the laws of radiation. If we
{159} accept the law of Dalton and Gay-Lussac, it follows that this
result is independent of any peculiar properties in the air
employed; and thus this measure has an additional character of
generality and simplicity which make it still more probable that it
is the true standard. This opinion is further supported by the
attempts to include such facts in a theory; but before we can treat
of such theories, we must speak of some other doctrines which have
been introduced.


_Sect._ 2.--_Specific Heat.--Change of Consistence._

IN the attempts to obtain measures of heat, it was found that bodies
had different capacities for heat; for the same quantity of heat,
however measured, would raise, in different degrees, the temperature
of different substances. The notion of different capacities for heat
was thus introduced, and each body was thus assumed to have a
specific _capacity for heat_, according to the quantity of heat
which it required to raise it through a given scale of heat.[35\10]
The term "capacity for heat" was introduced by Dr. Irvine, a pupil
of Dr. Black. For this term, Wilcke, the Swedish physicist,
substituted "specific heat;" in analogy with "specific gravity."

[Note 35\10: See Crawford, _On Heat_, for the History of Specific
Heat.]

It was found, also, that the capacity of the same substance was
different in the same substance at different temperatures. It
appears from experiments of MM. Dulong and Petit, that, in general,
the capacity of liquids and solids increases as we ascend in the
scale of temperature.

But one of the most important thermotic facts is, that by the sudden
contraction of any mass, its temperature is increased. This is
peculiarly observable in gases, as, for example, common air. The
amount of the increase of temperature by sudden condensation, or of
the cold produced by sudden rarefaction, is an important datum,
determining the velocity of sound, as we have already seen, and
affecting many points of meteorology. The coefficient which enters
the calculation in the former case depends on the ratio of two
specific heats of air under different conditions; one belonging to
it when, varying in density, the pressure is constant by which the
air is contained; the other, when, varying in density, it is
contained in a constant space.

A leading fact, also, with regard to the operation of heat on bodies
{160} is, that it changes their _form_, as it is often called, that
is, their condition as solid, liquid, or air. Since the term "form"
is employed in too many and various senses to be immediately
understood when it is intended to convey this peculiar meaning, I
shall use, instead of it, the term _consistence_, and shall hope to
be excused, even when I apply this word to gases, though I must
acknowledge such phraseology to be unusual. Thus there is a change
of consistence when solids become liquid, or liquids gaseous; and
the laws of such changes must be fundamental facts of our
thermotical theories. We are still in the dark as to many of the
laws which belong to this change; but one of them, of great
importance, has been discovered, and to that we must now proceed.


_Sect._ 3.--_The Doctrine of Latent Heat._

The Doctrine of Latent Heat refers to such changes of consistence as
we have just spoken of. It is to this effect; that during the
conversion of solids into liquids, or of liquids into vapors, there
is communicated to the body heat which is not indicated by the
thermometer. The heat is absorbed, or becomes _latent_; and, on the
other hand, on the condensation of the vapor to a liquid, or the
liquid to a solid consistency, this heat is again given out and
becomes sensible. Thus a pound of ice requires twenty times as long
a time, in a warm room, to raise its temperature seven degrees, as a
pound of ice-cold water does. A kettle placed on a fire, in four
minutes had its temperature raised to the boiling point, 212°: and
this temperature continued stationary for twenty minutes, when the
whole was boiled away. Dr. Black inferred from these facts that a
large quantity of heat is absorbed by the ice in becoming water, and
by the water in becoming steam. He reckoned from the above
experiments, that ice, in melting, absorbs as much heat as would
raise ice-cold water through 140° of temperature: and that water, in
evaporating, absorbs as much heat as would raise it through 940°.

That snow requires a great quantity of heat to melt it; that water
requires a great quantity of heat to convert it into steam; and that
this heat is not indicated by a rise in the thermometer, are facts
which it is not difficult to observe; but to separate these from all
extraneous conditions, to group the cases together, and to seize
upon the general law by which they are connected, was an effort of
inductive insight, which has been considered, and deservedly, as one
of the most striking {161} events in the modern history of physics.
Of this step the principal merit appears to belong to Black.

[2nd Ed.] [In the first edition I had mentioned the names of De Luc
and of Wilcke, in connexion with the discovery of Latent Heat, along
with the name of Black. De Luc had observed, in 1755, that ice, in
melting, did not rise above the freezing-point of temperature till
the whole was melted. De Luc has been charged with plagiarizing
Black's discovery, but, I think, without any just ground. In his
_Idées sur la Météorologique_ (1787), he spoke of Dr. Black as "the
first who had attempted the determinations of the quantities of
latent heat." And when Mr. Watt pointed out to him that from this
expression it might be supposed that Black had not discovered the
fact itself, he acquiesced, and redressed the equivocal expression
in an Appendix to the volume.[36\10]

[Note 36\10: See his _Letter_ to the Editors of the _Edinburgh
Review_, No. xii. p. 502, of the _Review_.]

Black never published his own account of the doctrine of Latent
Heat: but he delivered it every year after 1760 in his Lectures. In
1770, a surreptitious publication of his Lectures was made by a
London bookseller, and this gave a view of the leading points of Dr.
Black's doctrine. In 1772, Wilcke, of Stockholm, read a paper to the
Royal Society of that city, in which the absorption of heat by
melting ice is described; and in the same year, De Luc of Geneva
published his _Recherches sur les Modifications de l'Atmosphère_,
which has been alleged to contain the doctrine of latent heat, and
which the author asserts to have been written in ignorance of what
Black had done. At a later period, De Luc, adopting, in part.
Black's expression, gave the name of _latent fire_ to the heat
absorbed.[37\10]

[Note 37\10: See _Ed. Rev._ No. vi. p. 20.]

It appears that Cavendish determined the amount of heat produced by
condensing steam, and by thawing snow, as early as 1765. He had
perhaps already heard something of Black's investigations, but did
not accept his term "latent heat".**[38\10]]

[Note 38\10: See Mr. V. Harcourt's _Address_ to the Brit. Assoc. in
1839, and the _Appendix_.]

The consequences of Black's principle are very important, for upon
it is founded the whole doctrine of evaporation; besides which, the
principle of latent heat has other applications. But the relations
of aqueous vapor to air are so important, and have been so long a
{162} subject of speculation, that we may with advantage dwell a
little upon them. The part of science in which this is done may be
called, as we have said, Atmology; and to that division of Thermotics
the following chapters belong.



{{163}}
ATMOLOGY.




CHAPTER III.

THE RELATION OF VAPOR AND AIR.


_Sect._ 1.--_The Boylean Law of the Air's Elasticity._

IN the Sixth Book (Chap. iv. Sect. 1.) we have already seen how the
conception on the laws of fluid equilibrium was, by Pascal and others,
extended to air, as well as water. But though air presses and is
pressed as water presses and is pressed, pressure produces upon air an
effect which it does not, in any obvious degree, produce upon water.
Air which is pressed is also _compressed_, or made to occupy a smaller
space; and is consequently also made more dense, or _condensed_; and
on the other hand, when the pressure upon a portion of air is
diminished, the air expands or is rarefied. These broad facts are
evident. They are expressed in a general way by saying that air is an
_elastic_ fluid, yielding in a certain degree to pressure, and
recovering its previous dimensions when the pressure is removed.

But when men had reached this point, the questions obviously offered
themselves, in what degree and according to what law air yields to
pressure; when it is compressed, what relation does the density bear
to the pressure? The use which had been made of tubes containing
columns of mercury, by which the pressure of portions of air was
varied and measured, suggested obvious modes of devising experiments
by which this question might be answered. Such experiments
accordingly were made by Boyle about 1650; and the result at which
he arrived was, that when air is thus compressed, the density is as
the pressure. Thus if the pressure of the atmosphere in its common
state be equivalent to 30 inches of mercury, as shown by the
barometer; if air included in a tube be pressed by 30 additional
inches of {164} mercury, its density will be doubled, the air being
compressed into one half the space. If the pressure be increased
threefold, the density is also trebled; and so on. The same law was
soon afterwards (in 1676) proved experimentally by Mariotte. And
this law of the air's elasticity, that the density is as the
pressure, is sometimes called the _Boylean Law_, and sometimes the
_Law of Boyle and Mariotte_.

Air retains its aerial character permanently; but there are other
aerial substances which appear as such, and then disappear or change
into some other condition. Such are termed _vapors_. And the
discovery of their true relation to air was the result of a long
course of researches and speculations.

[2nd Ed.] [It was found by M. Cagniard de la Tour (in 1823), that at
a certain temperature, a liquid, under sufficient pressure, becomes
clear transparent vapor or gas, having the same bulk as the liquid.
This condition Dr. Faraday calls the _Cagniard de la Tour_ state,
(the _Tourian_ state?) It was also discovered by Dr. Faraday that
carbonic-acid gas, and many other gases, which were long conceived
to be permanently elastic, are really reducible to a liquid state by
pressure.[39\10] And in 1835, M. Thilorier found the means of
reducing liquid carbonic acid to a solid form, by means of the cold
produced in evaporation. More recently Dr. Faraday has added several
substances usually gaseous to the list of those which could
previously be shown in the liquid state, and has reduced others,
including ammonia, nitrous oxide, and sulphuretted hydrogen, to a
solid consistency.[40\10] After these discoveries, we may, I think,
reasonably doubt whether all bodies are not capable of existing in
the three _consistencies_ of solid, liquid, and air.

[Note 39\10: _Phil. Trans._ 1823.]

[Note 40\10: Ib. Pt. 1. 1845.]

We may note that the law of Boyle and Mariotte is not exactly true
near the limit at which the air passes to the liquid state in such
cases as that just spoken of. The diminution of bulk is then more
rapid than the increase of pressure.

The transition of fluids from a liquid to an airy consistence
appears to be accompanied by other curious phenomena. See Prof.
Forbes's papers on the _Color of Steam under certain circumstances_,
and on the _Colors of the Atmosphere_, in the _Edin. Trans._ vol.
xiv.] {165}


_Sect._ 2.--_Prelude to Dalton's Doctrine of Evaporation._

VISIBLE clouds, smoke, distillation, gave the notion of Vapor; vapor
was at first conceived to be identical with air, as by Bacon.[41\10]
It was easily collected, that by heat, water might be converted into
vapor. It was thought that air was thus produced, in the instrument
called the _æolipile_, in which a powerful blast is caused by a
boiling fluid; but Wolfe showed that the fluid was not converted
into air, by using camphorated spirit of wine, and condensing the
vapor after it had been formed. We need not enumerate the doctrines
(if very vague hypotheses may be so termed) of Descartes, Dechales,
Borelli.[42\10] The latter accounted for the rising of vapor by
supposing it a mixture of fire and water; and thus, fire being much
lighter than air, the mixture also was light. Boyle endeavored to
show that vapors do not permanently float _in vacuo_. He compared
the mixture of vapor with air to that of salt with water. He found
that the pressure of the atmosphere affected the heat of boiling
water; a very important fact. Boyle proved this by means of the
air-pump; and he and his friends were much surprised to find that
when air was removed, water only just warm boiled violently. Huyghens
mentions an experiment of the same kind made by Papin about 1673.

[Note 41\10: Bacon's _Hist. Nat._ Cent. i. p. 27.]

[Note 42\10: They may be seen in Fischer, _Geschichte der Physik_,
vol. ii. p. 175.]

The ascent of vapor was explained in various ways in succession,
according to the changes which physical science underwent. It was a
problem distinctly treated of, at a period when hydrostatics had
accounted for many phenomena; and attempts were naturally made to
reduce this fact to hydrostatical principles. An obvious hypothesis,
which brought it under the dominion of these principles, was, to
suppose that the water, when converted into vapor, was divided into
small hollow globules;--thin pellicles including air or heat. Halley
gave such an explanation of evaporation; Leibnitz calculated the
dimensions of these little bubbles; Derham managed (as he supposed)
to examine them with a magnifying glass: Wolfe also examined and
calculated on the same subject. It is curious to see so much
confidence in so lame a theory; for if water became hollow globules
in order to rise as vapor, we require, in order to explain the
formation of these globules, new laws of nature, which are not even
hinted at by {166} the supporters of the doctrine, though they must
be far more complex than the hydrostatical law by which a hollow
sphere floats.

Newton's opinion was hardly more satisfactory; he[43\10] explained
evaporation by the repulsive power of heat; the parts of vapors,
according to him, being small, are easily affected by this force,
and thus become lighter than the atmosphere.

[Note 43\10: _Opticks_, Qu. 31.]

Muschenbroek still adhered to the theory of globules, as the
explanation of evaporation; but he was manifestly discontented with
it; and reasonably apprehended that the pressure of the air would
destroy the frail texture of these bubbles. He called to his aid a
rotation of the globules (which Descartes also had assumed); and,
not satisfied with this, threw himself on electrical action as a
reserve. Electricity, indeed, was now in favor, as hydrostatics had
been before; and was naturally called in, in all cases of
difficulty. Desaguliers, also, uses this agent to account for the
ascent of vapor, introducing it into a kind of sexual system of
clouds; according to him, the male fire (heat) does a part, and the
female fire (electricity) performs the rest. These are speculations
of small merit and no value.

In the mean time, Chemistry made great progress in the estimation of
philosophers, and had its turn in the explanation of the important
facts of evaporation. Bouillet, who, in 1742, placed the particles
of water in the interstices of those of air, may be considered as
approaching to the chemical theory. In 1748, the Academy of Sciences
of Bourdeaux proposed the ascent of vapors as the subject of a
prize; which was adjudged in a manner very impartial as to the
choice of a theory; for it was divided between Kratzenstein, who
advocated the bubbles, (the coat of which he determined to be
1⁄50,000th of an inch thick,) and Hamberger, who maintained the
truth to be the adhesion of particles of water to those of air and
fire. The latter doctrine had become much more distinct in the
author's mind when seven years afterwards (1750) he published his
_Elementa Physices_. He then gave the explanation of evaporation in
a phrase which has since been adopted,--the _solution of water in
air_; which he conceived to be of the same kind as other chemical
solutions.

This theory of solution was further advocated and developed by Le
Roi;[44\10] and in his hands assumed a form which has been
extensively adopted up to our times, and has, in many instances,
tinged the language commonly used. He conceived that air, like other
solvents, {167} might be _saturated_; and that when the water was
beyond the amount required for saturation, it appeared in a visible
form. The saturating quantity was held to depend mainly on warmth
and wind.

[Note 44\10: _Ac. R. Sc._ Paris, 1750.]

This theory was by no means devoid of merit; for it brought together
many of the phenomena, and explained a number of the experiments
which Le Roi made. It explained the facts of the transparency of
vapor, (for perfect solutions are transparent,) the precipitation of
water by cooling, the disappearance of the visible moisture by
warming it again, the increased evaporation by rain and wind; and
other observed phenomena. So far, therefore, the introduction of the
notion of the chemical solution of water in air was apparently very
successful. But its defects are of a very fatal kind; for it does
not at all apply to the facts which take place when air is excluded.

In Sweden, in the mean time,[45\10] the subject had been pursued in
a different, and in a more correct manner. Wallerius Ericsen had, by
various experiments, established the important fact, that water
evaporates in a _vacuum_. His experiments are clear and
satisfactory; and he inferred from them the falsity of the common
explanation of evaporation by the solution of water in _air_. His
conclusions are drawn in a very intelligent manner. He considers the
question whether water can be changed into air, and whether the
atmosphere is, in consequence, a mere collection of vapors; and on
good reasons, decides in the negative, and concludes the existence
of permanently-elastic air different from vapor. He judges, also,
that there are two causes concerned, one acting to produce the first
ascent of vapors, the other to support them afterwards. The first,
which acts in a vacuum, he conceives to be the mutual repulsion of
the particles; and since this force is independent of the presence
of other substances, this seems to be a sound induction. When the
vapors have once ascended into the air, it may readily be granted
that they are carried higher, and driven from side to side by the
currents of the atmosphere. Wallerius conceives that the vapor will
rise till it gets into air of the same density as itself, and being
then in equilibrium, will drift to and fro.

[Note 45\10: Fischer, _Gesch. Phys._ vol. v. p. 63.]

The two rival theories of evaporation, that of _chemical solution_
and that of _independent vapor_, were, in various forms, advocated
by the next generation of philosophers. De Saussure may be
considered as the leader on one side, and De Luc on the other. The
former maintained the solution theory, with some modifications of
his own. De {168} Luc denied all solution, and held vapor to be a
combination of the particles of water with fire, by which they
became lighter than air. According to him, there is always fire
enough present to produce this combination, so that evaporation goes
on at all temperatures.

This mode of considering independent vapor as a combination of fire
with water, led the attention of those who adopted that opinion to
the thermometrical changes which take place when vapor is formed and
condensed. These changes are important, and their laws curious. The
laws belong to the induction of latent heat, of which we have just
spoken; but a knowledge of them is not absolutely necessary in order
to enable us to understand the manner in which steam exists in air.

De Luc's views led him[46\10] also to the consideration of the
effect of pressure on vapor. He explains the fact that pressure will
condense vapor, by supposing that it brings the particles within the
distance at which the repulsion arising from fire ceases. In this
way, he also explains the fact, that though external pressure does
thus condense steam, the mixture of a body of air, by which the
pressure is equally increased, will not produce the same effect; and
therefore, vapors can exist in the atmosphere. They make no fixed
proportion of it; but at the same temperature we have the same
pressure arising _from them_, whether they are in air or not. As the
heat increases, vapor becomes capable of supporting a greater and
greater pressure, and at the boiling heat, it can support the
pressure of the atmosphere.

[Note 46\10: Fischer, vol. vii. p. 453. _Nouvelles Idées sur la
Météorologie_, 1787.]

De Luc also marked very precisely (as Wallerius had done) the
difference between vapor and air; the former being capable of change
of _consistence_ by cold or pressure, the latter not so. Pictet, in
1786, made a hygrometrical experiment, which appeared to him to
confirm De Luc's views; and De Luc, in 1792, published a concluding
essay on the subject in the _Philosophical Transactions_. Pictet's
_Essay on Fire_, in 1791, also demonstrated that "all the train of
hygrometrical phenomena takes place just as well, indeed rather
quicker, in a vacuum than in air, provided the same quantity of
moisture is present." This essay, and De Luc's paper, gave the
death-blow to the theory of the solution of water in air.

Yet this theory did not fall without an obstinate struggle. It was
taken up by the new school of French chemists, and connected with
their views of heat. Indeed, it long appears as the prevalent
opinion. {169} Girtanner,[47\10] in his _Grounds of the
Antiphlogistic Theory_, may be considered as one of the principal
expounders of this view of the matter. Hube, of Warsaw, was,
however, the strongest of the defenders of the theory of solution,
and published upon it repeatedly about 1790. Yet he appears to have
been somewhat embarrassed with the increase of the air's elasticity
by vapor. Parrot, in 1801, proposed another theory, maintaining that
De Luc had by no means successfully attacked that of solution, but
only De Saussure's superfluous additions to it.

[Note 47\10: Fischer, vol. vii. 473.]

It is difficult to see what prevented the general reception of the
doctrine of independent vapor; since it explained all the facts very
simply, and the agency of air was shown over and over again to be
unnecessary. Yet, even now, the solution of water in air is hardly
exploded. M. Gay Lussac,[48\10] in 1800, talks of the quantity of
water "held in solution" by the air; which, he says, varies
according to its temperature and density by a law which has not yet
been discovered. And Professor Robison, in the article "Steam," in
the _Encyclopædia Britannica_ (published about 1800), says,[49\10]
"Many philosophers imagine that spontaneous evaporation, at low
temperatures, is produced in this way (by elasticity alone). But we
cannot be of this opinion; and must still think that this kind of
evaporation is produced by the dissolving power of the air." He then
gives some reasons for his opinion. "When moist air is suddenly
rarefied, there is always a precipitation of water. But by this new
doctrine the very contrary should happen, because the tendency of
water to appear in the elastic form is promoted by removing the
external pressure." Another main difficulty in the way of the
doctrine of the mere mixture of vapor and air was supposed to be
this; that if they were so mixed, the heavier fluid would take the
lower part, and the lighter the higher part, of the space which they
occupied.

[Note 48\10: _Ann. Chim._ tom. xliii.]

[Note 49\10: Robison's _Works_, ii. 37.]

The former of these arguments was repelled by the consideration that
in the rarefaction of air, its specific heat is changed, and thus
its temperature reduced below the constituent temperature of the
vapor which it contains. The latter argument is answered by a
reference to Dalton's law of the mixture of gases. We must consider
the establishment of this doctrine in a new section, as the most
material step to the true notion of evaporation. {170}


_Sect._ 3.--_Dalton's Doctrine of Evaporation._

A PORTION of that which appears to be the true notion of evaporation
was known, with greater or less distinctness, to several of the
physical philosophers of whom we have spoken. They were aware that
the vapor which exists in air, in an invisible state, may be
condensed into water by cold: and they had noticed that, in any
state of the atmosphere, there is a certain temperature lower than
that of the atmosphere, to which, if we depress bodies, water forms
upon them in fine drops like dew; this temperature is thence called
the _dew-point_. The vapor of water which exists anywhere may be
reduced below the degree of heat which is necessary to constitute it
vapor, and thus it ceases to be vapor. Hence this temperature is
also called the _constituent temperature_. This was generally known
to the meteorological speculators of the last century, although, in
England, attention was principally called to it by Dr. Wells's
_Essay on Dew_, in 1814. This doctrine readily explains how the cold
produced by rarefaction of air, descending below the constituent
temperature of the contained vapor, may precipitate a dew; and thus,
as we have said, refutes one obvious objection to the theory of
independent vapor.

The other difficulty was first fully removed by Mr. Dalton. When his
attention was drawn to the subject of vapor, he saw insurmountable
objections to the doctrine of a chemical union of water and air. In
fact, this doctrine was a mere nominal explanation; for, on closer
examination, no chemical analogies supported it. After some
reflection, and in the sequel of other generalizations concerning
gases, he was led to the persuasion, that when air and steam are
mixed together, each follows its separate laws of equilibrium, the
particles of each being elastic with regard to those of their own
kind only: so that steam may be conceived as flowing among the
particles of air[50\10] "like a stream of water among pebbles;" and
the resistance which air offers to evaporation arises, not from its
weight, but from the inertia of its particles.

[Note 50\10: _Manchester Memoirs_, vol. v. p. 581.]

It will be found that the theory of independent vapor, understood
with these conditions, will include all the facts of the
case;--gradual evaporation in air; sudden evaporation in a vacuum;
the increase of {171} the air's elasticity by vapor; condensation by
its various causes; and other phenomena.

But Mr. Dalton also made experiments to prove his fundamental
principle, that if two different gases communicate, they will
diffuse themselves through each other;[51\10]--slowly, if the
opening of communication be small. He observes also, that all the
gases had equal solvent powers for vapor, which could hardly have
happened, had chemical affinity been concerned. Nor does the density
of the air make any difference.

[Note 51\10: _New System of Chemical Philosophy_, vol. i. p. 151.]

Taking all these circumstances into the account, Mr. Dalton
abandoned the idea of solution. "In the autumn of 1801," he says, "I
hit upon an idea which seemed to be exactly calculated to explain
the phenomena of vapor: it gave rise to a great variety of
experiments," which ended in fixing it in his mind as a true idea.
"But," he adds, "the theory was almost universally misunderstood,
and consequently reprobated."

Mr. Dalton answers various objections. Berthollet had urged that we
can hardly conceive the particles of an elastic substance added to
those of another, without increasing its elasticity. To this Mr.
Dalton replies by adducing the instance of magnets, which repel each
other, but do not repel other bodies. One of the most curious and
ingenious objections is that of M. Gough, who argues, that if each
gas is elastic with regard to itself alone, we should hear, produced
by one stroke, four sounds; namely, _first_, the sound through
aqueous vapor; _second_, the sound through azotic gas; _third_, the
sound through oxygen gas; _fourth_, the sound through carbonic acid.
Mr. Dalton's answer is, that the difference of time at which these
sounds would come is very small; and that, in fact, we do hear,
sounds double and treble.

In his _New System of Chemical Philosophy_, Mr. Dalton considers the
objections of his opponents with singular candor and impartiality.
He there appears disposed to abandon that part of the theory which
negatives the mutual repulsion of the particles of the two gases,
and to attribute their diffusion through one another to the
different size of the particles, which would, he thinks,[52\10]
produce the same effect.

[Note 52\10: _New System_, vol. i. p. 188.]

In selecting, as of permanent importance, the really valuable part
of this theory, we must endeavor to leave out all that is doubtful
or unproved. I believe it will be found that in all theories
hitherto {172} promulgated, all assertions respecting the properties
of the particles of bodies, their sizes, distances, attractions, and
the like, are insecure and superfluous. Passing over, then, such
hypotheses, the inductions which remain are these;--that two gases
which are in communication will, by the elasticity of each, diffuse
themselves in one another, quickly or slowly; and--that the quantity
of steam contained in a certain space of air is the same, whatever
be the air, whatever be its density, and even if there be a vacuum.
These propositions may be included together by saying, that one gas
is _mechanically mixed_ with another; and we cannot but assent to
what Mr. Dalton says of the latter fact,--"this is certainly the
touchstone of the mechanical and chemical theories." This _doctrine
of the mechanical mixture of gases_ appears to supply answers to all
the difficulties opposed to it by Berthollet and others, as Mr.
Dalton has shown;[53\10] and we may, therefore, accept it as well
established.

[Note 53\10: _New System_, vol. i. p. 160, &c.]

This doctrine, along with the _principle of the constituent
temperature of steam_, is applicable to a large series of
meteorological and other consequences. But before considering the
applications of theory to natural phenomena, which have been made,
it will be proper to speak of researches which were carried on, in a
great measure, in consequence of the use of steam in the arts: I
mean the laws which connect its elastic force with its constituent
temperature.


_Sect._ 4.--_Determination of the Laws of the Elastic Force of
Steam._

THE expansion of aqueous vapor at different temperatures is
governed, like that of all other vapors, by the law of Dalton and
Gay-Lussac, already mentioned; and from this, its elasticity, when
its expansion is resisted, will be known by the law of Boyle and
Mariotte; namely, by the rule that the pressure of airy fluids is as
the condensation. But it is to be observed, that this process of
calculation goes on the supposition that the steam is cut off from
contact with water, so that no more steam can be generated; a case
quite different from the common one, in which the steam is more
abundant as the heat is greater. The examination of the force of
vapor, when it is in contact with water, must be briefly noticed.

During the period of which we have been speaking, the progress of
the investigation of the laws of aqueous vapor was much accelerated
{173} by the growing importance of the steam-engine, in which those
laws operated in a practical form. James Watts, the main improver of
that machine, was thus a great contributor to speculative knowledge,
as well as to practical power. Many of his improvements depended on
the laws which regulate the quantity of heat which goes to the
formation or condensation of steam; and the observations which led
to these improvements enter into the induction of latent heat.
Measurements of the force of steam, at all temperatures, were made
with the same view. Watts's attention had been drawn to the
steam-engine in 1759, by Robison, the former being then an
instrument-maker, and the latter a student at the University of
Glasgow.[54\10] In 1761 or 1762, he tried some experiments on the
force of steam in a Papin's Digester;[55\10] and formed a sort of
working model of a steam-engine, feeling already his vocation to
develope the powers of that invention. His knowledge was at that
time principally derived from Desaguliers and Belidor, but his own
experiments added to it rapidly. In 1764 and 1765, he made a more
systematical course of experiments, directed to ascertain the force
of steam. He tried this force, however, only at temperatures above
the boiling-point; and inferred it at lower degrees from the
supposed continuity of the law thus obtained. His friend Robison,
also, was soon after led, by reading the account of some experiments
of Lord Charles Cavendish, and some others of Mr. Nairne, to examine
the same subject. He made out a table of the correspondence of the
elasticity and the temperature of vapor, from thirty-two to two
hundred and eighty degrees of Fahrenheit's thermometer.[56\10] The
thing here to be remarked, is the establishment of a law of the
pressure of steam, down to the freezing-point of water. Ziegler of
Basle, in 1769, and Achard of Berlin, in 1782, made similar
experiments. The latter examined also the elasticity of the vapor of
alcohol. Betancourt, in 1792, published his Memoir on the expansive
force of vapors; and his tables were for some time considered the
most exact. {174} Prony, in his _Architecture Hydraulique_ (1796),
established a mathematical formula,[57\10] on the experiments of
Betancourt, who began his researches in the belief that he was first
in the field, although he afterwards found that he had been
anticipated by Ziegler. Gren compared the experiments of Betancourt
and De Luc with his own. He ascertained an important fact, that when
water _boils_, the elasticity of the steam is equal to that of the
atmosphere. Schmidt at Giessen endeavored to improve the apparatus
used by Betancourt; and Biker, of Rotterdam, in 1800, made new
trials for the same purpose.

[Note 54\10: Robison's _Works_, vol. ii. p. 113.]

[Note 55\10: Denis Papin, who made many of Boyle's experiments for
him, had discovered that if the vapor be prevented from rising, the
water becomes hotter than the usual boiling-point; and had hence
invented the instrument called _Papin's Digester_. It is described
in his book, _La manière d'amolir les os et de faire cuire toutes
sorts de viandes en fort peu de temps et à peu de frais_. Paris,
1682.]

[Note 56\10: These were afterwards published in the _Encyclopædia
Britannica_; in the article "Steam," written by Robison.]

[Note 57\10: _Architecture Hydraulique_, Seconde Partie, p. 163.]

In 1801, Mr. Dalton communicated to the Philosophical Society of
Manchester his investigations on this subject; observing truly, that
though the forces at high temperatures are most important when steam
is considered as a mechanical agent, the progress of philosophy is
more immediately interested in accurate observations on the force at
low temperatures. He also found that his elasticities for
equidistant temperatures resembled a _geometrical progression_, but
with a ratio constantly diminishing. Dr. Ure, in 1818, published in
the _Philosophical Transactions_ of London, experiments of the same
kind, valuable from the high temperatures at which they were made,
and for the simplicity of his apparatus. The law which he thus
obtained approached, like Dalton's, to a _geometrical progression_.
Dr. Ure says, that a formula proposed by M. Biot gives an error of
near nine inches out of seventy-five, at a temperature of 266
degrees. This is very conceivable, for if the formula be wrong at
all, the geometrical progress rapidly inflames the error in the
higher portions of the scale. The elasticity of steam, at high
temperatures, has also been experimentally examined by Mr. Southern,
of Soho, and Mr. Sharpe, of Manchester. Mr. Dalton has attempted to
deduce certain general laws from Mr. Sharpe's experiments; and other
persons have offered other rules, as those which govern the force of
steam with reference to the temperature: but no rule appears yet to
have assumed the character of an established scientific truth. Yet
the law of the expansive force of steam is not only required in
order that the steam-engine may be employed with safety and to the
best advantage; but must also be an important point in every
consistent thermotical theory.

[2nd Ed.] [To the experiments on steam made by private physicists,
are to be added the experiments made on a grand scale by order of
the governments of France and of America, with a view to {175}
legislation on the subject of steam-engines. The French experiments
were made in 1823, under the direction of a commission consisting of
some of the most distinguished members of the Academy of Sciences;
namely, MM. de Prony, Arago, Girard, and Dulong. The American
experiments were placed in the hands of a committee of the Franklin
Institute of the State of Pennsylvania, consisting of Prof. Bache
and others, in 1830. The French experiments went as high as 435° of
Fahrenheit's thermometer, corresponding to a pressure of 60 feet of
mercury, or 24 atmospheres. The American experiments were made up to
a temperature of 346°, which corresponded to 274 inches of mercury,
more than 9 atmospheres. The extensive range of these experiments
affords great advantages for determining the law of the expansive
force. The French Academy found that their experiments indicated an
increase of the elastic force according to the _fifth_ power of a
binominal 1 + _mt_, where _t_ is the temperature. The American
Institute were led to a _sixth_ power of a like binominal. Other
experimenters have expressed their results, not by powers of the
temperature, but by geometrical ratios. Dr. Dalton had supposed that
the expansion of mercury being as the square of the true temperature
above its freezing-point, the expansive force of steam increases in
geometrical ratio for equal increments of temperature. And the
author of the article _Steam_ in the Seventh Edition of the
_Encyclopædia Britannica_ (Mr. J. S. Russell), has found that the
experiments are best satisfied by supposing mercury, as well as
steam, to expand in a geometrical ratio for equal increments of the
true temperature.

It appears by such calculation, that while dry gas increases in the
ratio of 8 to 11, by an increase of temperature from freezing to
boiling water; steam in contact with water, by the same increase of
temperature above boiling water, has its expansive force increased
in the proportion of 1 to 12. By an equal increase of temperature,
mercury expands in about the ratio of 8 to 9.

Recently, MM. Magnus of Berlin, Holzmann and Regnault, have made
series of observations on the relation between temperature and
elasticity of steam.[58\10]

[Note 58\10: See Taylor's _Scientific Memoirs_, Aug. 1845, vol. iv.
part xiv., and _Ann. de Chimie_.]

Prof. Magnus measured his temperatures by an air-thermometer; a
process which, I stated in the first edition, seemed to afford the
best promise of simplifying the law of expansion. His result is,
that the {176} elasticity proceeds in a geometric series when the
temperature proceeds in an arithmetical series nearly; the
differences of temperature for equal augmentations of the ratio of
elasticity being somewhat greater for the higher temperatures.

The forces of the vapors of other liquids in contact with their
liquids, determined by Dr. Faraday, as mentioned in Chap. ii. Sect.
1, are analogous to the elasticity of steam here spoken of.]


_Sect._ 5.--_Consequences of the Doctrine of
Evaporation.--Explanation of Rain, Dew, and Clouds._

THE discoveries concerning the relations of heat and moisture which
were made during the last century, were principally suggested by
meteorological inquiries, and were applied to meteorology as fast as
they rose. Still there remains, on many points of this subject, so
much doubt and obscurity, that we cannot suppose the doctrines to
have assumed their final form; and therefore we are not here called
upon to trace their progress and connexion. The principles of
atmology are pretty well understood; but the difficulty of observing
the conditions under which they produce their effects in the
atmosphere is so great, that the precise theory of most
meteorological phenomena is still to be determined.

We have already considered the answers given to the question:
According to what rules does transparent aqueous vapor resume its
form of visible water? This question includes, not only the problems
of Rain and Dew, but also of Clouds; for clouds are not vapor, but
water, vapor being always invisible. An opinion which attracted much
notice in its time, was that of Hutton, who, in 1784, endeavored to
prove that if two masses of air saturated with transparent vapor at
different temperatures are mixed together, the precipitation of
water in the form either of cloud or of drops will take place. The
reason he assigned for the opinion was this: that the temperature of
the mixture is a mean between the two temperatures, but that the
force of the vapor in the mixture, which is the mean of the forces
of the two component vapors, will be greater than that which
corresponds to the mean temperature, since the force increases
faster than the temperature;[59\10] and hence some part of the vapor
will be precipitated. This doctrine, it will be seen, speaks of
vapor as "saturating" air, and is {177} therefore, in this form,
inconsistent with Dalton's principle; but it is not difficult to
modify the expression so as to retain the essential part of the
explanation.

[Note 59\10: _Edin. Trans._ vol. 1. p. 42.]

_Dew._--The principle of a "constituent temperature" of steam, and
the explanation of the "dew-point," were known, as we have said
(chap. iii. sect. 3,) to the meteorologists of the last century; but
we perceive how incomplete their knowledge was, by the very gradual
manner in which the consequences of this principle were traced out.
We have already noticed, as one of the books which most drew
attention to the true doctrine, in this country at least, Dr.
Wells's _Essay on Dew_, published in 1814. In this work the author
gives an account of the progress of his opinions;[60\10] "I was
led," he says, "in the autumn of 1784, by the event of a rude
experiment, to think it probable that the formation of dew is
attended with the production of cold." This was confirmed by the
experiments of others. But some years after, "upon considering the
subject more closely, I began to suspect that Mr. Wilson, Mr. Six,
and myself, had all committed an error in regarding the cold which
accompanies the dew, as an _effect_ of the formation of the dew." He
now considered it rather as the _cause_: and soon found that he was
able to account for the circumstances of this formation, many of
them curious and paradoxical, by supposing the bodies on which dew
is deposited, to be cooled down, by radiation into the clear
night-sky, to the proper temperature. The same principle will
obviously explain the formation of mists over streams and lakes when
the air is cooler than the water; which was put forward by Davy,
even in 1810, as a new doctrine, or at least not familiar.

[Note 60\10: _Essay on Dew_, p. 1.]

_Hygrometers._--According as air has more or less of vapor in
comparison with that which its temperature and pressure enable it to
contain, it is more or less humid; and an instrument which measures
the degrees of such a gradation is a _hygrometer_. The hygrometers
which were at first invented, were those which measured the moisture
by its effect in producing expansion or contraction in certain
organic substances; thus De Saussure devised a hair-hygrometer, De
Luc a whalebone-hygrometer, and Dalton used a piece of whipcord. All
these contrivances were variable in the amount of their indications
under the same circumstances; and, moreover, it was not easy to know
the physical meaning of the degree indicated. The dew-point, or
constituent temperature of the vapor which exists in the air, is, on
{178} the other hand, both constant and definite. The determination
of this point, as a datum for the moisture of the atmosphere, was
employed by Le Roi, and by Dalton (1802), the condensation being
obtained by cold water:[61\10] and finally, Mr. Daniell (1812)
constructed an instrument, where the condensing temperature was
produced by evaporation of ether, in a very convenient manner. This
invention (_Daniell's Hygrometer_) enables us to determine the
quantity of vapor which exists in a given mass of the atmosphere at
any time of observation.

[Note 61\10: Daniell, _Met. Ess._ p. 142. _Manch. Mem._ vol. v.
p. 581.]

[2nd Ed.] [As a happy application of the Atmological Laws which have
been discovered, I may mention the completion of the theory and use
of the _Wet-bulb Hygrometer_; an instrument in which, from the
depression of temperature produced by wetting the bulb of a
thermometer, we infer the further depression which would produce
dew. Of this instrument the history is thus summed up by Prof.
Forbes:--"Hutton invented the method; Leslie revived and extended
it, giving probably the earliest, though an imperfect theory;
Gay-Lussac, by his excellent experiments and reasoning from them,
completed the theory, so far as perfectly dry air is concerned;
Ivory extended the theory; which was reduced to practice by Auguste
and Bohnenberger, who determined the constant with accuracy. English
observers have done little more than confirm the conclusions of our
industrious Germanic neighbors; nevertheless the experiments of
Apjohn and Prinsep must ever be considered as conclusively settling
the value of the coefficient near the one extremity of the scale, as
those of Kæmtz have done for the other."[62\10]

[Note 62\10: _Second Report on Meteorology_, p. 101.]

Prof. Forbes's two Reports _On the Recent Progress and Present State
of Meteorology_ given among the _Reports of the British Association_
for 1832 and 1840, contain a complete and luminous account of recent
researches on this subject. It may perhaps be asked why I have not
given Meteorology a place among the Inductive Sciences; but if the
reader refers to these accounts, or any other adequate view of the
subject, he will see that Meteorology is not a single Inductive
Science, but the application of several sciences to the explanation
of terrestrial and atmospheric phenomena. Of the sciences so
applied, Thermotics and Atmology are the principal ones. But others
also come into play; as Optics, in the explanation of Rainbows,
Halos, {179} Parhelia, Coronæ, Glories, and the like; Electricity,
in the explanation of Thunder and Lightning, Hail, Aurora Borealis;
to which others might be added.]

_Clouds._--When vapor becomes visible by being cooled below its
constituent temperature, it forms itself into a very fine watery
powder, the diameter of the particles of which this powder consists
being very small: they are estimated by various writers, from
1⁄100,000th to 1⁄20,000th of an inch.[63\10] Such particles, even if
solid, would descend very slowly; and very slight causes would
suffice for their suspension, without recurring to the hypothesis of
vesicles, of which we have already spoken. Indeed that hypothesis
will not explain the fact, except we suppose these vesicles filled
with a rarer air than that of the atmosphere; and, accordingly,
though this hypothesis is still maintained by some,[64\10] it is
asserted as a fact of observation, proved by optical or other
phenomena, and not deduced from the suspension of clouds. Yet the
latter result is still variously explained by different
philosophers: thus, M. Gay-Lussac[65\10] accounts for it by upward
currents of air, and Fresnel explains it by the heat and rarefaction
of air in the interior of the cloud.

[Note 63\10: Kæmtz, _Met._ i. 393.]

[Note 64\10: Ib. i. 393. Robison, ii. 13.]

[Note 65\10: _Ann. Chim._ xxv. 1822.]

_Classification of Clouds._--A classification of clouds can then
only be consistent and intelligible when it rests upon their
atmological conditions. Such a system was proposed by Mr. Luke
Howard, in 1802-3. His primary modifications are, _Cirrus_,
_Cumulus_, and _Stratus_, which the Germans have translated by terms
equivalent in English to _feather-cloud_, _heap-cloud_, and
_layer-cloud_. The cumulus increases by accumulations on its top,
and floats in the air with a horizontal base; the stratus grows from
below, and spreads along the earth; the cirrus consists of fibres in
the higher regions of the atmosphere, which grow every way. Between
the simple modifications are intermediate ones, _cirro-cumulus_ and
_cirro-stratus_; and, again, compound ones, the _cumulo-stratus_ and
the _nimbus_, or _rain-cloud_. These distinctions have been
generally accepted all over Europe: and have rendered a description
of all the processes which go on in the atmosphere far more definite
and clear than it could be made before their use.

I omit a mass of facts and opinions, supposed laws of phenomena and
assigned causes, which abound in meteorology more than in any other
science. The slightest consideration will show us what a great {180}
amount of labor, of persevering and combined observation, the
progress of this branch of knowledge requires. I do not even speak
of the condition of the more elevated parts of the atmosphere. The
diminution of temperature as we ascend, one of the most marked of
atmospheric facts, has been variously explained by different
writers. Thus Dalton[66\10] (1808) refers it to a principle "that
each atom of air, in the same perpendicular column, is possessed of
the same degree of heat," which principle he conceives to be
entirely empirical in this case. Fourier says[67\10] (1817), "This
phenomenon results from several causes: one of the principal is the
progressive extinction of the rays of heat in the successive strata
of the atmosphere."

[Note 66\10: _New Syst. of Chem._ vol. i. p. 125.]

[Note 67\10: _Ann. Chim._ vi. 285.]

Leaving, therefore, the application of thermotical and atmological
principles in particular cases, let us consider for a moment the
general views to which they have led philosophers.




CHAPTER IV.

PHYSICAL THEORIES OF HEAT.


WHEN we look at the condition of that branch of knowledge which,
according to the phraseology already employed, we must call _Physical
Thermotics_, in opposition to Formal Thermotics, which gives us
detached laws of phenomena, we find the prospect very different from
that which was presented to us by physical astronomy, optics, and
acoustics. In these sciences, the maintainers of a distinct and
comprehensive theory have professed at least to show that it
explains and includes the principal laws of phenomena of various
kinds; in Thermotics, we have only attempts to explain a part of the
facts. We have here no example of an hypothesis which, assumed in
order to explain one class of phenomena, has been found also to
account exactly for another; as when central forces led to the
precession of the equinoxes, or when the explanation of polarization
explained also double refraction; or when the pressure of the
atmosphere, as measured by the barometer, gave the true velocity of
sound. Such coincidences, or _consiliences_, as I have elsewhere
called them, are the test of truth; and thermotical theories cannot
yet exhibit credentials of this kind. {181}

On looking back at our view of this science, it will be seen that it
may be distinguished into two parts; the Doctrines of Conduction and
Radiation, which we call Thermotics proper; and the Doctrines
respecting the relation of Heat, Airs, and Moisture, which we have
termed Atmology. These two subjects differ in their bearing on our
hypothetical views.

_Thermotical Theories._--The phenomena of radiant heat, like those
of radiant light, obviously admit of general explanation in two
different ways;--by the emission of material particles, or by the
propagation of undulations. Both these opinions have found
supporters. Probably most persons, in adopting Prevost's theory of
exchanges, conceive the radiation of heat to be the radiation of
matter. The undulation hypothesis, on the other hand, appears to be
suggested by the production of heat by friction, and was accordingly
maintained by Rumford and others. Leslie[68\10] appears, in a great
part of his _Inquiry_, to be a supporter of some undulatory
doctrine, but it is extremely difficult to make out what his
undulating medium is; or rather, his opinions wavered during his
progress. In page 31, he asks, "What is this calorific and
frigorific fluid? and after keeping the reader in suspense for a
moment, he replies,
  "Quod petis hic est.
It is merely the ambient AIR." But at page 150, he again asks the
question, and, at page 188, he answers, "It is the same subtile
matter that, according to its different modes of existence,
constitutes either heat or light." A person thus vacillating between
two opinions, one of which is palpably false, and the other laden
with exceeding difficulties which he does not even attempt to
remove, had little right to protest against[69\10] "the sportive
freaks of some intangible _aura_;" to rank all other hypotheses than
his own with the "occult qualities of the schools;" and to class the
"prejudices" of his opponents with the tenets of those who
maintained the _fuga vacui_ in opposition to Torricelli. It is worth
while noticing this kind of rhetoric, in order to observe, that it
may be used just as easily on the wrong side as on the right.

[Note 68\10: _An Experimental Inquiry into the Nature and
Propagation of Heat_, 1804.]

[Note 69\10: Ib. p. 47.]

Till recently, the theory of material heat, and of its propagation
by emission, was probably the one most in favor with those who had
studied mathematical thermotics. As we have said, the laws of {182}
conduction, in their ultimate analytical form, were almost identical
with the laws of motion of fluids. Fourier's principle also, that
the radiation of heat takes place from points below the surface, and
is intercepted by the superficial particles, appears to favor the
notion of material emission.

Accordingly, some of the most eminent modern French mathematicians
have accepted and extended the hypothesis of a material caloric. In
addition to Fourier's doctrine of molecular extra-radiation, Laplace
and Poisson have maintained the hypothesis of _molecular
intra-radiation_, as the mode in which conduction takes place; that
is, they say that the particles of bodies are to be considered as
_discrete_, or as points separated from each other, and acting on
each other at a distance; and the conduction of heat from one part
to another, is performed by radiation between all neighboring
particles. They hold that, without this hypothesis, the differential
equations expressing the conditions of conduction cannot be made
homogeneous: but this assertion rests, I conceive, on an error, as
Fourier has shown, by dispensing with the hypothesis. The necessity
of the hypothesis of discrete molecular action in bodies, is
maintained in all cases by M. Poisson; and he has asserted Laplace's
theory of capillary attraction to be defective on this ground, as
Laplace asserted Fourier's reasoning respecting heat to be so. In
reality, however, this hypothesis of discrete molecules cannot be
maintained as a physical truth; for the law of molecular action,
which is assumed in the reasoning, after answering its purpose in
the progress of calculation, vanishes in the result; the conclusion
is the same, whatever law of the intervals of the molecules be
assumed. The definite integral, which expresses the whole action, no
more proves that this action is actually made of the differential
parts by means of which it was found, than the processes of finding
the weight of a body by integration, prove it to be made up of
differential weights. And therefore, even if we were to adopt the
emission theory of heat, we are by no means bound to take along with
it the hypothesis of discrete molecules.

But the recent discovery of the refraction, polarization, and
depolarization of heat, has quite altered the theoretical aspect of
the subject, and, almost at a single blow, ruined the emission
theory. Since heat is reflected and refracted like light, analogy
would lead us to conclude that the mechanism of the processes is the
same in the two cases. And when we add to these properties the
property of polarization, it is scarcely possible to believe
otherwise than that heat consists in {183} transverse vibrations;
for no wise philosopher would attempt an explanation by ascribing
poles to the emitted particles, after the experience which Optics
affords, of the utter failure of such machinery.

But here the question occurs, If heat consists in vibrations, whence
arises the extraordinary identity of the laws of its propagation
with the laws of the flow of matter? How is it that, in conducted
heat, this vibration creeps slowly from one part of the body to
another, the part first heated remaining hottest; instead of leaving
its first place and travelling rapidly to another, as the vibrations
of sound and light do? The answer to these questions has been put in
a very distinct and plausible form by that distinguished
philosopher, M. Ampère, who published a _Note on Heat and Light
considered as the results of Vibratory Motion_,[70\10] in 1834 and
1835; and though this answer is an hypothesis, it at least shows
that there is no fatal force in the difficulty.

[Note 70\10: _Bibliothèque Universelle de Genève_, vol. xlix. p.
225. _Ann. Chim._ tom. lvii. p. 434.]

M. Ampère's hypothesis is this; that bodies consist of solid
molecules, which may be considered as arranged at intervals in a
very rare ether; and that the vibrations of the molecules, causing
vibrations of the ether and caused by them, constitute heat. On
these suppositions, we should have the phenomena of conduction
explained; for if the molecules at one end of a bar be hot, and
therefore in a state of vibration, while the others are at rest, the
vibrating molecules propagate vibrations in the ether, but these
vibrations do not produce heat, except in proportion as they put the
quiescent molecules of the bar in vibration; and the ether being
very rare compared with the molecules, it is only by the repeated
impulses of many successive vibrations that the nearest quiescent
molecules are made to vibrate; after which they combine in
communicating the vibration to the more remote molecules. "We then
find necessarily," M. Ampère adds, "the same equations as those
found by Fourier for the distribution of heat, setting out from the
same hypothesis, that the temperature or heat transmitted is
proportional to the difference of the temperatures."

Since the undulatory hypothesis of heat can thus answer all obvious
objections, we may consider it as upon its trial, to be confirmed or
modified by future discoveries; and especially by an enlarged
knowledge of the laws of the polarization of heat.

[2nd Ed.] [Since the first edition was written, the analogies
between light and heat have been further extended, as I have already
stated. It {184} has been discovered by MM. Biot and Melloni that
quartz impresses a circular polarization upon heat; and by Prof.
Forbes that mica, of a certain thickness, produces phenomena such as
would be produced by the impression of circular polarization of the
supposed transversal vibrations of radiant heat; and further, a
rhomb of rock-salt, of the shape of the glass rhomb which verified
Fresnel's extraordinary anticipation of the circular polarization of
light, verified the expectation, founded upon other analogies, of
the polarization of heat. By passing polarized heat through various
thicknesses of mica, Prof. Forbes has attempted to calculate the
length of an undulation for heat.

These analogies cannot fail to produce a strong disposition to
believe that light and heat, essences so closely connected that they
can hardly be separated, and thus shown to have so many curious
properties in common, are propagated by the same machinery; and thus
we are led to an Undulatory Theory of Heat.

Yet such a Theory has not yet by any means received full
confirmation. It depends upon the analogy and the connexion of the
Theory of Light, and would have little weight if those were removed.
For the separation of the rays in double refraction, and the
phenomena of periodical intensity, the two classes of facts out of
which the Undulatory Theory of Optics principally grew, have neither
of them been detected in thermotical experiments. Prof. Forbes has
assumed alternations of heat for increasing thicknesses of mica, but
in his experiments we find only one _maximum_. The occurrence of
alternate maxima and minima under the like circumstances would
exhibit visible waves of heat, as the fringes of shadows do of
light, and would thus add much to the evidence of the theory.

Even if I conceived the Undulatory Theory of Heat to be now
established, I should not venture, as yet, to describe its
establishment as an event in the history of the Inductive Sciences.
It is only at an interval of time after such events have taken place
that their history and character can be fully understood, so as to
suggest lessons in the Philosophy of Science.]

_Atmological Theories._--Hypotheses of the relations of heat and air
almost necessarily involve a reference to the forces by which the
composition of bodies is produced, and thus cannot properly be
treated of, till we have surveyed the condition of chemical
knowledge. But we may say a few words on one such hypothesis; I mean
the hypothesis on the subject of the atmological laws of heat,
proposed by Laplace, in the twelfth Book of the _Mécanique Céléste_,
and published in 1823. {185} It will be recollected that the main
laws of phenomena for which we have to account, by means of such an
hypothesis, are the following:--

(1.) The law of Boyle and Mariotte, that the elasticity of an air
varies as its density. See Chap. iii., Sect. 1 of this Book.

(2.) The Law of Gay-Lussac and Dalton, that all airs expand equally
by heat. See Chap. ii. Sect. 1.

(3.) The production of heat by sudden compression. See Chap. ii.
Sect. 2.

(4.) Dalton's principle of the mechanical mixture of airs. See Chap.
iii. Sect. 3.

(5.) The Law of expansion of solids and fluids by heat. See Chap.
ii. Sect. 1.

(6.) Changes of consistence by heat, and the doctrine of latent
heat. See Chap. ii. Sect. 3.

(7.) The Law of the expansive force of steam. See Chap. iii. Sect. 4.

Besides these, there are laws of which it is doubtful whether they
are or are not included in the preceding, as the low temperature of
the air in the higher parts of the atmosphere. (See Chap. iii.
Sect. 5.)

Laplace's hypothesis[71\10] is this:--that bodies consist of
particles, each of which gathers round it, by its attraction, a
quantity of caloric: that the particles of the bodies attract each
other, besides attracting the caloric, and that the particles of the
caloric repel each other.

[Note 71\10: _Méc. Cél._ t. v. p. 89.]

In gases, the particles of the bodies are so far removed, that their
mutual attraction is insensible, and the matter tends to expand by
the mutual repulsion of the caloric. He conceives this caloric to be
constantly radiating among the particles; the density of this
internal radiation is the _temperature_, and he proves that, on this
supposition, the elasticity of the air will be as the density, and
as this temperature. Hence follow the three first rules above
stated. The same suppositions lead to Dalton's principle of mixtures
(4), though without involving his mode of conception; for Laplace
says that whatever the mutual action of two gases be, the whole
pressure will be equal to the sum of the separate pressures.[72\10]
Expansion (5), and the changes of consistence (6), are explained by
supposing[73\10] that in solids, the mutual attraction of the
particles of the body is the greatest force; in liquids, the
attraction of the particles for the caloric; in airs, the repulsion
of {186} the caloric. But the doctrine of latent heat again
modifies[74\10] the hypothesis, and makes it necessary to include
latent heat in the calculation; yet there is not, as we might
suppose there would be if the theory were the true one, any
confirmation of the hypothesis resulting from the new class of laws
thus referred to. Nor does it appear that the hypothesis accounts
for the relation between the elasticity and the temperature of steam.

[Note 72\10: Ib. p. 110.]

[Note 73\10: Ib. p. 92.]

[Note 74\10: _Méc. Cél._ t. v. p. 93.]

It will be observed that Laplace's hypothesis goes entirely upon the
materiality of heat, and is inconsistent with any vibratory theory;
for, as Ampère remarks, "It is clear that if we admit heat to
consist in vibrations, it is a contradiction to attribute to heat
(or caloric) a repulsive force of the particles which would be a
cause of vibration."

An unfavorable judgment of Laplace's Theory of Gases is suggested by
looking for that which, in speaking of Optics, was mentioned as the
great characteristic of a true theory; namely, that the hypotheses,
which were assumed in order to account for one class of facts, are
found to explain another class of a different nature:--the consilience
of inductions. Thus, in thermotics, the law of an intensity of
radiation proportional to the sine of the angle of the ray with the
surface, which is founded on direct experiments of radiation, is found
to be necessary in order to explain the tendency of neighboring bodies
to equality of temperature; and this leads to the higher
generalization, that heat is radiant from points below the surface.
But in the doctrine of the relation of heat to gases, as delivered by
Laplace, there is none of this unexpected confirmation; and though he
explains some of the leading laws, his assumptions bear a large
proportion to the laws explained. Thus, from the assumption that the
repulsion of gases arises from the mutual repulsion of the particles
of caloric, he finds that the pressure in any gas is as the square of
the density and of the quantity of caloric;[75\10] and from the
assumption that the temperature is the internal radiation, he finds
that this temperature is as the density and the square of the
caloric.[76\10] Hence he obtains the law of Boyle and Mariotte, and
that of Dalton and Gay-Lussac. But this view of the subject requires
other assumptions when we come to latent heat; and accordingly, he
introduces, to express the latent heat, a new quantity.[77\10] Yet
this quantity produces no effect on his calculations, nor does he
apply his reasoning to any problem in which latent heat is concerned.
{187}

[Note 75\10: P = 2 π H K ρ^2_c_^2 (1) p. 107.]

[Note 76\10: _q_' Π (_a_) = ρ_c_^2 (2) p. 108.]

[Note 77\10: The quantity _i_, p. 113.]

Without, then, deciding upon this theory, we may venture to say that
it is wanting in all the prominent and striking characteristics
which we have found in those great theories which we look upon as
clearly and indisputably established.

_Conclusion._--We may observe, moreover, that heat has other
bearings and effects, which, as soon as they have been analysed into
numerical laws of phenomena, must be attended to in the formation of
thermotical theories. Chemistry will probably supply many such;
those which occur to us, we must examine hereafter. But we may
mention as examples of such, MM. De la Rive and Marcet's law, that
the specific heat of all gases is the same;[78\10] and MM. Dulong
and Petit's law, that single atoms of all simple bodies have the
same capacity for heat.[79\10] Though we have not yet said anything
of the relation of different gases, or explained the meaning of
_atoms_ in the chemical sense, it will easily be conceived that
these are very general and important propositions.

[Note 78\10: _Ann. Chim._ xxxv. (1827.)]

[Note 79\10: Ib. x. 397.]

Thus the science of Thermotics, imperfect as it is, forms a
highly-instructive part of our survey; and is one of the cardinal
points on which the doors of those chambers of physical knowledge
must turn which hitherto have remained closed. For, on the one hand,
this science is related by strong analogies and dependencies to the
most complete portions of our knowledge, our mechanical doctrines
and optical theories; and on the other, it is connected with
properties and laws of a nature altogether different,--those of
chemistry; properties and laws depending upon a new system of
notions and relations, among which clear and substantial general
principles are far more difficult to lay hold of and with which the
future progress of human knowledge appears to be far more concerned.
To these notions and relations we must now proceed; but we shall
find an intermediate stage, in certain subjects which I shall call
the _Mechanico-chemical_ Sciences; viz., those which have to do with
Magnetism, Electricity, and Galvanism.



{{189}}
BOOK XI.


_THE MECHANICO-CHEMICAL SCIENCES._


HISTORY OF ELECTRICITY.


  PARVA metu primo: mox sese extollit in auras,
  Ingrediturque solo, et caput inter nubila condit.
          _Æn._ iv. 176.

  A timid breath at first, a transient touch,
  How soon it swells from little into much!
  Runs o'er the ground, and springs into the air,
  And fills the tempest's gloom, the lightning's glare;
  While denser darkness than the central storm
  Conceals the secrets of its inward form.



{{191}}
INTRODUCTION.

_Of the Mechanico-Chemical Sciences._


UNDER the title of Mechanico-Chemical Sciences, I include the laws
of Magnetism, Electricity, Galvanism, and the other classes of
phenomena closely related to these, as Thermo-electricity. This
group of subjects forms a curious and interesting portion of our
physical knowledge; and not the least of the circumstances which
give them their interest, is that double bearing upon mechanical and
chemical principles, which their name is intended to imply. Indeed,
at first sight they appear to be purely Mechanical Sciences; the
attractions and repulsions, the pressure and motion, which occur in
these cases, are referrible to mechanical conceptions and laws, as
completely as the weight or fall of terrestrial bodies, or the
motion of the moon and planets. And if the phenomena of magnetism
and electricity had directed us only to such laws, the corresponding
sciences must have been arranged as branches of mechanics. But we
find that, on the other side, these phenomena have laws and bearings
of a kind altogether different. Magnetism is associated with
Electricity by its mechanical analogies; and, more recently, has
been discovered to be still more closely connected with it by
physical influence; electric is identified with galvanic agency; but
in galvanism, decomposition, or some action of that kind,
universally appears; and these appearances lead to very general
laws. Now composition and decomposition are the subjects of
Chemistry; and thus we find that we are insensibly but irresistibly
led into the domain of that science. The highest generalizations to
which we can look, in advancing from the elementary facts of
electricity and galvanism, must involve chemical notions; we must
therefore, in laying out the platform of these sciences, make
provision for that convergence of mechanical and chemical theory,
which they are to exhibit as we ascend.

We must begin, however, with stating the mechanical phenomena of
these sciences, and the reduction of such phenomena to laws. In this
point of view, the phenomena of which we have to speak are those in
which bodies exhibit attractions and repulsions, peculiarly
determined by their nature and circumstances; as the magnet, and a
{192} piece of amber when rubbed. Such results are altogether
different from the universal attraction which, according to Newton's
discovery, prevails among all particles of matter, and to which
cosmical phenomena are owing. But yet the difference of these
special attractions, and of cosmical attraction, was at first so far
from being recognized, that the only way in which men could be led
to conceive or assent to an action of one body upon another at a
distance, in cosmical cases, was by likening it to magnetic
attraction, as we have seen in the history of Physical Astronomy.
And we shall, in the first part of our account, not dwell much upon
the peculiar conditions under which bodies are magnetic or electric,
since these conditions are not readily reducible to mechanical laws;
but, taking the magnetic or electric character for granted, we shall
trace its effects.

The habit of considering magnetic action as the type or general case
of attractive and repulsive agency, explains the early writers
having spoken of Electricity as a kind of Magnetism. Thus Gilbert,
in his book _De Magnete_ (1600), has a chapter,[1\11] _De coitione
Magniticâ, primumque de Succini attractione, sive verius corporum ad
Succinum applicatione_. The manner in which he speaks, shows us how
mysterious the fact of attraction then appeared; so that, as he
says, "the magnet and amber were called in aid by philosophers as
illustrations, when our sense is in the dark in abstruse inquiries,
and when our reason can go no further. Gilbert speaks of these
phenomena like a genuine inductive philosopher, reproving[2\11]
those who before him had "stuffed the booksellers' shops by copying
from one another extravagant stories concerning the attraction of
magnets and amber, without giving any reason from experiment." He
himself makes some important steps in the subject. He distinguishes
magnetic from _electric_ forces,[3\11] and is the inventor of the
latter name, derived from ἤλεκτρον, _electron_, amber. He observes
rightly, that the electric force attracts all light bodies, while
the magnetic force attracts iron only; and he devises a satisfactory
apparatus by which this is shown. He gives[4\11] a considerable list
of bodies which possess the electric property; "Not only amber and
agate attract small bodies, as some think, but diamond, sapphire,
carbuncle, opal, amethyst, Bristol gem, beryli, crystal, glass,
glass of antimony, spar of various kinds, sulphur, mastic,
sealing-wax," and other substances which he mentions. Even his
speculations on the general laws of these phenomena, though vague
and erroneous, as {193} at that period was unavoidable, do him no
discredit when compared with the doctrines of his successors a
century and a half afterwards. But such speculations belong to a
succeeding part of this history.

[Note 1\11: Lib. ii. cap. 2.]

[Note 2\11: _De Magnete_, p. 48.]

[Note 3\11: Ib. p. 52.]

[Note 4\11: Ib. p. 48.]

In treating of these Sciences, I will speak of Electricity in the
first place; although it is thus separated by the interposition of
Magnetism from the succeeding subjects (Galvanism, &c.) with which
its alliance seems, at first sight, the closest, and although some
general notions of the laws of magnets were obtained at an earlier
period than a knowledge of the corresponding relations of electric
phenomena: for the theory of electric attraction and repulsion is
somewhat more simple than of magnetic; was, in fact, the first
obtained; and was of use in suggesting and confirming the
generalization of magnetic laws.




CHAPTER 1.

DISCOVERY OF LAWS OF ELECTRIC PHENOMENA.


WE have already seen what was the state of this branch of knowledge
at the beginning of the seventeenth century; and the advances made
by Gilbert. We must now notice the additions which it subsequently
received, and especially those which led to the discovery of general
laws, and the establishment of the theory; events of this kind being
those of which we have more peculiarly to trace the conditions and
causes. Among the facts which we have thus especially to attend to,
are the electric attractions of small bodies by amber and other
substances when rubbed. Boyle, who repeated and extended the
experiments of Gilbert, does not appear to have arrived at any new
general notions; but Otto Guericke of Magdeburg, about the same
time, made a very material step, by discovering that there was an
electric force of repulsion as well as of attraction. He found that
when a globe of sulphur had attracted a feather, it afterwards
repelled it, till the feather had been in contact with some other
body. This, when verified under a due generality of circumstances,
forms a capital fact in our present subject. Hawkesbee, who wrote in
1709 (_Physico-Mechanical Experiments_) also observed various of the
effects of attraction and repulsion upon threads hanging loosely.
But the person who appears to have first fully seized the general
law of these facts, is {194} Dufay, whose experiments appear in the
Memoirs of the French Academy, in 1733, 1734, and 1737.[5\11] "I
discovered," he says, "a very simple principle, which accounts for a
great part of the irregularities, and, if I may use the term, the
caprices that seem to accompany most of the experiments in
electricity. This principle is, that electric bodies attract all
those that are not so, and repel them as soon as they are become
electric by the vicinity or contact of the electric body. . . . Upon
applying this principle to various experiments of electricity, any
one will be surprised at the number of obscure and puzzling facts
which it clears up." By the help of this principle, he endeavors to
explain several of Hawkesbee's experiments.

[Note 5\11: Priestley's _History of Electricity_, p. 45, and the
Memoirs quoted.]

A little anterior to Dufay's experiments were those of Grey, who, in
1729, discovered the properties of _conductors_. He found that the
attraction and repulsion which appear in electric bodies are
exhibited also by other bodies in contact with the electric. In this
manner he found that an ivory ball, connected with a glass tube by a
stick, a wire, or a packthread, attracted and repelled a feather, as
the glass itself would have done. He was then led to try to extend
this communication to considerable distances, first by ascending to
an upper window and hanging down his ball, and, afterwards, by
carrying the string horizontally supported on loops. As his success
was complete in the former case, he was perplexed by failure in the
latter; but when he supported the string by loops of silk instead of
hempen cords, he found it again become a conductor of electricity.
This he ascribed at first to the smaller thickness of the silk,
which did not carry off so much of the electric virtue; but from
this explanation he was again driven, by finding that wires of brass
still thinner than the silk destroyed the effect. Thus Grey
perceived that the efficacy of the support depended on its being
silk, and he soon found other substances which answered the same
purpose. The difference, in fact, depended on the supporting
substance being electric, and therefore not itself a conductor; for
it soon appeared from such experiments, and especially[6\11] from
those made by Dufay, that substances might be divided into
_electrics per se_, and _non-electrics_, or _conductors_. These
terms were introduced by Desaguliers,[7\11] and gave a permanent
currency to the results of the labors of Grey and others.

[Note 6\11: _Mém. Acad. Par._ 1734.]

[Note 7\11: Priestley, p. 66.]

Another very important discovery belonging to this period is, that
{195} of the two kinds of electricity. This also was made by Dufay.
"Chance," says he, "has thrown in my way another principle more
universal and remarkable than the preceding one, and which casts a new
light upon the subject of electricity. The principle is, that there
are two distinct kinds of electricity, very different from one
another; one of which I call _vitreous_, the other _resinous_,
electricity. The first is that of glass, gems, hair, wool, &c.; the
second is that of amber, gum-lac, silk, &c. The characteristic of
these two electricities is, that they repel themselves and attract
each other." This discovery does not, however, appear to have drawn so
much attention as it deserved. It was published in 1735; (in the
Memoirs of the Academy _for_ 1733;) and yet in 1747, Franklin and his
friends at Philadelphia, who had been supplied with electrical
apparatus and information by persons in England well acquainted with
the then present state of the subject, imagined that they were making
observations unknown to European science, when they were led to assert
two conditions of bodies, which were in fact the opposite
electricities of Dufay, though the American experimenters referred
them to a single element, of which electrized bodies might have either
excess or defect. "Hence," Franklin says, "have arisen some new terms
among us: we say B," who receives a spark from glass, "and bodies in
like circumstances, is electrized _positively_; A," who communicates
his electricity to glass, "_negatively_; or rather B is electrized
_plus_, A _minus_." Dr. (afterwards Sir William) Watson had, about the
same time, arrived at the same conclusions, which he expresses by
saying that the electricity of A was _more rare_, and that of B _more
dense_, than it naturally would have been.[8\11] But that which gave
the main importance to this doctrine was its application to some
remarkable experiments, of which we must now speak.

[Note 8\11: Priestley, p. 115.]

Electric action is accompanied, in many cases, by light and a
crackling sound. Otto Guericke[9\11] observes that his
sulphur-globe, when rubbed in a dark place, gave faint flashes, such
as take place when sugar is crushed. And shortly after, a light was
observed at the surface of the mercury in the barometer, when
shaken, which was explained at first by Bernoulli, on the then
prevalent Cartesian principles; but, afterwards, more truly by
Hawkesbee, as an electrical phenomenon. Wall, in 1708, found sparks
produced by rubbing amber, and Hawkesbee observed the light and the
_snapping_, as he calls it, under various modifications. But the
electric spark from a living body, which, as {196} Priestley
says,[10\11] "makes a principal part of the diversion of gentlemen
and ladies who come to see experiments in electricity," was first
observed by Dufay and the Abbé Nollet. Nollet says[11\11] he "shall
never forget the surprise which the first electric spark ever drawn
from the human body excited, both in M. Dufay and in himself." The
drawing of a spark from the human body was practised in various
forms, one of which was familiarly known as the "electrical kiss."
Other exhibitions of electrical light were the electrical star,
electrical rain, and the like.

[Note 9\11: _Experimenta Magdeburgica_, 1672, lib. iv. cap. 15.]

[Note 10\11: P. p. 47.]

[Note 11\11: Priestley, p. 47. Nollet, _Leçons de Physique_, vol.
vi. p. 408.]

As electricians determined more exactly the conditions of electrical
action, they succeeded in rendering more intense those sudden
actions which the spark accompanies, and thus produced the electric
_shock_. This was especially done in the _Leyden phial_. This
apparatus received its name, while the discovery of its property was
attributed to Cunæus, a native of Leyden, who, in 1746, handling a
vessel containing water in communication with the electrical
machine, and happening thus to bring the inside and the outside into
connexion, received a sudden shock in his arms and breast. It
appears, however,[12\11] that a shock had been received under nearly
the same circumstances in 1746, by Von Kleist, a German prelate, at
Camin, in Pomerania. The strangeness of this occurrence, and the
suddenness of the blow, much exaggerated the estimate which men
formed of its force. Muschenbroek, after taking one shock, declared
he would not take a second for the kingdom of France; though Boze,
with a more magnanimous spirit, wished[13\11] that he might die by
such a stroke, and have the circumstances of the experiment recorded
in the Memoirs of the Academy. But we may easily imagine what a new
fame and interest this discovery gave to the subject of electricity.
It was repeated in all parts of the world, with various
modifications: and the shock was passed through a line of several
persons holding hands; Nollet, in the presence of the king of
France, sent it through a circle of 180 men of the guards, and along
a line of men and wires of 900 toises;[14\11] and experiments of the
same kind were made in England, principally under the direction of
Watson, on a scale so large as to excite the admiration of
Muschenbroek; who says, in a letter to Watson, "Magnificentissimis
tuis experimentis superasti conatus omnium." The result was, that
the transmission of electricity through a length of 12,000 feet was,
to sense, instantaneous. {197}

[Note 12\11: Fischer, v. 490.]

[Note 13\11: Fischer, p. 84.]

[Note 14\11: Ibid. v. 512.]

The essential circumstances of the electric shock were gradually
unravelled. Watson found that it did not increase in proportion
either to the contents of the phial or the size of the globe by
which the electricity was excited; that the outside coating of the
glass (which, in the first form of the experiment, was only a film
of water), and its contents, might be varied in different ways. To
Franklin is due the merit of clearly pointing out most of the
circumstances on which the efficacy of the Leyden phial depends. He
showed, in 1747,[15\11] that the inside of the bottle is electrized
positively, the outside negatively; and that the shock is produced
by the restoration of the equilibrium, when the outside and inside
are brought into communication suddenly. But in order to complete
this discovery, it remained to be shown that the electric matter was
collected entirely at the surface of the glass, and that the
opposite electricities on the two opposite sides of the glass were
accumulated by their mutual attraction. Monnier the younger
discovered that the electricity which bodies can receive, depends
upon their surface rather than their mass, and Franklin[16\11] soon
found that "the whole force of the bottle, and power of giving a
shock, is in the glass itself." This they proved by decanting the
water out of an electrized into another bottle, when it appeared
that the second bottle did not become electric, but the first
remained so. Thus it was found "that the non-electrics, in contact
with the glass, served only to unite the force of the several parts."

[Note 15\11: _Letters_, p. 13.]

[Note 16\11: _Letters_, iv. Sect. 16.]

So far as the effect of the coating of the Leyden phial is
concerned, this was satisfactory and complete: but Franklin was not
equally successful in tracing the action of the electric matter upon
itself, in virtue of which it is accumulated in the phial; indeed,
he appears to have ascribed the effect to some property of the
glass. The mode of describing this action varied, accordingly as two
electric _fluids_ were supposed (with Dufay,) or one, which was the
view taken by Franklin. On this latter supposition the parts of the
electric fluid repel each other, and the excess in one surface of
the glass expels the fluid from the other surface. This kind of
action, however, came into much clearer view in the experiments of
Canton, Wilcke, and Æpinus. It was principally manifested in the
attractions and repulsions which objects exert when they are in the
neighborhood of electrized bodies; or in the _electrical
atmosphere_, using the phraseology of the time. At present we say
that bodies are electrized _by induction_, when they are {198} thus
made electric by the electric attraction and repulsion of other
bodies. Canton's experiments were communicated to the Royal Society
in 1753, and show that the electricity on each body acts upon the
electricity of another body, at a distance, with a repulsive energy.
Wilcke, in like manner, showed that parts of non-electrics, plunged
in electric atmospheres, acquire an electricity opposite to that of
such atmospheres. And Æpinus devised a method of examining the
nature of the electricity at any part of the surface of a body, by
means of which he ascertained its distribution, and found that it
agreed with such a law of self-repulsion. His attempt to give
mathematical precision to this induction was one of the most
important steps towards electrical theory, and must be spoken of
shortly, in that point of view. But in the mean time we may observe,
that this doctrine was applied to the explanation of the Leyden jar;
and the explanation was confirmed by charging a plate of air, and
obtaining a shock from it, in a manner which the theory pointed out.

Before we proceed to the history of the theory, we must mention some
other of the laws of phenomena which were noticed, and which theory
was expected to explain. Among the most celebrated of these, were
the effect of sharp points in conductors, and the phenomena of
electricity in the atmosphere. The former of these circumstances was
one of the first which Franklin observed as remarkable. It was found
that the points of needles and the like throw off and draw off the
electric virtue; thus a bodkin, directed towards an electrized ball,
at six or eight inches' distance, destroyed its electric action. The
latter subject, involving the consideration of thunder and
lightning, and of many other meteorological phenomena, excited great
interest. The comparison of the electric spark to lightning had very
early been made; but it was only when the discharge had been
rendered more powerful in the Leyden jar, that the comparison of the
effects became very plausible. Franklin, about 1750, had offered a
few somewhat vague conjectures[17\11] respecting the existence of
electricity in the clouds; but it was not till Wilcke and Æpinus had
obtained clear notions of the effect of electric matter at a
distance, that the real condition of the clouds could be well
understood. In 1752, however,[18\11] D'Alibard, and other French
philosophers, were desirous of verifying Franklin's conjecture of
the analogy of thunder and electricity. This they did by erecting a
pointed iron rod, forty feet high, {199} at Marli: the rod was found
capable of giving out electrical sparks when a thunder-cloud passed
over the place. This was repeated in various parts of Europe, and
Franklin suggested that a communication with the clouds might be
formed by means of a kite. By these, and similar means, the
electricity of the atmosphere was studied by Canton in England,
Mazeas in France, Beccaria in Italy, and others elsewhere. These
essays soon led to a fatal accident, the death of Richman at
Petersburg, while he was, on Aug. 6th, 1753, observing the
electricity collected from an approaching thunder-cloud, by means of
a rod which he called an electrical gnomon: a globe of blue fire was
seen to leap from the rod to the head of the unfortunate professor,
who was thus struck dead.

[Note 17\11: Letter v.]

[Note 18\11: Franklin, p. 107.]

[2nd Ed.] [As an important application of the doctrines of
electricity, I may mention the contrivances employed to protect
ships from the effects of lightning. The use of conductors in such
cases is attended with peculiar difficulties. In 1780 the French
began to turn their attention to this subject, and Le Roi was sent
to Brest and the various sea-ports of France for that purpose.
Chains temporarily applied in the rigging had been previously
suggested, but he endeavored to place, he says, such conductors in
ships as might be fixed and durable. He devised certain long linked
rods, which led from a point in the mast-head along a part of the
rigging, or in divided stages along the masts, and were fixed to
plates of metal in the ship's sides communicating with the sea. But
these were either unable to stand the working of the rigging, or
otherwise inconvenient, and were finally abandoned.[19\11]

[Note 19\11: See Le Roi's Memoir in the _Hist. Acad. Sc._ for 1790.]

The conductor commonly used in the English Navy, till recently,
consisted of a flexible copper chain, tied, when occasion required,
to the mast-head, and reaching down into the sea; a contrivance
recommended by Dr. Watson in 1762. But notwithstanding this
precaution, the shipping suffered greatly from the effects of
lightning.

Mr. Snow Harris (now Sir William Snow Harris), whose electrical
labors are noticed above, proposed to the Admiralty, in 1820, a plan
which combined the conditions of ship-conductors, so desirable, yet
so difficult to secure:--namely, that they should be permanently
fixed, and sufficiently large, and yet should in no way interfere
with the motion of the rigging, or with the sliding masts. The
method which he proposed was to make the masts themselves conductors
of electricity, {200} by incorporating with them, in a peculiar way,
two laminæ of sheet-copper, uniting these with the metallic masses
in the hull by other laminæ, and giving the whole a free
communication with the sea. This method was tried experimentally,
both on models and to a large extent in the navy itself; and a
Commission appointed to examine the result reported themselves
highly satisfied with Mr. Harris's plan, and strongly recommended
that it should be fully carried out in the Navy.[20\11]]

[Note 20\11: See Mr. Snow Harris's paper in _Phil. Mag._ March, 1841.]

It is not here necessary to trace the study of atmospheric
electricity any further: and we must now endeavor to see how these
phenomena and laws of phenomena which we have related, were worked
up into consistent theories; for though many experimental
observations and measures were made after this time, they were
guided by the theory, and may be considered as having rather
discharged the office of confirming than of suggesting it.

We may observe also that we have now described the period of most
extensive activity and interest in electrical researches. These
naturally occurred while the general notions and laws of the
phenomena were becoming, and were not yet become, fixed and clear.
At such a period, a large and popular circle of spectators and
amateurs feel themselves nearly upon a level, in the value of their
trials and speculations, with more profound thinkers: at a later
period, when the subject is become a science, that is, a study in
which all must be left far behind who do not come to it with
disciplined, informed, and logical minds, the cultivators are far
more few, and the shout of applause less tumultuous and less loud.
We may add, too, that the experiments, which are the most striking
to the senses, lose much of their impressiveness with their novelty.
Electricity, to be now studied rightly, must be reasoned upon
mathematically; how slowly such a mode of study makes its way, we
shall see in the progress of the theory, which we must now proceed
to narrate.

[2nd Ed.] [A new mode of producing electricity has excited much
notice lately. In October, 1840, one of the workmen in attendance
upon a boiler belonging to the Newcastle and Durham Railway,
reported that the boiler was full of fire; the fact  being, that
when he placed his hand near it an electrical spark was given out.
This drew the attention of Mr. Armstrong and Mr. Pattinson, who made
the circumstance publicly known.[21\11] Mr. Armstrong pursued the
investigation {201} with great zeal, and after various conjectures
was able to announce[22\11] that the electricity was excited at the
point where the steam is subject to friction in its emission. He
found too that he could produce a like effect by the emission of
condensed air. Following out his views, he was able to construct,
for the Polytechnic Institution in London, a "Hydro-electric
Machine," of greater power than any electrical machine previously
made. Dr. Faraday took up the investigation as the subject of the
Eighteenth Series of his _Researches_, sent to the Royal Society,
Jan. 26, 1842; and in this he illustrated, with his usual command of
copious and luminous experiments, a like view;--that the electricity
is produced by the friction of the particles of the water carried
along by the **steam. And thus this is a new manifestation of that
electricity, which, to distinguish it from voltaic electricity, is
sometimes called _Friction Electricity_ or _Machine Electricity_.
Dr. Faraday has, however, in the course of this investigation,
brought to light several new electrical relations of bodies.]

[Note 21\11: _Phil. Mag._ Oct 1840.]

[Note 22\11: _Phil. Mag._ Jan. 1848, dated Dec. 9, 1841.]




CHAPTER II.

THE PROGRESS OF ELECTRICAL THEORY.


THE cause of electrical phenomena, and the mode of its operation,
were naturally at first spoken of in an indistinct and wavering
manner. It was called the electric _fire_, the electric _fluid_; its
effects were attributed to _virtues_, _effluvia_, _atmospheres_.
When men's mechanical ideas became somewhat more distinct, the
motions and tendencies to motion were ascribed to _currents_, in the
same manner as the cosmical motions had been in the Cartesian
system. This doctrine of currents was maintained by Nollet, who
ascribed all the phenomena of electrized bodies to the
contemporaneous afflux and efflux of electrical matter. It was an
important step towards sound theory, to get rid of this notion of
moving fluids, and to consider attraction and repulsion as statical
forces; and this appears to have been done by others about the same
time. Dufay[23\11] considered that he had proved the existence of
two electricities, the vitreous and the resinous, and conceived each
{202} of these to be a fluid which repelled its own parts and
attracted those of the other: this is, in fact, the outline of the
theory which recently has been considered as the best established;
but from various causes it was not at once, or at least not
generally adopted. The hypothesis of the excess and defect of a
single fluid is capable of being so treated as to give the same
results with the hypothesis of two opposite fluids and happened to
obtain the preference for some time. We have already seen that this
hypothesis, according to which electric phenomena arose from the
excess and defect of a generally diffused fluid, suggested itself to
Watson and Franklin about 1747. Watson found that when an electric
body was excited, the electricity was not created, but collected;
and Franklin held, that when the Leyden jar was charged, the
quantity of electricity was unaltered, though its distribution was
changed. Symmer[24\11] maintained the existence of two fluids; and
Cigna supplied the main defect which belonged to this tenet in the
way in which Dufay held it, by showing that the two opposite
electricities were usually produced at the same time. Still the
apparent simplicity of the hypothesis of one fluid procured it many
supporters. It was that which Franklin adopted, in his explanation
of the Leyden experiment; and though after the first conception of
an electrical charge as a disturbance of equilibrium, there was
nothing in the development or details of Franklin's views which
deserved to win for them any peculiar authority, his reputation, and
his skill as a writer, gave a considerable influence to his
opinions. Indeed, for a time he was considered, over a large part of
Europe, as the creator of the science, and the terms[25\11]
_Franklinism_, _Franklinist_, _Franklinian system_, occur in almost
every page of continental publications on the subject. Yet the
electrical phenomena to the knowledge of which Franklin added least,
those of induction, were those by which the progress of the theory
was most promoted. These, as we have already said, were at first
explained by the hypothesis of electrical atmospheres. Lord Mahon
wrote a treatise, in which this hypothesis was mathematically
treated; yet the hypothesis was very untenable, for it would not
account for the most obvious cases of induction, such as the Leyden
jar, except the atmosphere was supposed to penetrate glass.

[Note 23\11: _Ac. Par._ 1733, p. 467]

[Note 24\11: _Phil. Trans._ 1759.]

[Note 25\11: Priestley, p. 160.]

The phenomena of electricity by induction, when fairly considered by
a person of clear notions of the relations of space and force, were
seen to accommodate themselves very generally to the conception
{203} introduced by Dufay;[26\11] of two electricities each
repelling itself and attracting the other. If we suppose that there
is only one fluid, which repels itself and attracts all other
matter, we obtain, in many cases, the same general results as if we
suppose two fluids; thus, if an electrized body, overcharged with
the single fluid, act upon a ball, it drives the electric fluid in
the ball to the further side by its repulsion, and then attracts the
ball by attracting the matter of the ball more than it repels the
fluid which is upon the ball. If we suppose two fluids, the
positively electrized body draws the negative fluid to the nearer
side of the ball, repels the positive fluid to the opposite side,
and attracts the ball on the whole, because the attracted fluid is
nearer than that which is repelled. The verification of either of
these hypotheses, and the determination of their details, depended
necessarily upon experiment and calculation. It was under the
hypothesis of a single fluid that this trial was first properly
made. Æpinus of Petersburg published, in 1759, his _Tentamen Theoriæ
Electricitatis et Magnetismi_; in which he traces mathematically the
consequences of the hypothesis of an electric fluid, attracting all
other matter, but repelling itself; the law of force of this
repulsion and attraction he did not pretend to assign precisely,
confining himself to the supposition that the mutual force of the
particles increases as the distance decreases. But it was found,
that in order to make this theory tenable, an additional supposition
was required, namely, that the particles of bodies repel each other
as much as they attract the electric fluid.[27\11] For if two
bodies, A and B, be in their natural electrical condition, they
neither attract nor repel each other. Now, in this case, the fluid
in A attracts the matter in B and repels the fluid in B with equal
energy, and thus no tendency to motion results from the fluid in A;
and if we further suppose that the _matter_ in A attracts the fluid
in B and _repels the matter_ in B with equal energy, we have the
resulting mutual inactivity of the two bodies explained; but without
the latter supposition, there would be a mutual attraction: or we
may put the truth more simply thus; two negatively electrized bodies
repel each other; if negative electrization were merely the
abstraction of the fluid which is the repulsive element, this result
could not follow except there were a repulsion in the bodies
themselves, independent of the fluid. And thus Æpinus found himself
compelled to assume this mutual repulsion of material particles; he
had, in fact, the {204} alternative of this supposition, or that of
two fluids, to choose between, for the mathematical results of both
hypotheses are the same. Wilcke, a Swede, who had at first asserted
and worked out the Æpinian theory in its original form, afterwards
inclined to the opinion of Symmer; and Coulomb, when, at a later
period, he confirmed the theory by his experiments and determined
the law of force, did not hesitate to prefer[28\11] the theory of
two fluids, "because," he says, "it appears to me contradictory to
admit at the same time, in the particles of bodies, an attractive
force in the inverse ratio of the squares of the distances, which is
demonstrated by universal gravitation, and a repulsive force in the
same inverse ratio of the squares of the distances; a force which
would necessarily be infinitely great relatively to the action of
gravitation." We may add, that by forcing us upon this doctrine of
the universal repulsion of matter, the theory of a single fluid
seems quite to lose that superiority in the way of simplicity which
had originally been its principal recommendation.

[Note 26\11: _Mém. A. P._ 1733, p. 467.]

[Note 27\11: Robison, vol. iv. p. 18.]

[Note 28\11: _Mém. Ac. P._ 1788, p. 671.]

The mathematical results of the supposition of Æpinus, which are, as
Coulomb observes,[29\11] the same as of that of the two fluids, were
traced by the author himself in the work referred to, and shown to
agree, in a great number of cases, with the observed facts of
electrical induction, attraction, and repulsion. Apparently this
work did not make its way very rapidly through Europe; for in 1771,
Henry Cavendish stated[30\11] the same hypothesis in a paper read
before the Royal Society; which he prefaces by saying, "Since I
first wrote the following paper, I find that this way of accounting
for the phenomena of electricity is not new. Æpinus, in his
_Tentamen Theoriæ Electricitatis et Magnetismi_, has made use of the
same, or nearly the same hypothesis that I have; and the conclusions
he draws from it agree nearly with mine as far as he goes."

[Note 29\11: _Ac. P._ 1788, p. 672.]

[Note 30\11: _Phil. Trans._ 1771, vol. lxi.]

The confirmation of the theory was, of course, to be found in the
agreement of its results with experiment; and in particular, in the
facts of electrical induction, attraction, and repulsion, which
suggested the theory. Æpinus showed that such a confirmation
appeared in a number of the most obvious cases; and to these,
Cavendish added others, which, though not obvious, were of such a
nature that the calculations, in general difficult or impossible,
could in these instances be easily performed; as, for example, cases
in which there are plates or globes at the two extremities of a long
wire. In all these cases of {205} electrical action the theory was
justified. But in order to give it full confirmation, it was to be
considered whether any other facts, not immediately assumed in the
foundation of the theory, were explained by it; a circumstance
which, as we have seen, gave the final stamp of truth to the
theories of astronomy and optics. Now we appear to have such
confirmation, in the effect of points, and in the phenomena of the
electrical discharge. The theory of neither of these was fully
understood by Cavendish, but he made an approach to the true view of
them. If one part of a conducting body be a sphere of small radius,
the electric fluid upon the surface of this sphere will, it appears
by calculation, be more dense, and tend to escape more
energetically, in proportion as the radius of the sphere is smaller;
and, therefore, if we consider a point as part of the surface of a
sphere of imperceptible radius, it follows from the theory that the
effort of the fluid to escape at that place will be enormous; so
that it may easily be supposed to overcome the resisting causes. And
the discharge may be explained in nearly the same manner; for when a
conductor is brought nearer and nearer to an electrized body, the
opposite electricity is more and more accumulated by attraction on
the side next to the electrized body; its tension becomes greater by
the increase of its quantity and the diminution of the distance, and
at last it is too strong to be contained, and leaps out in the form
of a spark.

The light, sound, and mechanical effects produced by the electric
discharge, made the electric _fluid_ to be not merely considered as
a mathematical hypothesis, useful for reducing phenomena to formulæ
(as for a long time the magnetic fluid was), but caused it to be at
once and universally accepted as a physical reality, of which we
learn the existence by the common use of the senses, and of which
measures and calculations are only wanted to teach us the laws.

The applications of the theory of electricity which I have
principally considered above, are those which belong to conductors,
in which the electric fluid is perfectly moveable, and can take that
distribution which the forces require. In non-conducting or electric
bodies, the conditions to which the fluid is subject are less easy
to determine; but by supposing that the fluid moves with great
difficulty among the particles of such bodies,--that nevertheless it
may be dislodged and accumulated in parts of the surface of such
bodies, by friction and other modes of excitement; and that the
earth is an inexhaustible reservoir of electric matter,--the
principal facts of excitation and the like receive a tolerably
satisfactory explanation. {206}

The theory of Æpinus, however, still required to have the law of
action of the particles of the fluid determined. If we were to call
to mind how momentous an event in physical astronomy was the
determination of the law of the cosmical forces, the inverse square
of the distance, and were to suppose the importance and difficulty
of the analogous step in this case to be of the same kind, this
would be to mistake the condition of science at that time. The
leading idea, the conception of the possibility of explaining
natural phenomena by means of the action of forces, on rigorously
mechanical principles, had already been promulgated by Newton, and
was, from the first, seen to be peculiarly applicable to electrical
phenomena; so that the very material step of clearly proposing the
problem, often more important than the solution of it, had already
been made. Moreover the confirmation of the truth of the assumed
cause in the astronomical case depended on taking the right law; but
the electrical theory could be confirmed, in a general manner at
least, without this restriction. Still it was an important discovery
that the law of the inverse square prevailed in these as well as in
cosmical attractions.

It was impossible not to conjecture beforehand that it would be so.
Cavendish had professed in his calculations not to take the exponent
of the inverse power, on which the force depended, to be strictly 2,
but to leave it indeterminate between 1 and 3; but in his
applications of his results, he obviously inclines to the assumption
that it is 2. Experimenters tried to establish this in various ways.
Robison,[31\11] in 1769, had already proved that the law of force is
very nearly or exactly the inverse square; and Meyer[32\11] had
discovered, but not published, the same result. The clear and
satisfactory establishment of this truth is due to Coulomb, and was
one of the first steps in his important series of researches on this
subject. In his first paper[33\11] in the _Memoirs_ of the Academy
for 1785, he proves this law for small globes; in his second Memoir
he shows it to be true for globes one and two feet in diameter. His
invention of the _torsion-balance_, which measures very small forces
with great certainty and exactness, enabled him to set this question
at rest for ever.

[Note 31\11: _Works_, iv. p. 68.]

[Note 32\11: _Biog. Univ._ art. _Coulumb_, by Biot.]

[Note 33\11: _Mém. A. P._ 1785, pp. 569, 578.]

The law of force being determined for the particles of the electric
fluid, it now came to be the business of the experimenter and the
{207} mathematician to compare the results of the theory in detail
with those of experimental measures. Coulomb undertook both portions
of the task. He examined the electricity of portions of bodies by
means of a little disk (his _tangent plane_) which he applied to
them and then removed, and which thus acted as a sort of electric
_taster_. His numerical results (the intensity being still measured
by the torsion-balance) are the fundamental facts of the theory of
the electrical fluid. Without entering into detail, we may observe
that he found the electricity to be entirely collected at the
surface of conductors (which Beccaria had before shown to be the
case), and that he examined and recorded the electric intensity at
the surface of globes, cylinders, and other conducting bodies,
placed within each other's influence in various ways.

The mathematical calculation of the distribution of two fluids, all
the particles of which attract and repel each other according to the
above law, was a problem of no ordinary difficulty; as may easily be
imagined, when it is recollected that the attraction and repulsion
determine the distribution, and the distribution reciprocally
determines the attraction and repulsion. The problem was of the same
nature as that of the figure of the earth; and its rigorous solution
was beyond the powers of the analysis of Coulomb's time. He obtained,
however, approximate solutions with much ingenuity; for instance, in a
case in which it was obvious that the electric fluid would be most
accumulated at and near the equator of a certain sphere, he calculated
the action of the sphere on two suppositions: first, that the fluid
was all collected precisely at the equator; and next, that it was
uniformly diffused over the surface; and he then assumed the actual
case to be intermediate between these two. By such artifices he was
able to show that the results of his experiments and of his
calculations gave an agreement sufficiently near to entitle him to
consider the theory as established on a solid basis.

Thus, at this period, mathematics was behind experiment; and a problem
was proposed, in which theoretical numerical results were wanted for
comparison with observation, but could not be accurately obtained; as
was the case in astronomy also, till the time of the approximate
solution of the Problem of Three Bodies, and the consequent formation
of the Tables of the Moon and Planets on the theory of universal
gravitation. After some time, electrical theory was relieved from this
reproach, mainly in consequence of the progress which astronomy had
occasioned in pure mathematics. About 1801, {208} there appeared in
the _Bulletin des Sciences_,[34\11] an exact solution of the problem
of the distribution of electric fluid on a spheroid, obtained by M.
Biot, by the application of the peculiar methods which Laplace had
invented for the problem of the figure of the planets. And in 1811, M.
Poisson applied Laplace's artifices to the case of two spheres acting
upon one another in contact, a case to which many of Coulomb's
experiments were referrible; and the agreement of the results of
theory and observation, thus extricated from Coulomb's numbers,
obtained above forty years previously, was very striking and
convincing.[35\11] It followed also from Poisson's calculations, that
when two electrized spheres are brought near each other, the
accumulation of the opposite electricities on their nearest points
increases without limit as the spheres approach to contact; so that
before the contact takes place, the external resistance will be
overcome, and a _spark_ will pass.

[Note 34\11: No. li.]

[Note 35\11: _Mém. A. P._ 1811.]

Though the relations of non-conductors to electricity, and various
other circumstances, leave many facts imperfectly explained by the
theory, yet we may venture to say that, as a theory which gives the
laws of the phenomena, and which determines the distribution of
those elementary forces, on the surface of electrized bodies, from
which elementary forces (whether arising from the presence of a
fluid or not,) the total effects result, the doctrine of Dufay and
Coulomb, as developed in the analysis of Poisson, is securely and
permanently established. This part of the subject has been called
_statical electricity_. In the establishment of the theory of this
branch of science, we must, I conceive, allow to Dufay more merit
than is generally ascribed to him; since he saw clearly, and
enunciated in a manner which showed that he duly appreciated their
capital character, the two chief principles,--the conditions of
electrical attraction and repulsion, and the apparent existence of
two kinds of electricity. His views of attraction are, indeed,
partly expressed in terms of the Cartesian hypothesis of vortices,
then prevalent in France; but, at the time when he wrote, these
forms of speech indicated scarcely anything besides the power of
attraction. Franklin's real merit as a discoverer was, that he was
one of the first who distinctly conceived the electrical _charge_ as
a derangement of equilibrium. The great fame which, in his day, he
enjoyed, arose from the clearness and spirit with which he narrated
his discoveries; from his dealing with electricity in the imposing
form of thunder and lightning; and partly, perhaps, from his
character as an {209} American and a politician; for he was already,
in 1736, engaged in public affairs as clerk to the General Assembly
of Pennsylvania, though it was not till a later period of his life
that his admirers had the occasion of saying of him
  Eripuit cœlis fulmen sceptrumque tyrannis;
  Born to control all lawless force, all fierce and baleful sway,
  The thunder's bolt, the tyrant's rod, alike he wrenched away.

Æpinus and Coulomb were two of the most eminent physical
philosophers of the last century, and labored in the way peculiarly
required by that generation; whose office it was to examine the
results, in particular subjects, of the general conception of
attraction and repulsion, as introduced by Newton. The reasonings of
the Newtonian period had, in some measure, anticipated all possible
theories resembling the electrical doctrine of Æpinus and Coulomb;
and, on that account, this doctrine could not be introduced and
confirmed in a sudden and striking manner, so as to make a great
epoch. Accordingly, Dufay, Symmer, Watson, Franklin, Æpinus and
Coulomb, have all a share in the process of induction. With
reference to these founders of the theory of electricity, Poisson
holds the same place which Laplace holds with reference to Newton.

The reception of the Coulombian theory (so we most call it, for the
Æpinian theory implies one fluid only,) has hitherto not been so
general as might have been reasonably expected from its very
beautiful accordance with the facts which it contemplates. This has
partly been owing to the extreme abstruseness of the mathematical
reasoning which it employs, and which put it out of the reach of
most experimenters and writers of works of general circulation. The
theory of Æpinus was explained by Robison in the _Encyclopædia
Britannica_; the analysis of Poisson has recently been presented to
the public in the _Encyclopædia Metropolitana_, but is of a kind not
easily mastered even by most mathematicians. On these accounts
probably it is, that in English compilations of science, we find,
even to this day, the two theories of one and of two fluids stated
as if they were nearly on a par in respect of their experimental
evidence. Still we may say that the Coulombian theory is probably
assented to by all who have examined it, at least as giving the laws
of phenomena; and I have not heard of any denial of it from such a
quarter, or of any attempt to show it to be erroneous by detailed
and measured experiments. Mr. Snow Harris {210} has recently[36\11]
described some important experiments and measures; but his apparatus
was of such a kind that the comparison of the results with the
Coulombian theory was not easy; and indeed the mathematical problems
which Mr. Harris's combinations offered, require another Poisson for
their solution. Still the more obvious results are such as agree
with the theory, even in the cases in which their author considered
them to be inexplicable. For example, he found that by doubling the
quantity of electricity of a conductor, it attracted a body with
four times the force; but the body not being insulated, would have
its electricity also doubled by induction, and thus the fact was
what the theory required.

[Note 36\11: _Phil. Trans._ 1834, p. 2.]

Though it is thus highly probable that the Coulombian theory of
electricity (or the Æpinian, which is mathematically equivalent)
will stand as a true representation of the law of the elementary
actions, we must yet allow that it has not received that complete
evidence, by means of experiments and calculations added to those of
its founders, which the precedents of other permanent sciences have
led us to look for. The experiments of Coulomb, which he used in the
establishment of the theory, were not very numerous, and they were
limited to a peculiar form of bodies, namely spheres. In order to
form the proper _sequel_ to the promulgation of this theory, to give
a full _confirmation_, and to ensure its general _reception_, we
ought to have experiments more numerous and more varied (such as
those of Mr. Harris are) shown to agree in all respects with results
calculated from the theory. This would, as we have said, be a task
of labor and difficulty; but the person who shall execute it will
deserve to be considered as one of the real founders of the true
doctrine of electricity. To show that the coincidence between theory
and observation, which has already been proved for spherical
conductors, obtains also for bodies of other forms, will be a step
in electricity analogous to what was done in astronomy, when it was
shown that the law of gravitation applied to comets as well as to
planets.

But although we consider the views of Æpinus or Coulomb in a very
high degree probable as a _formal theory_, the question is very
different when we come to examine them as a _physical theory_;--that
is, when we inquire whether there really is a material electric
fluid or fluids.

_Question of One or Two Fluids._--In the first place as to the
question whether the fluids are one or two;--Coulomb's introduction
of {211} the hypothesis of two fluids has been spoken of as a reform
of the theory of Æpinus; it would probably have been more safe to
have called his labors an advance in the calculation, and in the
comparison of hypothesis with experiment, than to have used language
which implied that the question, between the rival hypotheses of one
or two fluids, could be treated as settled. For, in reality, if we
assume, as Æpinus does, the mutual repulsion of all the particles of
matter, in addition to the repulsion of the particles of the
electric fluid for one another and their attraction for the
particles of matter, the one fluid of Æpinus will give exactly the
same results as the two fluids of Coulomb. The mathematical formulæ
of Coulomb and of Poisson express the conditions of the one case as
well as of the other; the interpretation only being somewhat
different. The place of the forces of the resinous fluid is supplied
by the excess of the forces ascribed to the matter above the forces
of the fluid, in the parts where the electric fluid is deficient.

The obvious argument against this hypothesis is, that we ascribe to
the particles of matter a mutual repulsion, in addition to the
mutual attraction of universal gravitation, and that this appears
incongruous. Accordingly, Æpinus says, that when he was first driven
to this proposition it horrified him.[37\11] But we may answer it in
this way very satisfactorily:--If we suppose the mutual repulsion of
matter to be somewhat less than the mutual attraction of matter and
electric fluid, it will follow, as a consequence of the hypothesis,
that besides all obvious electrical action, the particles of matter
would attract each other with forces varying inversely as the square
of the distance. Thus gravitation itself becomes an electrical
phenomenon, arising from the residual excess of attraction over
repulsion; and the fact which is urged against the hypothesis
becomes a confirmation of it. By this consideration the prerogative
of simplicity passes over to the side of the hypothesis of one
fluid; and the rival view appears to lose at least all its
superiority.

[Note 37\11: Neque diffiteor cum ipsa se mihi offerret . . . . me ad
ipsam quodammodo  exhorruisse. _Tentamen Theor. Elect._ p. 39.]

Very recently, M. Mosotti[38\11] has calculated the results of the
Æpinian theory in a far more complete manner than had previously
been performed; using Laplace's coefficients, as Poisson had done
for the {212} Coulombian theory. He finds that, from the supposition
of a fluid and of particles of matter exercising such forces as that
theory assumes (with the very allowable additional supposition that
the particles are small compared with their distances), it follows
that the particles would exert a force, repulsive at the smallest
distances, a little further on vanishing, afterwards attractive, and
at all sensible distances attracting in proportion to the inverse
square of the distance. Thus there would be a position of stable
equilibrium for the particles at a very small distance from each
other, which may be, M. Mosotti suggests, that equilibrium on which
their physical structure depends. According to this view, the
resistance of bodies to compression and to extension, as well as the
phenomena of statical electricity and the mutual gravitation of
matter, are accounted for by the same hypothesis of a single fluid
or ether. A theory which offers a prospect of such a generalization
is worth attention; but a very clear and comprehensive view of the
doctrines of several sciences is requisite to prepare us to estimate
its value and probable success.

[Note 38\11: _Sur les Forces qui régissent la Constitution
Intérieure des Corps._ Turin. 1836.]

_Question of the Material Reality of the Electric Fluid._--At first
sight the beautiful accordance of the experiments with calculations
founded upon the attractions and repulsions of the two hypothetical
fluids, persuade us that the hypotheses must be the real state of
things. But we have already learned that we must not trust to such
evidence too readily. It is a curious instance of the mutual
influence of the histories of two provinces of science, but I think
it will be allowed to be just, to say that the discovery of the
polarization of heat has done much to shake the theory of the
electric fluids as a physical reality. For the doctrine of a
material caloric appeared to be proved (from the laws of conduction
and radiation) by the same kind of mathematical evidence (the
agreement of laws respecting the elementary actions with those of
fluids), which we have for the doctrine of material electricity. Yet
we now seem to see that heat cannot be matter, since its rays have
_sides_, in a manner in which a stream of particles of matter cannot
have sides without inadmissible hypotheses. We see, then, that it
will not be contrary to precedent, if our electrical theory,
representing with perfect accuracy the _laws_ of the actions, in all
their forms, simple and complex, should yet be fallacious as a view
of the _cause_ of the actions.

Any true view of electricity must include, or at least be consistent
with, the other classes of the phenomena, as well as this statical
electrical action; such as the conditions of excitation and
retention of {213} electricity; to which we may add, the connexion
of electricity with magnetism and with chemistry;--a vast field, as
yet dimly seen. Now, even with regard to the simplest of these
questions, the cause of the retention of electricity at the surface
of bodies, it appears to be impossible to maintain Coulomb's
opinion, that this is effected by the resistance of air to the
passage of electricity. The other questions are such as Coulomb did
not attempt to touch; they refer, indeed, principally to laws not
suspected at his time. How wide and profound a theory must be which
deals worthily with these, we shall obtain some indications in the
succeeding part of our history.

But it may be said on the other side, that we have the evidence of
our senses for the reality of an electric fluid;--we see it in the
spark; we hear it in the explosion; we feel it in the shock; and it
produces the effects of mechanical violence, piercing and tearing
the bodies through which it passes. And those who are disposed to
assert a real fluid on such grounds, may appear to be justified in
doing so, by one of Newton's "Rules of Philosophizing," in which he
directs the philosopher to assume, in his theories, "causes which
are true." The usual interpretation of a "vera causa," has been,
that it implies causes which, independently of theoretical
calculations, are known to exist by their mechanical effects; as
gravity was familiarly known to exist on the earth, before it was
extended to the heavens. The electric fluid might seem to be such a
_vera causa_.

To this I should venture to reply, that this reasoning shows how
delusive the Newtonian rule, so interpreted, may be. For a moment's
consideration will satisfy us that none of the circumstances, above
adduced, can really prove material currents, rather than vibrations,
or other modes of agency. The spark and shock are quite insufficient
to supply such a proof. Sound is vibrations,--light is vibrations;
vibrations may affect our nerves, and may rend a body, as when
glasses are broken by sounds. Therefore all these supposed
indications of the reality of the electric fluid are utterly
fallacious. In truth, this mode of applying Newton's rule consists
in elevating our first rude and unscientific impressions into a
supremacy over the results of calculation, generalization, and
systematic induction.[**39\11] {214}

[Note **39\11: On the subject of this Newtonian Rule of
Philosophizing, see further _Phil. Ind. Sc._ B. xii. c. 13. I have
given an account of the history and evidence of the Theory of
Electricity in the _Reports of the British Association_ for 1835.
I may seem there to have spoken more favorably of the Theory as a
Physical Theory than I have done here. This difference is
principally due to a consideration of the present aspect of the
Theory of Heat.]

Thus our conclusion with regard to this subject is, that if we wish
to form a stable physical theory of electricity, we must take into
account not only the laws of statical electricity, which we have
been chiefly considering, but the laws of other kinds of agency,
different from the electric, yet connected with it. For the
electricity of which we have hitherto spoken, and which is commonly
excited by friction, is identical with galvanic action, which is a
result of chemical combinations, and belongs to chemical philosophy.
The connexion of these different kinds of electricity with one
another leads us into a new domain; but we must, in the first place,
consider their mechanical laws. We now proceed to another branch of
the same subject, Magnetism.



{{215}}
BOOK XII.


_MECHANICO-CHEMICAL SCIENCES._

(CONTINUED.)


HISTORY OF MAGNETISM.


  EFFICE, ut interea fera munera militiaï
  Per maria ac terras omneis sopita quiescant.
  Nam tu sola potes tranquilla pace juvare
  Mortales; quoniam belli fera munera Mavors
  Armipotens regit, in gremium qui sæpe tuum se
  Rejicit, æterno devictus vulnere amoris;
  Atque ita suspiciens tereti cervice reposta,
  Pascit amore avidos inhians in te, Dea, visus,
  Eque tuo pendet resupini spiritus ore.
  Hunc tu, Diva, tuo recubantem corpore sancto
  Circumfusa super, suaves ex ore loquelas
  Funde, petens placidam Romanis, incluta, pacem.
          LUCRET. i. 31.

  O charming Goddess, whose mysterious sway
  The unseen hosts of earth and sky obey;
  To whom, though cold and hard to all besides,
  The Iron God by strong affection glides.
  Flings himself eager to thy close embrace,
  And bends his head to gaze upon thy face;
  Do thou, what time thy fondling arms are thrown
  Around his form, and he is all thy own,
  Do thou, thy Rome to save, thy power to prove,
  Beg him to grant a boon for thy dear love;
  Beg him no more in battle-fields to deal.
  Or crush the nations with his mailed heel.
  But, touched and softened by a worthy flame,
  Quit sword and spear, and seek a better fame.
  Bid him to make all war and slaughter cease,
  And ply his genuine task in arts of peace;
  And by thee guided o'er the trackless surge,
  Bear wealth and joy to ocean's farthest verge.



{{217}}
CHAPTER I.

DISCOVERY OF LAWS OF MAGNETIC PHENOMENA.


THE history of Magnetism is in a great degree similar to that of
Electricity, and many of the same persons were employed in the two
trains of research. The general fact, that the magnet attracts iron,
was nearly all that was known to the ancients, and is frequently
mentioned and referred to; for instance, by Pliny, who wonders and
declaims concerning it, in his usual exaggerated style.[1\12] The
writers of the Stationary Period, in this subject as in others,
employed themselves in collecting and adorning a number of
extravagant tales, which the slightest reference to experiment would
have disproved; as, for example, that a magnet, when it has lost its
virtue, has it restored by goat's blood. Gilbert, whose work _De
Magnete_ we have already mentioned, speaks with becoming indignation
and pity of this bookish folly, and repeatedly asserts the paramount
value of experiments. He himself, no doubt, acted up to his own
precepts; for his work contains all the fundamental facts of the
science, so fully examined indeed, that even at this day we have
little to add to them. Thus, in his first Book, the subjects of the
third, fourth, and fifth Chapters are,--that the magnet has
poles,--that we may call these poles the north and the south
pole,--that in two magnets the north pole of each attracts the south
pole and repels the north pole of the other. This is, indeed, the
cardinal fact on which our generalizations rest; and the reader will
perceive at once its resemblance to the leading phenomena of
statical electricity.

[Note 1\12: _Hist. Nat._ lib. xxxvi. c. 25.]

But the doctrines of magnetism, like those of heat, have an
additional claim on our notice from the manner in which they are
exemplified in the globe of the earth. The subject of _terrestrial
magnetism_ forms a very important addition to the general facts of
magnetic attraction and repulsion. The property of the magnet by
which it directs its poles exactly or nearly north and south, when
once discovered, was of immense importance to the mariner. It does
not {218} appear easy to trace with certainty the period of this
discovery. Passing over certain legends of the Chinese, as at any
rate not bearing upon the progress of European science,[2\12] the
earliest notice of this property appears to be contained in the Poem
of Guyot de Provence, who describes the needle as being magnetized,
and then placed in or on a straw, (floating on water, as I presume:)
  Puis se torne la pointe toute
  Contre l'estoile sans doute;
that is, it turns towards the pole-star. This account would make the
knowledge of this property in Europe anterior to 1200. It was
afterwards found[3\12] that the needle does not point exactly
towards the north. Gilbert was aware of this deviation, which he
calls the _variation_, and also, that it is different in different
places.[4\12] He maintained on theoretical principles also,[5\12]
that at the same place the variation is constant; probably in his
time there were not any recorded observations by which the truth of
this assertion could be tested; it was afterwards found to be false.
The alteration of the variation in proceeding from one place to
another was, it will be recollected, one of the circumstances which
most alarmed the companions of Columbus in 1492. Gilbert says,[6\12]
"Other learned men have, in long navigations, observed the
differences of magnetic variations, as Thomas Hariot, Robert Hues,
Edward Wright, Abraham Kendall, all Englishmen: others have invented
magnetic instruments and convenient modes of observation, such as
are requisite for those who take long voyages, as William Borough in
his Book concerning the variation of the compass, William Barlo in
his supplement, William Norman in his _New Attractive_. This is that
Robert Norman (a good seaman and an ingenious artificer,) who first
discovered the _dip_ of magnetic iron." This important discovery was
made[7\12] in 1576. From the time when the difference of the
variation of the compass in different places became known, it was
important to mariners to register the variation in all parts of the
world. Halley was appointed to the command of a ship in the Royal
Navy by the Government of William and Mary, with orders "to seek by
observation the discovery of the rule for the variation of the
compass." He published Magnetic Charts, which {219} have been since
corrected and improved by various persons. The most recent are those
of Mr. Yates in 1817, and of M. Hansteen. The dip, as well as the
variation, was found to be different in different places. M.
Humboldt, in the course of his travels, collected many such
observations. And both the observations of variation and of dip
seemed to indicate that the earth, as to its effect on the magnetic
needle, may, approximately at least, be considered as a magnet, the
poles of which are not far removed from the earth's poles of
rotation. Thus we have a _magnetic equator_, in which the needle has
no dip, and which does not deviate far from the earth's equator;
although, from the best observations, it appears to be by no means a
regular circle. And the phenomena, both of the dip and of the
variation, in high northern latitudes, appear to indicate the
existence of a pole below the surface of the earth to the north of
Hudson's Bay. In his second remarkable expedition into those
regions, Captain Ross is supposed to have reached the place of this
pole; the dipping-needle there pointing vertically downwards, and
the variation-compass turning towards this point in the adjacent
regions. We shall hereafter have to consider the more complete and
connected views which have been taken of terrestrial magnetism.

[Note 2\12: _Enc. Met._ art. _Magnetism_, p. 736.]

[Note 3\12: Before 1269. _Enc. Met._ p. 737.]

[Note 4\12: _De Magnete_, lib. iv. c. 1.]

[Note 5\12: c. 3.]

[Note 6\12: Lib. i. c. 1.]

[Note 7\12: _Enc. Met._ p. 738.]

In 1633, Gellibrand discovered that the variation is not constant,
as Gilbert imagined, but that at London it had diminished from
eleven degrees east in 1580, to four degrees in 1633. Since that
time the variation has become more and more westerly; it is now
about twenty-five degrees west, and the needle is supposed to have
begun to travel eastward again.

The next important fact which appeared with respect to terrestrial
magnetism was, that the position of the needle is subject to a small
_diurnal_ variation: this was discovered in 1722, by Graham, a
philosophical instrument-maker, of London. The daily variation was
established by one thousand observations of Graham, and confirmed by
four thousand more made by Canton, and is now considered to be out
of dispute. It appeared also, by Canton's researches, that the
diurnal variation undergoes an annual inequality, being nearly a
quarter of a degree in June and July, and only half that quantity in
December and January.

Having thus noticed the principal facts which belong to terrestrial
magnetism, we must return to the consideration of those phenomena
which gradually led to a consistent magnetic theory. Gilbert
observed that both smelted iron and hammered iron have the magnetic
virtue, {220} though in a weaker degree than the magnet
itself,[8\12] and he asserted distinctly that the magnet is merely
an ore of iron, (lib. i. c. 16, Quod magnes et vena ferri idem
sunt.) He also noted the increased energy which magnets acquire by
being _armed_; that is, fitted with a cap of polished iron at each
pole.[9\12] But we do not find till a later period any notice of the
distinction which exists between the magnetical properties of soft
iron and of hard steel;--the latter being susceptible of being
formed into _artificial magnets_, with permanent poles; while soft
iron is only _passively magnetic_, receiving a temporary polarity
from the action of a magnet near it, but losing this property when
the magnet is removed. About the middle of the last century, various
methods were devised of making artificial magnets, which exceeded in
power all magnetic bodies previously known.

[Note 8\12: Lib. i. c. 9-13.]

[Note 9\12: Lib. ii. c. 17.]

The remaining experimental researches had so close an historical
connexion with the theory, that they will be best considered along
with it, and to that, therefore, we now proceed.




CHAPTER II.

PROGRESS OF MAGNETIC THEORY.


THEORY OF MAGNETIC ACTION.--The assumption of a fluid, as a mode of
explaining the phenomena, was far less obvious in magnetic than in
electric cases, yet it was soon arrived at. After the usual
philosophy of the middle ages, the "forms" of Aquinas, the "efflux"
of Cusanus, the "vapors" of Costæus, and the like, which are
recorded by Gilbert,[10\12] we have his own theory, which he also
expresses by ascribing the effects to a "formal efficiency;"--a
"_form_ of primary globes; the proper entity and existence of their
homogeneous parts, which we may call a primary and radical and
astral _form_;"--of which forms there is one in the sun, one in the
moon, one in the earth, the latter being the magnetic virtue.

[Note 10\12: Gilb. lib. ii. c. 3, 4]

Without attempting to analyse the precise import of these expressions,
we may proceed to Descartes's explanation of magnetic phenomena. The
mode in which he presents this subject[11\12] is, perhaps, the {221}
most persuasive of his physical attempts. If a magnet be placed among
iron filings, these arrange themselves in curved lines, which proceed
from one pole of the magnet to the other. It was not difficult to
conceive these to be the traces of currents of ethereal matter which
circulate through the magnet, and which are thus rendered sensible
even to the eye. When phenomena could not be explained by means of one
vortex, several were introduced. Three Memoirs on Magnetism, written
on such principles, had the prize adjudged[12\12] by the French
Academy of Sciences in 1746.

[Note 11\12: _Prin. Phil._ pars c. iv. 146.]

[Note 12\12: Coulomb, 1789, p. 482.]

But the Cartesian philosophy gradually declined; and it was not
difficult to show that the _magnetic curves_, as well as other
phenomena, would, in fact, result from the attraction and repulsion
of two poles. The analogy of magnetism with electricity was so
strong and clear, that similar theories were naturally proposed for
the two sets of facts; the distinction of bodies into conductors and
electrics in the one case, corresponding to the distinction of soft
and hard steel, in their relations to magnetism. Æpinus published a
theory of magnetism and electricity at the same time (1759); and the
former theory, like the latter, explained the phenomena of the
opposite poles as results of the excess and defect of a magnetic
"fluid," which was dislodged and accumulated in the ends of the
body, by the repulsion of its own particles, and by the attraction
of iron or steel, as in the case of induced electricity. The Æpinian
theory of magnetism, as of electricity, was recast by Coulomb, and
presented in a new shape, with two fluids instead of one. But before
this theory was reduced to calculation, it was obviously desirable,
in the first place, to determine the law of force.

In magnetic, as in electric action, the determination of the law of
attraction of the particles was attended at first with some
difficulty, because the action which a finite magnet exerts is a
compound result of the attractions and repulsions of many points.
Newton had imagined the attractive force of magnetism to be
inversely as the cube of the distance; but Mayer in 1760, and
Lambert a few years later, asserted the law to be, in this as in
other forces, the inverse square. Coulomb has the merit of having
first clearly confirmed this law, by the use of his
torsion-balance.[13\12] He established, at the same time, other very
important facts, for instance, "that the directive magnetic force,
which the earth exerts upon a needle, is a constant quantity,
parallel {222} to the magnetic meridian, and passing through the
same point of the needle whatever be its position." This was the
more important, because it was necessary, in the first place, to
allow for the effect of the terrestrial force, before the mutual
action of the magnets could be extricated from the phenomena.[14\12]
Coulomb then proceeded to correct the theory of magnetism.

[Note 13\12: _Mem. A. P._ 1784, 2d Mem. p. 593.]

[Note 14\12: p. 603.]

Coulomb's reform of the Æpinian theory, in the case of magnetism, as
in that of electricity, substituted two fluids (an _austral_ and a
_boreal_ fluid,) for the single fluid; and in this way removed the
necessity under which Æpinus found himself, of supposing all the
particles of iron and steel and other magnetic bodies to have a
peculiar repulsion for each other, exactly equal to their attraction
for the magnetic fluid. But in the case of magnetism, another
modification was necessary. It was impossible to suppose here, as in
the electrical phenomena, that one of the fluids was accumulated on
one extremity of a body, and the other fluid on the other extremity;
for though this might appear, at first sight, to be the case in a
magnetic needle, it was found that when the needle was cut into two
halves, the half in which the austral fluid had seemed to
predominate, acquired immediately a boreal pole opposite to its
austral pole, and a similar effect followed in the other half. The
same is true, into however many parts the magnetic body be cut. The
way in which Coulomb modified the theory so as to reconcile it with
such facts, is simple and satisfactory. He supposes[15\12] the
magnetic body to be made up of "molecules or integral parts," or, as
they were afterwards called by M. Poisson, "magnetic elements." In
each of these elements, (which are extremely minute,) the fluids can
be separated, so that each element has an austral and a boreal pole;
but the austral pole of an element which is adjacent to the boreal
pole of the next, neutralizes, or nearly neutralizes, its effect; so
that the sensible magnetism appears only towards the extremities of
the body, as it would do if the fluids could permeate the body
freely. We shall have exactly the same result, as to sensible
magnetic force, on the one supposition and on the other, as Coulomb
showed.[16\12]

[Note 15\12: _Mem. A. P._ 1789, p. 488.]

[Note 16\12: _Mem. A. P._ p. 492.]

The theory, thus freed from manifest incongruities, was to be
reduced to calculation, and compared with experiment; this was done
in Coulomb's Seventh Memoir.[17\12] The difficulties of calculation
in this, as in the electric problem, could not be entirely
surmounted by the analysis of Coulomb; but by various artifices, he
obtained theoretically the {223} relative amount of magnetism at
several points of a needle,[18\12] and the proposition that the
directive force of the earth on similar needles saturated with
magnetism, was as the cube of their dimensions; conclusions which
agreed with experiment.

[Note 17\12: _A. P._ 1789.]

[Note 18\12: p. 485.]

The agreement thus obtained was sufficient to give a great
probability to the theory; but an improvement of the methods of
calculation and a repetition of experiments, was, in this as in
other cases, desirable, as a confirmation of the labors of the
original theorist. These requisites, in the course of time, were
supplied. The researches of Laplace and Legendre on the figure of
the earth had (as we have already stated,) introduced some very
peculiar analytical artifices, applicable to the attractions of
spheroids; and these methods were employed by M. Biot in 1811, to
show that on an elliptical spheroid, the thickness of the fluid in
the direction of the radius would be as the distance from the
centre.[19\12] But the subject was taken up in a more complete
manner in 1824 by M. Poisson, who obtained general expressions for
the attractions or repulsions of a body of any form whatever,
magnetized by influence, upon a given point; and in the case of
spherical bodies was able completely to solve the equations which
determine these forces.[20\12]

[Note 19\12: _Bull. des Sc._ No. li.]

[Note 20\12: _A. P._ for 1821 and 2, published 1826.]

Previously to these theoretical investigations, Mr. Barlow had made
a series of experiments on the effect of an iron sphere upon a
compass needle; and had obtained empirical formulæ for the amount of
the deviation of the needle, according to its dependence upon the
position and magnitude of the sphere. He afterwards deduced the same
formulæ from a theory which was, in fact, identical with that of
Coulomb, but which he considered as different, in that it supposed
the magnetic fluids to be entirely collected at the surface of the
sphere. He had indeed found, by experiment, that the surface was the
only part in which there was any sensible magnetism; and that a thin
shell of iron would produce the same effect as a solid ball of the
same diameter.

But this was, in fact, a most complete verification of Coulomb's
theory. For though that theory did not suppose the magnetism to be
collected solely at the surface, as Mr. Barlow found it, it followed
from the theory, that the _sensible_ magnetic intensity assumed the
same distribution (namely, a surface distribution,) as if the fluids
could permeate the whole body, instead of the "magnetic elements"
only. Coulomb, indeed, had not expressly noticed the result, that
the sensible {224} magnetism would be confined to the surface of
bodies; but he had found that, in a long needle, the magnetic fluid
might be supposed to be concentrated very near the extremities, just
as it is in a long electric body. The theoretical confirmation of
this rule among the other consequences of the theory,--that the
sensible magnetism would be collected at the surface,--was one of
the results of Poisson's analysis. For it appeared that if the sum
of the electric elements of the body was equal to the whole body,
there would be no difference between the action of a solid sphere
and very thin shell.

We may, then, consider the Coulombian theory to be fully established
and verified, as a representation of the laws of magnetical
phenomena. We may add, as a remarkable and valuable example of an
ulterior step in the course of sciences, the application of the laws
of the distribution of magnetism to the purposes of navigation. It
had been found that the mass of iron which exists in a ship produces
a deviation in the direction of the compass-needle, which was termed
"local attraction," and which rendered the compass an erroneous
guide. Mr. Barlow proposed to correct this by a plate of iron placed
near the compass; the plate being of comparatively small mass, but,
in consequence of its expanded form, and its proximity to the
needle, of equivalent effect to the disturbing cause.

[2nd Ed.] [This proposed arrangement was not successful, because as
the ship turns into different positions, it may be considered as
revolving round a vertical axis; and as this does not coincide with
the magnetic axis, the relative magnetic position of the disturbing
parts of the ship, and of the correcting plate, will be altered, so
that they will not continue to counteract each other. In high
magnetic latitudes the correcting plate was used with success.

But when iron ships became common, a correction of the effect of the
iron upon the ship's compass in the general case became necessary.
Mr. Airy devised the means of making this correction. By placing a
magnet and a mass of iron in certain positions relative to the
compass, the effect of the rest of the iron in the ship is
completely counteracted in all positions.[21\12]]

[Note 21\12: See _Phil. Trans._ 1836.]

But we have still to trace the progress of the theory of terrestrial
magnetism.

_Theory of Terrestrial Magnetism._--Gilbert had begun a plausible
course of speculation on this point. "We must reject," he
says,[22\12] "in {225} the first place, that vulgar opinion of
recent writers concerning magnetic mountains, or a certain magnetic
rock, or an imaginary pole at a certain distance from the pole of
the earth." For, he adds, "we learn by experience, that there is no
such fixed pole or term in the earth for the variation." Gilbert
describes the whole earth as a magnetic globe, and attributes the
variation to the irregular form of its protuberances, the solid
parts only being magnetic. It was not easy to confirm or refute this
opinion, but other hypotheses were tried by various writers; for
instance, Halley had imagined, from the forms of the lines of equal
variation, that there must be four magnetic poles; but Euler[23\12]
showed that the "Halleian lines" would, for the most part, result
from the supposition of two magnetic poles, and assigned their
position so as to represent pretty well the known state of the
variation all over the world in 1744. But the variation was not the
only phenomenon which required to be taken into account; the dip at
different places, and also the intensity of the force, were to be
considered. We have already mentioned M. de Humboldt's collection of
observations of the dip. These were examined by M. Biot, with the
view of reducing them to the action of two poles in the supposed
terrestrial magnetic axis. Having, at first, made the distance of
these poles from the centre of the earth indefinite, he found that
his formulæ agreed more and more nearly with the observations, as
the poles were brought nearer; and that fact and theory coincided
tolerably well when both poles were at the centre. In 1809,[24\12]
Krafft simplified this result, by showing that, on this supposition,
the tangent of the dip was twice the tangent of the latitude of the
place as measured from the magnetic equator. But M. Hansteen, who
has devoted to the subject of terrestrial magnetism a great amount
of labor and skill, has shown that, taking together all the
observations which we possess, we are compelled to suppose four
magnetic poles; two near the north pole, and two near the south
pole, of the terrestrial globe; and that these poles, no two of
which are exactly opposite each other, are all in motion, with
different velocities, some moving to the east and some to the west.
This curious collection of facts awaits the hand of future
theorists, when the ripeness of time shall invite them to the task.

[Note 22\12: Lib. iv. c. 1. _De Variatione._]

[Note 23\12: _Ac. Berlin_, 1757.]

[Note 24\12: _Enc. Met._ p. 742.]

[2nd Ed.] [I had thus written in the first edition. The theorist who
was needed to reduce this accumulation of facts to their laws, {226}
had already laid his powerful hand upon them; namely, M. Gauss, a
mathematician not inferior to any of the great men who completed the
theory of gravitation. And institutions had been established for
extending the collection of the facts pertaining to it, on a scale
which elevates Magnetism into a companionship with Astronomy. M.
Hansteen's _Magnetismus der Erde_ was published in 1819. His
conclusions respecting the position of the four magnetic "poles"
excited so much interest in his own country, that the Norwegian
_Storthing_, or parliament, by a unanimous vote, provided funds for
a magnetic expedition which he was to conduct along the north of
Europe and Asia; and this they did at the very time when they
refused to make a grant to the king for building a palace at
Christiania. The expedition was made in 1828-30, and verified
Hansteen's anticipations as to the existence of a region of magnetic
convergence in Siberia, which he considered as indicating a "pole"
to the north of that country. M. Erman also travelled round the
earth at the same time, making magnetic observations.

About the same time another magnetical phenomenon attracted
attention. Besides the general motion of the magnetic poles, and the
diurnal movements of the needle, it was found that small and
irregular disturbances take place in its position, which M. de
Humboldt termed _magnetic storms_. And that which excited a strong
interest on this subject was the discovery that these magnetic
storms, seen only by philosophers who watch the needle with
microscopic exactness, rage simultaneously over large tracts of the
surface of our globe. This was detected about 1825 by a comparison
of the observations of M. Arago at Paris with simultaneous
observations of M. Kupffer at Kasan in Russia, distant more than 47
degrees of longitude.

At the instance of M. de Humboldt, the Imperial Academy of Russia
adopted with zeal the prosecution of this inquiry, and formed a chain
of magnetic stations across the whole of the Russian empire. Magnetic
observations were established at Petersburg and at Kasan, and
corresponding observations were made at Moscow, at Nicolaieff in the
Crimea, and Barnaoul and Nertchinsk in Siberia, at Sitka in Russian
America, and even at Pekin. To these magnetic stations the Russian
government afterwards added, Catharineburg in Russia Proper,
Helsingfors in Finland, Teflis in Georgia. A comparison of the results
obtained at four of these stations made by MM. de Humboldt and Dove,
in the year 1830, showed that the magnetic disturbances were
simultaneous, and were for the most parallel in their progress. {227}

Important steps in the prosecution of this subject were soon after
made by M. Gauss, the great mathematician of Göttingen. He contrived
instruments and modes of observation far more perfect than any
before employed, and organized a system of comparative observations
throughout Europe. In 1835, stations for this purpose were
established at Altona, Augsburg, Berlin, Breda, Breslau, Copenhagen,
Dublin, Freiberg, Göttingen, Greenwich, Hanover, Leipsic, Marburg,
Milan, Munich, Petersburg, Stockholm, and Upsala. At these places,
six times in the year, observations were taken simultaneously, at
intervals of five minutes for 24 hours. The _Results of the Magnetic
Association_ (Resultaten des Magnetischen Vereins) were published by
MM. Gauss and Weber, beginning in 1836.

British physicists did not at first take any leading part in these
plans. But in 1836, Baron Humboldt, who by his long labors and
important discoveries in this subject might be considered as
peculiarly entitled to urge its claims, addressed a letter to the
Duke of Sussex, then President of the Royal Society, asking for the
co-operation of this country in so large and hopeful a scheme for
the promotion of science. The Royal Society willingly entertained
this appeal; and the progress of the cause was still further
promoted when it was zealously taken up by the British Association
for the Advancement of Science, assembled at Newcastle in 1838. The
Association there expressed its strong interest in the German system
of magnetic observations; and at the instigation of this body, and
of the Royal Society, four complete magnetical observatories were
established by the British government, at Toronto, St. Helena, the
Cape of Good Hope, and Van Diemen's Land. The munificence of the
Directors of the East India Company founded and furnished an equal
number at Simla (in the Himalayah), Madras, Bombay, and Sincapore.
Sir Thomas Brisbane added another at his own expense at Kelso, in
Scotland. Besides this, the government sent out a naval expedition
to make discoveries (magnetic among others), in the Antarctic
regions, under the command of Sir James Ross. Other states lent
their assistance also, and founded or reorganized their magnetic
observatories. Besides those already mentioned, one was established
by the French government at Algiers; one by the Belgian, at
Brussels; two by Austria, at Prague and Milan; one by Prussia, at
Breslau; one by Bavaria, at Munich; one by Spain, at Cadiz; there
are two in the United States, at Philadelphia and Cambridge; one at
Cairo, founded by the Pasha of Egypt; and in India, one at
Trevandrum, established by the Rajah of Travancore; and one by {228}
the King of Oude, at Lucknow. At all these distant stations the same
plan was followed out, by observations strictly simultaneous, made
according to the same methods, with the same instrumental means.
Such a scheme, combining world-wide extent with the singleness of
action of an individual mind, is hitherto without parallel.

At first, the British stations were established for three years
only; but it was thought advisable to extend this period three years
longer, to end in 1845. And when the termination of that period
arrived, a discussion was held among the magneticians themselves,
whether it was better to continue the observations still, or to
examine and compare the vast mass of observations already collected,
so as to see to what results and improvements of methods they
pointed. This question was argued at the meeting of the British
Association at Cambridge in that year; and the conference ended in
the magneticians requesting to have the observations continued, at
some of the observatories for an indefinite period, at others, till
the year 1848. In the mean time the Antarctic expedition had brought
back a rich store of observations, fitted to disclose the magnetic
condition of those regions which it had explored. These were
_discussed_, and their results exhibited, in the _Philosophical
Transactions_ for 1843, by Col. Sabine, who had himself at various
periods, made magnetic observations in the Arctic regions, and in
several remote parts of the globe, and had always been a zealous
laborer in this fruitful field. The general mass of the observations
was placed under the management of Professor Lloyd, of Dublin, who
has enriched the science of magnetism with several valuable
instruments and methods, and who, along with Col. Sabine, made a
magnetic survey of the British Isles in 1835 and 1836.

I do not dwell upon magnetic surveys of various countries made by
many excellent observers; as MM. Quetelet, Forbes, Fox, Bache and
others.

The facts observed at each station were, the _intensity_ of the
magnetic force; the _declination_ of the needle from the meridian,
sometimes called the _variation_; and its _inclination_ to the
horizon, _the dip_;--or at least, some elements equivalent to these.
The values of these elements at any given time, if known, can be
expressed by charts of the earth's surface, on which are drawn the
_isodynamic_, _isogonal_, and _isoclinal_ curves. The second of
these kinds of charts contain the "Halleian lines" spoken of in a
previous page. Moreover the magnetic elements at each place are to
be observed in such a {229} manner as to determine both their
_periodical_ variations (the changes which occur in the period of a
day, and of a year), the _secular_ changes, as the gradual increase
or diminution of the declination at the same place for many years;
and the _irregular_ fluctuations which, as we have said, are
simultaneous over a large part, or the whole, of the earth's surface.

When these Facts have been ascertained over the whole extent of the
earth's surface, we shall still have to inquire what is the Cause of
the changes in the forces which these phenomena disclose. But as a
basis for all speculation on that subject, we must know the law of the
phenomena, and of the forces which immediately produce them. I have
already said that Euler tried to account for the Halleian lines by
means of _two_ magnetic "poles," but that M. Hansteen conceived it
necessary to assume _four_. But an entirely new light has been thrown
upon this subject by the beautiful investigations of Gauss, in his
_Theory of Terrestrial Magnetism_, published in 1839. He remarks that
the term "poles," as used by his predecessors, involves an assumption
arbitrary, and, as it is now found, false; namely, that certain
definite points, two, four, or more, acting according to the laws of
ordinary magnetical poles, will explain the phenomena. He starts from
a more comprehensive assumption, that magnetism is distributed
throughout the mass of the earth in an unknown manner. On this
assumption he obtains a function _V_, by the differentials of which
the elements of the magnetic force at any point will be expressed.
This function _V_ is well known in physical astronomy, and is obtained
by summing all the elements of magnetic force in each particle, each
multiplied by the reciprocal of its distance; or as we may express it,
by taking the sum of each element and its proximity jointly. Hence it
has been proposed[25\12] to term this function the "_integral
proximity_" of the attracting mass.[26\12] By using the most refined
{230} mathematical artifices for deducing the values of _V_ and its
differentials in converging series, he is able to derive the
coefficients of these series from the observed magnetic elements at
certain places, and hence, to calculate them for all places. The
comparison of the calculation with the observed results is, of course,
the test of the truth of the theory.

[Note 25\12: _Quart. Rev._ No. 131, p. 283.]

[Note 26\12: The function V is of constant occurrence in
investigations respecting attractions. It is introduced by Laplace
in his investigations respecting the attractions of spheroids, _Méc.
Cél._ Livr. III. Art. 4. Mr. Green and Professor Mac Cullagh have
proposed to term this function the _Potential_ of the system; but
this term (though suggested, I suppose, by analogy with the
substantive _Exponential_), does not appear convenient in its form.
On the other hand, the term _Integral Proximity_ does not indicate
that which gives the function its peculiar claim to distinction;
namely, that its differentials express the power or attraction of
the system. Perhaps _Integral Potentiality_, or _Integral
Attractivity_, would be a term combining the recommendations of both
the others.]

The degree of convergence of the series depends upon the unknown
distribution of magnetism within the earth. "If we could venture to
assume," says M. Gauss, "that the members have a sensible influence
only as far as the fourth order, complete observations from eight
points would be sufficient, theoretically considered, for the
determination of the coefficients." And under certain limitations,
making this assumption, as the best we can do at present, M. Gauss
obtains from eight places, 24 coefficients (each supplying three
elements), and hence calculates the magnetic elements (intensity,
variation and dip) at 91 places in all parts of the earth. He finds
his calculations approach the observed values with a degree of
exactness which appears to be quite convincing as to the general
truth of his results; especially taking into account how entirely
unlimited is his original hypothesis.

It is one of the most curious results of this investigation that
according to the most simple meaning which we can give to the term
"pole" the earth has only _two_ magnetic poles; that is, two points
where the direction of the magnetic force is vertical. And thus the
_isogonal curves_ may be looked upon as _deformations_ of the curves
deduced by Euler from the supposition of two poles, the deformation
arising from this, that the earth does not contain a single definite
magnet, but irregularly diffused magnetical elements, which still
have collectively a distinct resemblance to a single magnet. And
instead of Hansteen's Siberian pole, we have a Siberian region in
which the needles converge; but if the apparent convergence be
pursued it nowhere comes to a point; and the like is the case in the
Antarctic region. When the 24 Gaussian elements at any time are
known the magnetic condition of the globe is known, just as the
mechanical condition of the solar system is known, when we know the
elements of the orbits of the satellites and planets and the mass of
each. And the comparison of this magnetic condition of the globe at
distant periods of time cannot fail to supply materials for future
researches and speculations with regard to the agencies by which the
condition of the earth is determined. The condition of which we here
speak must necessarily be its _mechanico-chemical_ condition, being
expressed, as it will be, in terms of the mechanico-chemical
sciences. The {231} investigations I have been describing belong to
the mechanical side of the subject: but when philosophers have to
consider the causes of the secular changes which are found to occur
in this mechanical condition, they cannot fail to be driven to
electrical, that is, chemical agencies and laws.

I can only allude to Gauss's investigations respecting the _Absolute
Measure_ of the Earth's Magnetic Force. To determine the ratio of the
magnetic force of the earth to that of a known magnet, Poisson
proposed to observe the time of vibration of a second magnet. The
method of Gauss, now universally adopted, consists in observing the
position of equilibrium of the second magnet when deflected by the
first.

The manner in which the business of magnetic observation has been
taken up by the governments of our time makes this by far the
greatest scientific undertaking which the world has ever seen. The
result will be that we shall obtain in a few years a knowledge of
the magnetic constitution of the earth which otherwise it might have
required centuries to accumulate. The secular magnetic changes must
still require a long time to reduce to their laws of phenomena,
except observation be anticipated or assisted by some happy
discovery as to the cause of these changes. But besides the special
gain to magnetic science by this great plan of joint action among
the nations of the earth, there is thereby a beginning made in the
recognition and execution of the duty of forwarding science in
general by national exertions. For at most of the magnetic
observatories, meteorological observations are also carried on; and
such observations, being far more extensive, systematic, and
permanent than those which have usually been made, can hardly fail
to produce important additions to science. But at any rate they do
for science that which nations can do, and individuals cannot; and
they seek for scientific truths in a manner suitable to the respect
now professed for science and to the progress which its methods have
made. Nor are we to overlook the effect of such observations as
means of training men in the pursuit of science. "There is amongst
us," says one of the magnetic observers, "a growing recognition of
the importance, both for science and for practical life, of forming
exact observers of nature. Hitherto astronomy alone has afforded a
very partial opportunity for the formation of fine observers, of
which few could avail themselves. Experience has shown that magnetic
observations may serve as excellent training schools in this
respect."[27\12]] {232}

[Note 27\12: _Letter_ of W. Weber. _Brit. Assoc. Rep._ 1845, p. 17.]

The various other circumstances which terrestrial magnetism
exhibits,--the diurnal and annual changes of the position of the
compass-needle;--the larger secular change which affects it in the
course of years;--the difference of intensity at different places,
and other facts, have naturally occupied philosophers with the
attempt to determine, both the laws of the phenomena and their
causes. But these attempts necessarily depend, not upon laws of
statical magnetism, such as they have been explained above; but upon
the laws by which the production and intensity of magnetism in
different cases are regulated;--laws which belong to a different
province, and are related to a different set of principles. Thus,
for example, we have not attempted to explain the discovery of the
laws by which heat influences magnetism; and therefore we cannot now
give an account of those theories of the facts relating to
terrestrial magnetism, which depend upon the influence of
temperature. The conditions of excitation of magnetism are best
studied by comparing this force with other cases where the same
effects are produced by very different apparent agencies; such as
galvanic and thermo-electricity. To the history of these we shall
presently proceed.

_Conclusion._--The hypothesis of magnetic fluids, as physical
realities, was never widely or strongly embraced, as that of
electric fluids was. For though the hypothesis accounted, to a
remarkable degree of exactness, for large classes of the phenomena,
the presence of a material fluid was not indicated by facts of a
different kind, such as the spark, the discharge from points, the
shock, and its mechanical effects. Thus the belief of a peculiar
magnetic fluid or fluids was not forced upon men's minds; and the
doctrine above stated was probably entertained by most of its
adherents, chiefly as a means of expressing the laws of phenomena in
their elementary form.

One other observation occurs here. We have seen that the supposition
of a fluid moveable from one part of bodies to another, and capable
of accumulation in different parts of the surface, appeared at first
to be as distinctly authorized by magnetic as by electric phenomena;
and yet that it afterwards appeared, by calculation, that this must
be considered as a derivative result; no real transfer of fluid
taking place except within the limits of the insensible particles of
the body. Without attempting to found a formula of philosophizing on
this circumstance, we may observe, that this occurrence, like the
disproof of heat as a material fluid, shows the possibility of an
hypothesis which shall very exactly satisfy many phenomena, and yet
be incomplete: it {233} shows, too, the necessity of bringing facts
of all kinds to bear on the hypothesis; thus, in this case it was
requisite to take into account the facts of junction and separation
of magnetic bodies, as well as their attractions and repulsions.

If we have seen reason to doubt the doctrine of electric fluids as
physical realities, we cannot help pronouncing upon the magnetic
fluids as having still more insecure claims to a material existence,
even on the grounds just stated. But we may add considerations still
more decisive; for at a further stage of discovery, as we shall see,
magnetic and electric action were found to be connected in the
closest manner, so as to lead to the persuasion of their being
different effects of one common cause. After those discoveries, no
philosopher would dream of assuming electric fluids and magnetic
fluids as two distinct material agents. Yet even now the nature of
the dependence of magnetism upon any other cause is extremely
difficult to conceive. But till we have noticed some of the
discoveries to which we have alluded, we cannot even speculate about
that dependence. We now, therefore, proceed to sketch the history of
these discoveries.



{{235}}
BOOK XIII.

_MECHANICO-CHEMICAL SCIENCES._

(CONTINUED.)


HISTORY OF GALVANISM,
OR
VOLTAIC ELECTRICITY.


  Percusssæ gelido trepidant sub pectore fibræ,
  Et nova desuetis subrepens vita medullis
  Miscetur morti: tunc omnis palpitat artus
  Tenduntur nervi; nec se tellure cadaver
  Paullatim per membra levat; terrâque repulsum est
  Erectumque simul.
          LUCAN. vi. 752.

  The form which lay before inert and dead,
  Sudden a piercing thrill of change o'erspread;
  Returning life gleams in the stony face,
  The fibres quiver and the sinews brace,
  Move the stiff limbs;--nor did the body rise
  With tempered strength which genial life supplies,
  But upright starting, its full stature held,
  As though the earth the supine corse repelled.



{{237}}
CHAPTER I.

DISCOVERY OF VOLTAIC ELECTRICITY.


WE have given the name of _mechanico-chemical_ to the class of
sciences now under our consideration; for these sciences are
concerned with cases in which mechanical effects, that is,
attractions and repulsions, are produced; while the conditions under
which these effects occur, depend, as we shall hereafter see, on
chemical relations. In that branch of these sciences which we have
just treated of, Magnetism, the mechanical phenomena were obvious,
but their connexion with chemical causes was by no means apparent,
and, indeed, has not yet come under our notice.

The subject to which we now proceed, Galvanism, belongs to the same
group, but, at first sight, exhibits only the other, the chemical,
portion of the features of the class; for the connexion of galvanic
phenomena with chemical action was soon made out, but the mechanical
effects which accompany them were not examined till the examination
was required by a new train of discovery. It is to be observed, that
I do not include in the class of mechanical effects the convulsive
motions in the limbs of animals which are occasioned by galvanic
action; for these movements are produced, not by attraction and
repulsion, but by muscular irritability; and though they indicate
the existence of a peculiar agency, cannot be used to measure its
intensity and law.

The various examples of the class of agents which we here
consider,--magnetism, electricity, galvanism, electro-magnetism,
thermo-electricity,--differ from each other principally in the
circumstances by which they are called into action; and these
differences are in reality of a chemical nature, and will have to be
considered when we come to treat of the inductive steps by which the
general principles of chemical theory are established. In the
present part of our task, therefore, we must take for granted the
chemical conditions on which the excitation of these various kinds
of action depends, and trace the history of the discovery of their
mechanical laws only. This rule will much abridge the account we
have here to give of the progress of discovery in the provinces to
which I have just referred. {238}

The first step in this career of discovery was that made by Galvani,
Professor of Anatomy at Bologna. In 1790, electricity, as an
experimental science, was nearly stationary. The impulse given to
its progress by the splendid phenomena of the Leyden phial had
almost died away; Coulomb was employed in systematizing the theory
of the electric fluid, as shown by its statical effects; but in all
the other parts of the subject, no great principle or new result had
for some time been detected. The first announcement of Galvani's
discovery in 1791 excited great notice, for it was given forth as a
manifestation of electricity under a new and remarkable character;
namely, as residing in the muscles of animals.[1\13] The limbs of a
dissected frog were observed to move, when touched with pieces of
two different metals; the agent which produced these motions was
conceived to be identified with electricity, and was termed _animal
electricity_; and Galvani's experiments were repeated, with various
modifications, in all parts of Europe, exciting much curiosity, and
giving rise to many speculations.

[Note 1\13: _De Viribus Electricis in Motu Musculari_, Comm. Bonon.
t. vii. 1792.]

It is our business to determine the character of each great
discovery which appears in the progress of science. Men are fond of
repeating that such discoveries are most commonly the result of
accident; and we have seen reason to reject this opinion, since that
preparation of thought by which the accident produces discovery is
the most important of the conditions on which the successful event
depends. Such accidents are like a spark which discharges a gun
already loaded and pointed. In the case of Galvani, indeed, the
discovery may, with more propriety than usual, be said to have been
casual; but in the form in which it was first noted, it exhibited no
important novelty. His frog was lying on a table near the conductor
of an electrical machine, and the convulsions appeared only when a
spark was taken from the machine. If Galvani had been as good a
physicist as he was an anatomist, he would probably have seen that
the movements so occasioned proved only that the muscles or nerves,
or the two together, formed a very sensitive indicator of electrical
action. It was when he produced such motions by contact of metals
alone, that he obtained an important and fundamental fact in science.

The analysis of this fact into its real and essential conditions was
the work of Alexander Volta, another Italian professor. Volta,
indeed, possessed that knowledge of the subject of electricity which
made a hint like that of Galvani the basis of a new science. Galvani
appears {239} never to have acquired much general knowledge of
electricity: Volta, on the other hand, had labored at this branch of
knowledge from the age of eighteen, through a period of nearly
thirty years; and had invented an _electrophorus_ and an _electrical
condenser_, which showed great experimental skill. When he turned
his attention to the experiments made by Galvani, he observed that
the author of them had been far more surprised than he needed to be,
at those results in which an electrical spark was produced; and that
it was only in the cases in which no such apparatus was employed,
that the observations could justly be considered as indicating a new
law, or a new kind of electricity.[2\13] He soon satisfied
himself[3\13] (about 1794) that the essential conditions of this
kind of action depended on the metals; that it is brought into play
most decidedly when two different metals touch each other, and are
connected by any moist body;--and that the parts of animals which
had been used discharged the office both of such moist bodies, and
of very sensitive electrometers. The _animal_ electricity of Galvani
might, he observed, be with more propriety called _metallic_
electricity.

[Note 2\13: _Phil. Trans._ 1793, p. 21.]

[Note 3\13: See Fischer, viii. 625.]

The recognition of this agency as a peculiar kind of _electricity_,
arose in part perhaps, at first, from the confusion made by Galvani
between the cases in which his electrical machine was, and those in
which it was not employed. But the identity was confirmed by its
being found that the known difference of electrical conductors and
non-conductors regulated the conduction of the new influence. The
more exact determination of the new facts to those of electricity
was a succeeding step of the progress of the subject.

The term "animal electricity" has been superseded by others, of
which _galvanism_ is perhaps the most familiar. I think it will
appear from what has been said, that Volta's office in this
discovery is of a much higher and more philosophical kind than that
of Galvani; and it would, on this account, be more fitting to employ
the term _voltaic electricity_; which, indeed, is very commonly
used, especially by our most recent and comprehensive writers.

Volta more fully still established his claim as the main originator
of this science by his next step. When some of those who repeated
the experiments of Galvani had expressed a wish that there was some
method of multiplying the effect of _this_ electricity, such as the
Leyden phial supplies for common electricity, they probably thought
their wishes far from a realization. But the _voltaic pile_, which
Volta {240} described in the _Philosophical Transactions_ for 1800,
completely satisfies this aspiration; and was, in fact, a more
important step in the history of electricity than the Leyden jar had
been. It has since undergone various modifications, of which the
most important was that introduced by **Cruickshanks, who[4\13]
substituted a trough for a pile. But in all cases the principle of
the instrument was the same;--a continued repetition of the triple
combination of two metals and a fluid in contact, so as to form a
circuit which returns into itself.

[Note 4\13: Fischer, viii. p. 683.]

Such an instrument is capable of causing effects of great intensity;
as seen both in the production of light and heat, and in chemical
changes. But the discovery with which we are here concerned, is not
the details and consequences of the effects, (which belong to
chemistry,) but the analysis of the conditions under which such
effects take place; and this we may consider as completed by Volta
at the epoch of which we speak.




CHAPTER II.

RECEPTION AND CONFIRMATION OF THE DISCOVERY OF VOLTAIC ELECTRICITY.


GALVANI'S experiments excited a great interest all over Europe, in
consequence partly of a circumstance which, as we have seen, was
unessential, the muscular contractions and various sensations which
they occasioned. Galvani himself had not only considered the animal
element of the circuit as the origin of the electricity, but had
framed a theory,[5\13] in which he compared the muscles to charged
jars, and the nerves to the discharging wires; and a controversy
was, for some time, carried on, in Italy, between the adherents of
Galvani and those of Volta.[6\13]

[Note 5\13: Ib. viii. 613.]

[Note 6\13: Ib. viii. 619.]

The galvanic experiments, and especially those which appeared to
have a physiological bearing, were verified and extended by a number
of the most active philosophers of Europe, and especially William
von Humboldt. A commission of the Institute of France, appointed in
1797, repeated many of the known experiments, but does not seem to
have decided any disputed points. The researches of this {241}
commission referred rather to the discoveries of Galvani than to
those of Volta: the latter were, indeed, hardly known in France till
the conquest of Italy by Bonaparte, in 1801. France was, at the
period of these discoveries, separated from all other countries by
war, and especially from England,[7\13] where Volta's Memoirs were
published.

[Note 7\13: _Biog. Univ._, art. _Volta_, (by Biot.)]

The political revolutions of Italy affected, in very different
manners, the two discoverers of whom we speak. Galvani refused to
take an oath of allegiance to the Cisalpine republic, which the
French conqueror established; he was consequently stripped of all
his offices; and deprived, by the calamities of the times, of most
of his relations, he sank into poverty, melancholy, and debility. At
last his scientific reputation induced the republican rulers to
decree his restoration to his professorial chair; but his claims
were recognised too late, and he died without profiting by this
intended favor, in 1798.

Volta, on the other hand, was called to Paris by Bonaparte as a man
of science, and invested with honors, emoluments, and titles. The
conqueror himself, indeed, was strongly interested by this train of
research.[8\13] He himself founded valuable prizes, expressly with a
view to promote its prosecution. At this period, there was something
in this subject peculiarly attractive to his Italian mind; for the
first glimpses of discoveries of great promise have always excited
an enthusiastic activity of speculation in the philosophers of
Italy, though generally accompanied with a want of precise thought.
It is narrated[9\13] of Bonaparte, that after seeing the
decomposition of the salts by means of the voltaic pile, he turned
to Corvisart, his physician, and said, "Here, doctor, is the image
of life; the vertebral column is the pile, the liver is the
negative, the bladder the positive, pole." The importance of voltaic
researches is not less than it was estimated by Bonaparte; but the
results to which it was to lead were of a kind altogether different
from those which thus suggested themselves to his mind. The
connexion of mechanical and chemical action was the first great
point to be dealt with; and for this purpose the laws of the
mechanical action of voltaic electricity were to be studied.

[Note 8\13: Becquerel, _Traité d'Electr._ t. i. p. 107.]

[Note 9\13: Ib. t. i. p. 108.]

It will readily be supposed that the voltaic researches, thus begun,
opened a number of interesting topics of examination and discussion.
These, however, it does not belong to our place to dwell upon at
present; since they formed parts of the theory of the subject, which
{242} was not completed till light had been thrown upon it from
other quarters. The identity of galvanism with electricity, for
instance, was at first, as we have intimated, rather conjectured
than proved. It was denied by Dr. Fowler, in 1793; was supposed to
be confirmed by Dr. Wells two years later; but was, still later,
questioned by Davy. The nature of the operation of the pile was
variously conceived. Volta himself had obtained a view of it which
succeeding researches confirmed, when he asserted,[10\13] in 1800,
that it resembled an electric battery feebly charged and constantly
renewing its charge. In pursuance of this view, the common
electrical action was, at a later period (for instance by Ampère, in
1820), called _electrical tension_, while the voltaic action was
called the _electrical current_, or _electromotive action_. The
different effects produced, by increasing the size and the number of
the plates in the voltaic trough, were also very remarkable. The
power of producing heat was found to depend on the size of the
plates; the power of producing chemical changes, on the other hand,
was augmented by the number of plates of which the battery
consisted. The former effect was referred to the increased
_quantity_, the latter to the _intensity_, of the electric fluid. We
mention these distinctions at present, rather for the purpose of
explaining the language in which the results of the succeeding
investigations are narrated, than with the intention of representing
the hypotheses and measures which they imply, as clearly
established, at the period of which we speak. For that purpose new
discoveries were requisite, which we have soon to relate.

[Note 10\13: _Phil. Trans._ p. 403.]




CHAPTER III.

DISCOVERY OF THE LAWS OF THE MUTUAL ATTRACTION AND REPULSION OF
VOLTAIC CURRENTS.--AMPÈRE.


IN order to show the place of voltaic electricity among the
mechanico-chemical sciences, we must speak of its mechanical laws as
separate from the laws of electro-magnetic action; although, in
fact, it was only in consequence of the forces which conducting
voltaic wires exert upon magnets, that those forces were detected
which they exert upon each {243} other. This latter discovery was
made by M. Ampère; and the extraordinary rapidity and sagacity with
which he caught the suggestion of such forces, from the
electro-magnetic experiments of M. Oersted, (of which we shall speak
in the next chapter,) well entitle him to be considered as a great
and independent discoverer. As he truly says,[11\13] "it by no means
followed, that because a conducting wire exerted a force on a
magnet, two conducting wires must exert a force on each other; for
two pieces of soft iron, both of which affect a magnet, do not
affect each other." But immediately on the promulgation of Oersted's
experiments, in 1820, Ampère leapt forwards to a general theory of
the facts, of which theory the mutual attraction and repulsion of
conducting voltaic wires was a fundamental supposition. The
supposition was immediately verified by direct trial; and the laws
of this attraction and repulsion were soon determined, with great
experimental ingenuity, and a very remarkable command of the
resources of analysis. But the experimental and analytical
investigation of the mutual action of voltaic or electrical
currents, was so mixed up with the examination of the laws of
electro-magnetism, which had given occasion to the investigation,
that we must not treat the two provinces of research as separate.
The mention in this place, premature as it might appear, of the
labors of Ampère, arises inevitably from his being the author of a
beautiful and comprehensive generalization, which not only included
the phenomena exhibited by the new combinations of Oersted, but also
disclosed forces which existed in arrangements already familiar,
although they had never been detected till the theory pointed out
how they were to be looked for.

[Note 11\13: _Théorie des Phénom. Electrodynamiques_, p. 113.]




CHAPTER IV.

DISCOVERY OF ELECTRO-MAGNETIC ACTION.--OERSTED.


THE impulse which the discovery of galvanism, in 1791, and that of
the voltaic pile, in 1800, had given to the study of electricity as
a mechanical science, had nearly died away in 1820. It was in that
year that M. Oersted, of Copenhagen, announced that the conducting
{244} wire of a voltaic circuit, acts upon a magnetic needle; and
thus recalled into activity that endeavor to connect magnetism with
electricity, which, though apparently on many accounts so hopeful,
had hitherto been attended with no success. Oersted found that the
needle has a tendency to place itself _at right angles_ to the
wire;--a kind of action altogether different from any which had been
suspected.

This observation was of vast importance; and the analysis of its
conditions and consequences employed the best philosophers in Europe
immediately on its promulgation. It is impossible, without great
injustice, to refuse great merit to Oersted as the author of the
discovery. We have already said that men appear generally inclined
to believe remarkable discoveries to be accidental, and the
discovery of Oersted has been spoken of as a casual insulated
experiment.[12\13] Yet Oersted had been looking for such an
_accident_ probably more carefully and perseveringly than any other
person in Europe. In 1807, he had published[13\13] a work, in which
he professed that his purpose was "to ascertain whether electricity,
in its most latent state, had any effect on the magnet." And he, as
I know from his own declaration, considered his discovery as the
natural sequel and confirmation of his early researches; as, indeed,
it fell in readily and immediately with speculations on these
subjects then very prevalent in Germany. It was an accident like
that by which a man guesses a riddle on which his mind has long been
employed.

[Note 12\13: See _Schelling ueber Faraday's Entdeckung_, p. 27.]

[Note 13\13: Ampère, p. 69.]

Besides the confirmation of Oersted's observations by many
experimenters, great additions were made to his facts: of these, one
of the most important was due to Ampère. Since the earth is in fact
magnetic, the voltaic wire ought to be affected by terrestrial
magnetism alone, and ought to tend to assume a position depending on
the position of the compass-needle. At first, the attempts to
produce this effect failed, but soon, with a more delicate
apparatus, the result was found to agree with the anticipation.

It is impossible here to dwell on any of the subsequent researches,
except so far as they are essential to our great object, the progress
towards a general theory of the subject. I proceed, therefore,
immediately to the attempts made towards this object. {245}




CHAPTER V.

DISCOVERY OF THE LAWS OF ELECTRO-MAGNETIC ACTION.


ON attempting to analyse the electro-magnetic phenomena observed by
Oersted and others into their simplest forms, they appeared, at
least at first sight, to be different from any mechanical actions
which had yet been observed. It seemed as if the conducting wire
exerted on the pole of the magnet a force which was not attractive
or repulsive, but _transverse_;--not tending to draw the point acted
on nearer, or to push it further off, in the line which reached from
the acting point, but urging it to move at right angles to this
line. The forces appeared to be such as Kepler had dreamt of in the
infancy of mechanical conceptions; rather than such as those of
which Newton had established the existence in the solar system, and
such as he, and all his successors, had supposed to be the only
kinds of force which exist in nature. The north pole of the needle
moved as if it were impelled by a vortex revolving round the wire in
one direction, while the south pole seemed to be driven by an
opposite vortex. The case seemed novel, and almost paradoxical.

It was soon established by experiments, made in a great variety of
forms, that the mechanical action was really of this transverse
kind. And a curious result was obtained, which a little while before
would have been considered as altogether incredible;--that this
force would cause a constant and rapid revolution of either of the
bodies about the other;--of the conducting wire about the magnet, or
of the magnet about the conducting wire. This was effected by Mr.
Faraday in 1821.

The laws which regulated the intensity of this force, with reference
to the distance and position of the bodies, now naturally came to be
examined. MM. Biot and Savart in France, and Mr. Barlow in England,
instituted such measures; and satisfied themselves that the
elementary force followed the law of magnitude of all known
elementary forces, in being inversely as the square of the distance;
although, in its direction, it was so entirely different from other
forces. But the investigation of the _laws of phenomena_ of the
subject was too closely connected with the choice of a mechanical
theory, to be established {246} previously and independently, as had
been done in astronomy. The experiments gave complex results, and
the analysis of these into their elementary actions was almost an
indispensable step in order to disentangle their laws. We must,
therefore, state the progress of this analysis.




CHAPTER VI.

THEORY OF ELECTRODYNAMICAL ACTION.


AMPÈRE'S THEORY.--Nothing can show in a more striking manner the
advanced condition of physical speculation in 1820, than the
reduction of the strange and complex phenomena of electromagnetism
to a simple and general theory as soon as they were published.
Instead of a gradual establishment of laws of phenomena, and of
theories more and more perfect, occupying ages, as in the case of
astronomy, or generations, as in the instances of magnetism and
electricity, a few months sufficed for the whole process of
generalization; and the experiments made at Copenhagen were
announced at Paris and London, almost at the same time with the
skilful analysis and comprehensive inductions of Ampère.

Yet we should err if we should suppose, from the celerity with which
the task was executed, that it was an easy one. There were required
in the author of such a theory, not only those clear conceptions of
the relations of space and force, which are the first conditions of
all sound theory, and a full possession of the experiments; but also
a masterly command of the mathematical arms by which alone the
victory could be gained, and a sagacious selection of proper
experiments which might decide the fate of the proposed hypothesis.

It is true, that the nature of the requisite hypothesis was not
difficult to see in a certain vague and limited way. The
conducting-wire and the magnetic needle had a tendency to arrange
themselves at right angles to one another. This might be represented
by supposing the wire to be made up of transverse magnetic needles,
or by supposing the needle to be made up of transverse
conducting-wires; for it was easy to conceive forces which should
bring corresponding elements, either magnetic or voltaic, into
parallel positions; and then the {247} general phenomena above
stated would be accounted for. And the choice between the two modes
of conception, appeared at first sight a matter of indifference. The
majority of philosophers at first adopted, or at least employed, the
former method, as Oersted in Germany, Berzelius in Sweden, Wollaston
in England.

Ampère adopted the other view, according to which the magnet is made
up of conducting-wires in a transverse position. But he did for his
hypothesis what no one did or could do for the other: he showed that
it was the only one which would account, without additional and
arbitrary suppositions, for the facts of _continued_ motion in
electromagnetic cases. And he further elevated his theory to a
higher rank of generality, by showing that it explained,--not only
the action of a conducting-wire upon a magnet, but also two other
classes of facts, already spoken of in this history,--the action of
magnets upon each other,--and the action of conducting-wires upon
each other.

The deduction of such particular cases from the theory, required, as
may easily be imagined, some complex calculations: but the deduction
being satisfactory, it will be seen that Ampère's theory conformed
to that description which we have repeatedly had to point out as the
usual character of a true and stable theory; namely, that besides
accounting for the class of phenomena which suggested it, it
supplies an unforeseen explanation of other known facts. For the
mutual action of magnets, which was supposed to be already reduced
to a satisfactory theoretical form by Coulomb, was not contemplated
by Ampère in the formation of his hypothesis; and the mutual action
of voltaic currents, though tried only in consequence of the
suggestion of the theory, was clearly a fact distinct from
electromagnetic action; yet all these facts flowed alike from the
theory. And thus Ampère brought into view a class of forces for
which the term "electromagnetic" was too limited, and which he
designated[14\13] by the appropriate term _electrodynamic_;
distinguishing them by this expression, as the forces of an electric
_current_, from the _statical_ effects of electricity which we had
formerly to treat of. This term has passed into common use among
scientific writers, and remains the record and stamp of the success
of the Amperian induction.

[Note 14\13: _Ann. de Chim._, tom. xx. p. 60 (1822).]

The first promulgation of Ampère's views was by a communication to
the French Academy of Sciences, September the 18th, 1820; Oersted's
discoveries having reached Paris only in the preceding July. {248}
At almost every meeting of the Academy during the remainder of that
year and the beginning of the following one, he had new
developements or new confirmations of his theory to announce. The
most hypothetical part of his theory,--the proposition that magnets
might be considered in their effects as identical with spiral
voltaic wires,--he asserted from the very first. The mutual
attraction and repulsion of voltaic wires,--the laws of this
action,--the deduction of the observed facts from it by
calculation,--the determination, by new experiments, of the constant
quantities which entered into his formulæ,--followed in rapid
succession. The theory must be briefly stated. It had already been
seen that parallel voltaic currents attracted each other; when,
instead of being parallel, they were situate in any directions, they
still exerted attractive and repulsive forces depending on the
distance, and on the directions of each element of both currents.
Add to this doctrine the hypothetical constitution of magnets,
namely, that a voltaic current runs round the axis of each particle,
and we have the means of calculating a vast variety of results which
may be compared with experiment. But the laws of the elementary
forces required further fixation. What _functions_ are the forces of
the distance and the directions of the elements?

To extract from experiment an answer to this inquiry was far from
easy, for the elementary forces were mathematically connected with
the observed facts, by a double mathematical integration;--a long,
and, while the constant coefficients remained undefined, hardly a
possible operation. Ampère made some trials in this way, but his
happier genius suggested to him a better path. It occurred to him,
that if his integrals, without being specially found, could be shown
to vanish upon the whole, under certain conditions of the problem,
this circumstance would correspond to arrangements of his apparatus
in which a state of equilibrium was preserved, however the form of
some of the parts might be changed. He found two such cases, which
were of great importance to the theory. The first of these cases
proved that the force exerted by any element of the voltaic wire
might be resolved into other forces by a theorem resembling the
well-known proposition of the parallelogram of forces. This was
proved by showing that the action of a straight wire is the same
with that of another wire which joins the same extremities, but is
bent and contorted in any way whatever. But it still remained
necessary to determine two fundamental quantities; one which
expressed the _power_ of the distance according to which the force
varied; the other, the {249} degree in which the force is affected
by the _obliquity_ of the elements. One of the general causes of
equilibrium, of which we have spoken, gave a relation between these
two quantities;[15\13] and as the power was naturally, and, as it
afterwards appeared, rightly conjectured to be the inverse square,
the other quantity also was determined; and the general problem of
electrodynamical action was fully solved.

[Note 15\13: Communication to the Acad. Sc., June 10, 1822. See
Ampère, _Recueil_, p. 292.]

If Ampère had not been an accomplished analyst, he would not have
been able to discover the condition on which the nullity of the
integral in this case depended.[16\13] And throughout his labors, we
find reason to admire, both his mathematical skill, and his
steadiness of thought; although these excellences are by no means
accompanied throughout with corresponding clearness and elegance of
exposition in his writings.

[Note 16\13: _Recueil_, p. 314.]

_Reception of Ampère's Theory._--Clear mathematical conceptions, and
some familiarity with mathematical operations, were needed by
readers also, in order to appreciate the evidence of the theory;
and, therefore, we need not feel any surprise if it was, on its
publication and establishment, hailed with far less enthusiasm than
so remarkable a triumph of generalizing power might appear to
deserve. For some time, indeed, the greater portion of the public
were naturally held in suspense by the opposing weight of rival
names. The Amperian theory did not make its way without contention
and competition. The electro-magnetic experiments, from their first
appearance, gave a clear promise of some new and wide
generalization; and held out a prize of honor and fame to him who
should be first in giving the right interpretation of the riddle. In
France, the emulation for such reputation is perhaps more vigilant
and anxious than it is elsewhere; and we see, on this as on other
occasions, the scientific host of Paris springing upon a new subject
with an impetuosity which, in a short time, runs into controversies
for priority or for victory. In this case, M. Biot, as well as
Ampère, endeavored to reduce the electro-magnetic phenomena to
general laws. The discussion between him and Ampère turned on some
points which are curious. M. Biot was disposed to consider as an
elementary action, the force which an element of a voltaic wire
exerts upon a magnetic particle, and which is, as we have seen, at
right angles to their mutual distance; and he conceived that {250}
the equal reaction which necessarily accompanies this action acts
oppositely to the action, not in the same line, but in a parallel
line, at the other extremity of the distance; thus forming a
primitive _couple_, to use a technical expression borrowed from
mechanics. To this Ampère objected,[17\13] that the _direct_
opposition of all elementary action and reaction was a universal and
necessary mechanical law. He showed too that such a couple as had
been assumed, would follow as a _derivative_ result from his theory.
And in comparing his own theory with that in which the voltaic wire
is assimilated to a collection of transverse magnets, he was also
able to prove that no such assemblage of forces acting to and from
fixed points, as the forces of magnets do act, could produce a
continued motion like that discovered by Faraday. This, indeed, was
only the well-known demonstration of the impossibility of a
perpetual motion. If, instead of a collection of magnets, the
adverse theorists had spoken of a magnetic _current_, they might
probably interpret their expressions so as to explain the facts;
that is, if they considered every element of such a current as a
magnet, and consequently, every point of it as being a north and a
south point at the same instant. But to introduce such a conception
of a magnetic current was to abandon all the laws of magnetic action
hitherto established; and consequently to lose all that gave the
hypothesis its value. The idea of an electric current, on the other
hand, was so far from being a new and hazardous assumption, that it
had already been forced upon philosophers from the time of Volta;
and in this current, the relation of _preceding_ and _succeeding_,
which necessarily existed between the extremities of any element,
introduced that relative polarity on which the success of the
explanations of the facts depended. And thus in this controversy,
the theory of Ampère has a great and undeniable superiority over the
rival hypotheses.

[Note 17\13: Ampère, _Théorie_, p. 154.]




CHAPTER VII.


CONSEQUENCES OF THE ELECTRODYNAMIC THEORY.

IT is not necessary to state the various applications which were
soon made of the electro-magnetic discoveries. But we may notice one
{251} of the most important,--the _Galvanometer_, an instrument
which, by enabling the philosopher to detect and to measure
extremely minute electrodynamic actions, gave an impulse to the
subject similar to that which it received from the invention of the
Leyden Phial, or the Voltaic Pile. The strength of the voltaic
current was measured, in this instrument, by the deflection produced
in a compass-needle; and its sensibility was multiplied by making
the wire pass repeatedly above and below the needle. Schweigger, of
Halle, was one of the first devisers of this apparatus.

The substitution of electro-magnets, that is, of spiral tubes
composed of voltaic wires, for common magnets, gave rise to a
variety of curious apparatus and speculations, some of which I shall
hereafter mention.

[2nd Ed.] [When a voltaic apparatus is in action, there may be
conceived to be a current of electricity running through its various
elements, as stated in the text. The force of this current in
various parts of the circuit has been made the subject of
mathematical investigation by M. Ohm.[18\13] The problem is in every
respect similar to that of the flow of heat through a body, and
taken generally, leads to complex calculations of the same kind. But
Dr. Ohm, by limiting the problem in the first place by conditions
which the usual nature and form of voltaic apparatus suggest, has
been able to give great simplicity to his reasonings. These
conditions are, the linear form of the conductors (wires) and the
steadiness of the electric state. For this part of the problem Dr.
Ohm's reasonings are as simple and as demonstrative as the
elementary propositions of Mechanics. The formulæ for the electric
force of a voltaic current to which he is led have been
experimentally verified by others, especially Fechner,[19\13]
Gauss,[20\13] Lenz, Jacobi, Poggendorf, and Pouillet.

[Note 18\13: _Die Galvanische Kette Mathematisch bearbeitet von Dr.
G. S. Ohm_, Berlin, 1827.]

[Note 19\13: _**Mass-bestimmungen über die Galvanische Kette._
Leipzig, 1831.]

[Note 20\13: _Results of the Magnetic Association._]

Among ourselves, Mr. Wheatstone has confirmed and applied the views
of M. Ohm, in a Memoir[21\13] _On New Instruments and Processes for
determining the Constants of a Voltaic Circuit_. He there remarks
that the clear ideas of electromotive forces and resistances,
substituted by Ohm for the vague notions of quantity and intensity
which have long been prevalent, give satisfactory explanations of
the most important difficulties, and express the laws of a vast
number of phenomena {252} in formulæ of remarkable simplicity and
generality. In this Memoir, Professor Wheatstone describes an
instrument which he terms _Rheostat_, because it brings to a common
standard the voltaic currents which are compared by it. He
generalizes the language of the subject by employing the term
_rheomotor_ for any apparatus which originates an electric current
(whether voltaic or thermoelectric, &c.) and _rheometer_ for any
instrument to measure the force of such a current. It appears that
the idea of constructing an instrument of the nature of the Rheostat
had occurred also to Prof. Jacobi, of St Petersburg.]

[Note 21\13: _Phil. Trans._ 1843. Pt. 11.]

The galvanometer led to the discovery of another class of cases in
which the electrodynamical action was called into play, namely,
those in which a circuit, composed of two metals only, became
electro-magnetic by _heating_ one part of it. This discovery of
_thermo-electricity_ was made by Professor Seebeck of Berlin, in
1822, and prosecuted by various persons; especially by Prof.
Cumming[22\13] of Cambridge, who, early in 1823, extended the
examination of this property to most of the metals, and determined
their thermo-electric order. But as these investigations exhibited
no new mechanical effects of electromotive forces, they do not now
further concern us; and we pass on, at present, to a case in which
such forces act in a manner different from any of those already
described.

[Note 22\13: _Camb. Trans._ vol. ii. p. 62. _On the Development of
Electro-Magnetism by Heat._]


DISCOVERY OF DIAMAGNETISM.

[2nd Ed.] [By the discoveries just related, a cylindrical spiral of
wire through which an electric current is passing is identified with
a magnet; and the effect of such a spiral is increased by placing in
it a core of soft iron. By the use of such a combination under the
influence of a voltaic battery, magnets are constructed far more
powerful than those which depend upon the permanent magnetism of
iron. The electro-magnet employed by Dr. Faraday in some of his
experiments would sustain a hundred-weight at either end.

By the use of such magnets Dr. Faraday discovered that, besides
iron, nickel and cobalt, which possess magnetism in a high degree,
many bodies are magnetic in a slight degree. And he made the further
very important discovery, that of those substances which are not
magnetic, many, perhaps all, possess an opposite property, in virtue
of which he terms them _diamagnetic_. The opposition is of this
{253} kind;--that magnetic bodies in the form of bars or needles,
if free to move, arrange themselves in the _axial_ line joining the
poles; diamagnetic bodies under the same circumstances arrange
themselves in an _equatorial_ position, perpendicular to the axial
line. And this tendency he conceives to be the result of one more
general; that whereas magnetic bodies are attracted to the poles of
a magnet, diamagnetic bodies are repelled from the poles. The list
of diamagnetic bodies includes all kinds of substances; not only
metals, as antimony, bismuth, gold, silver, lead, tin, zinc, but
many crystals, glass, phosphorus, sulphur, sugar, gum, wood, ivory;
and even flesh and fruit.

It appears that M. le Bailli had shown, in 1829, that both bismuth
and antimony and bismuth repelled the magnetic needle; and as Dr.
Faraday remarks, it is astonishing that such an experiment should
have remained so long without further results. M. Becquerel in 1827
observed, and quoted Coulomb as having also observed, that a needle
of wood under certain conditions pointed across the magnetic curves;
and also stated that he had found a needle of wood place itself
parallel to the wires of a galvanometer. This he referred to a
magnetism transverse to the length. But he does not refer the
phenomena to elementary repulsive action, nor show that they are
common to an immense class of bodies, nor distinguish this
diamagnetic from the magnetic class, as Faraday has taught us to do.

I do not dwell upon the peculiar phenomena of copper which, in the
same series of researches, are traced by Dr. Faraday to the combined
effect of its diamagnetic character, and the electric currents
excited in it by the electro-magnet; nor to the optical phenomena
manifested by certain transparent diamagnetic substances under
electric action; as already stated in Book ix.[23\13]]

[Note 23\13: See the _Twentieth Series of Experimental Researches in
Electricity_, read to the Royal Society, Dec. 18, 1845.]




CHAPTER VIII.

DISCOVERY OF THE LAWS OF MAGNETO-ELECTRIC INDUCTION.--FARADAY.

IT was clearly established by Ampère, as we have seen, that magnetic
action is a peculiar form of electromotive actions, and that, in
{254} this kind of agency, action and reaction are equal and
opposite. It appeared to follow almost irresistibly from these
considerations, that magnetism might be made to produce electricity,
as electricity could be made to imitate all the effects of
magnetism. Yet for a long time the attempts to obtain such a result
were fruitless. Faraday, in 1825, endeavored to make the
conducting-wire of the voltaic circuit excite electricity in a
neighboring wire by induction, as the conductor charged with common
electricity would have done, but he obtained no such effect. If this
attempt had succeeded, the magnet, which, for all such purposes, is
an assemblage of voltaic circuits, might also have been made to
excite electricity. About the same time, an experiment was made in
France by M. Arago, which really involved the effect thus sought;
though this effect was not extricated from the complex phenomenon,
till Faraday began his splendid career of discovery on this subject
in 1832. Arago's observation was, that the rapid revolution of a
conducting-plate in the neighborhood of a magnet, gave rise to a
force acting on the magnet. In England, Messrs. Barlow and Christie,
Herschel and Babbage, repeated and tried to analyse this experiment;
but referring the forces only to conditions of space and time, and
overlooking the real cause, the electrical currents produced by the
motion, these philosophers were altogether unsuccessful in their
labors. In 1831, Faraday again sought for electro-dynamical
induction, and after some futile trials, at last found it in a form
different from that in which he had looked for it. It was then seen,
that at the precise time of making or breaking the contact which
closed the galvanic circuit, a momentary effect was induced in a
neighboring wire, but disappeared instantly.[24\13] Once in
possession of this fact, Mr. Faraday ran rapidly up the ladder of
discovery, to the general point of view.--Instead of suddenly making
or breaking the contact of the inducing circuit, a similar effect
was produced by removing the inducible wire nearer to or further
from the circuit;[25\13]--the effects were increased by the
proximity of soft iron;[26\13]--when the soft iron was affected by
an ordinary magnet instead of the voltaic wire, the same effect
still recurred;[27\13]--and thus it appeared, that by making and
breaking magnetic contact, a momentary electric current was
produced. It was produced also by moving the magnet;[28\13]--or by
moving the wire with reference to the magnet.[29\13] Finally, it was
found that the earth might supply the place of a magnet {255} in
this as in other experiments;[30\13] and the mere motion of a wire,
under proper circumstances, produced in it, it appeared, a momentary
electric current.[31\13] These facts were curiously confirmed by the
results in special cases. They explained Arago's experiments: for
the momentary effect became permanent by the revolution of the
plate. And without using the magnet, a revolving plate became an
electrical machine;[32\13]--a revolving globe exhibited
electro-magnetic action,[33\13] the circuit being complete in the
globe itself without the addition of any wire;--and a mere motion of
the wire of a galvanometer produced an electro-dynamic effect upon
its needle.[34\13]

[Note 24\13: _Phil. Trans._ 1832, p. 127, First Series, Art. 10.]

[Note 25\13: Art. 18.]

[Note 26\13: Art. 28.]

[Note 27\13: Art. 37.]

[Note 28\13: Art. 39.]

[Note 29\13: Art. 53.]

[Note 30\13: Second Series, _Phil. Trans._ p. 163.]

[Note 31\13: Art. 141.]

[Note 32\13: Art. 150.]

[Note 33\13: Art. 164.]

[Note 34\13: Art. 171.]

But the question occurs, What is the general law which determines
the direction of electric currents thus produced by the joint
effects of motion and magnetism? Nothing but a peculiar steadiness
and clearness in his conceptions of space, could have enabled Mr.
Faraday to detect the law of this phenomenon. For the question
required that he should determine the mutual relations in space
which connect the magnetic poles, the position of the wire, the
direction of the wire's motion, and the electrical current produced
in it. This was no easy problem; indeed, the mere relation of the
magnetic to the electric forces, the one set being perpendicular to
the other, is of itself sufficient to perplex the mind; as we have
seen in the history of the electrodynamical discoveries. But Mr.
Faraday appears to have seized at once the law of the phenomena.
"The relation," he says,[35\13] "which holds between the magnetic
pole, the moving wire or metal, and the direction of the current
evolved, is very simple (so it seemed to him) although rather
difficult to express." He represents it by referring position and
motion to the "magnetic curves," which go from a magnetic pole to
the opposite pole. The current in the wire sets one way or the
other, according to the direction in which the motion of the wire
cuts these curves. And thus he was enabled, at the end of his Second
Series of _Researches_ (December, 1831), to give, in general terms,
the law of nature to which may be referred the extraordinary number
of new and curious experiments which he has stated;[36\13]--namely,
that if a wire move so as to cut a magnetic curve, a power is called
into action which tends to urge a magnetic current through the wire;
and that if a mass move so that its parts do not move in the same
direction across the magnetic curves, {256} and with the same angular
velocity, electrical currents are called into play in the mass.

[Note 35\13: First Series, Art. 114.]

[Note 36\13: Art. 256-264.]

This rule, thus simple from its generality, though inevitably
complex in every special case, may be looked upon as supplying the
first demand of philosophy, _the law of the phenomena_; and
accordingly Dr. Faraday has, in all his subsequent researches on
magneto-electric induction, applied this law to his experiments; and
has thereby unravelled an immense amount of apparent inconsistency
and confusion, for those who have followed him in his mode of
conceiving the subject.

But yet other philosophers have regarded these phenomena in other
points of view, and have stated the laws of the phenomena in a
manner different from Faraday's, although for the most part
equivalent to his. And these attempts to express, in the most simple
and general form, the law of the phenomena of magneto-electrical
induction, have naturally been combined with the expression of other
laws of electrical and magnetical phenomena. Further, these
endeavors to connect and generalize the Facts have naturally been
clothed in the garb of various Theories:--the _laws of phenomena_
have been expressed in terms of the supposed _causes of the
phenomena_; as fluids, attractions and repulsions, particles with
currents running through them or round them, physical lines of
force, and the like. Such views, and the conflict of them, are the
natural and hopeful prognostics of a theory which shall harmonize
their discords and include all that each contains of Truth. The
fermentation at present is perhaps too great to allow us to see
clearly the truth which lies at the bottom. But a few of the leading
points of recent discussions on these subjects will be noticed in
the Additions to this volume.




CHAPTER IX.

TRANSITION TO CHEMICAL SCIENCE.


THE preceding train of generalization may justly appear extensive,
and of itself well worthy of admiration. Yet we are to consider all
that has there been established as only one-half of the science to
which it belongs,--one limb of the colossal form of Chemistry. We
{257} have ascertained, we will suppose, the laws of Electric
Polarity; but we have then to ask, What is the relation of this
Polarity to Chemical Composition? This was the great problem which,
constantly present to the minds of electro-chemical inquirers, drew
them on, with the promise of some deep and comprehensive insight
into the mechanism of nature. Long tasks of research, though only
subsidiary to this, were cheerfully undertaken. Thus Faraday[37\13]
describes himself as compelled to set about satisfying himself of
the identity of common, animal, and voltaic electricity, as "the
decision of a doubtful point which interfered with the extension of
his views, and destroyed the strictness of reasoning." Having
established this identity, he proceeded with his grand undertaking
of electro-chemical research.

[Note 37\13: Dec. 1832. _Researches_, 266.]

The connexion of electrical currents with chemical action, though
kept out of sight in the account we have hitherto given, was never
forgotten by the experimenters; for, in fact, the modes in which
electrical currents were excited, were chemical actions;--the action
of acids and metals on each other in the voltaic trough, or in some
other form. The dependence of the electrical effect on these
chemical actions, and still more, the chemical actions produced by
the agency of the poles of the circuit, had been carefully studied;
and we must now relate with what success.

But in what terms shall we present this narration? We have spoken of
chemical actions,--but what kind of actions are these?
_Decomposition_; the _resolution_ of compounds into their
ingredients; the separation of _acids_ from _bases_; the reduction
of bodies to _simple elements_. These names open to us a new drama;
they are words which belong to a different set of relations of
things, a different train of scientific inductions, a different
system of generalizations, from any with which we have hitherto been
concerned. We must learn to understand these phrases, before we can
advance in our history of human knowledge.

And how are we to learn the meaning of this collection of words? In
what other language shall it be explained? In what terms shall we
define these new expressions? To this we are compelled to reply,
that we cannot translate these terms into any ordinary
language;--that we cannot define them in any terms already familiar
to us. Here, as in all other branches of knowledge, the meaning of
words is to be sought in the progress of thought; the history of
science is our {258} dictionary; the steps of scientific induction
are our definitions. It is only by going back through the successful
researches of men respecting the composition and elements of bodies,
that we can learn in what sense such terms must be understood, so as
to convey real knowledge. In order that they may have a meaning for
us, we must inquire what meaning they had in the minds of the
authors of our discoveries.

And thus we cannot advance a step, till we have brought up our
history of Chemistry to the level of our history of
Electricity;--till we have studied the progress of the analytical,
as well as the mechanical sciences. We are compelled to pause and
look backwards here; just as happened in the history of astronomy,
when we arrived at the brink of the great mechanical inductions of
Newton, and found that we must trace the history of Mechanics,
before we could proceed to mechanical Astronomy. The terms "force,
attraction, inertia, momentum," sent us back into preceding
centuries then, just as the terms "composition" and "element" send
us back now.

Nor is it to a small extent that we have thus to double back upon
our past advance. Next to Astronomy, Chemistry is one of the most
ancient of sciences;--the field of the earliest attempts of man to
command and understand nature. It has held men for centuries by a
kind of fascination; and innumerable and endless are the various
labors, the failures and successes, the speculations and
conclusions, the strange pretences and fantastical dreams, of those
who have pursued it. To exhibit all these, or give any account of
them, would be impossible; and for our design, it would not be
pertinent. To extract from the mass that which is to our purpose, is
difficult; but the attempt must be made. We must endeavor to analyse
the history of Chemistry, so far as it has tended towards the
establishment of general principles. We shall thus obtain a sight of
generalizations of a new kind, and shall prepare ourselves for
others of a higher order.



{{259}}
BOOK XIV.

_THE ANALYTICAL SCIENCE._

HISTORY OF CHEMISTRY.


  . . . . . . . Soon had his crew
  Opened into the hill a spacious wound,
  And digged out ribs of gold . . . .
  Anon out of the earth a fabric huge
  Rose like an exhalation, with the sound
  Of dulcet symphonies and voices sweet,
  Built like a temple.
          MILTON. _Paradise Lost_, i.



{{261}}
CHAPTER I.

IMPROVEMENT OF THE NOTION OF CHEMICAL ANALYSIS, AND RECOGNITION OF
IT AS THE SPAGIRIC ART.


THE doctrine of "the four elements" is one of the oldest monuments
of man's speculative nature; goes back, perhaps, to times anterior
to Greek philosophy; and as the doctrine of Aristotle and Galen,
reigned for fifteen hundred years over the Gentile, Christian, and
Mohammedan world. In medicine, taught as the doctrine of the four
"elementary qualities," of which the human body and all other
substances are compounded, it had a very powerful and extensive
influence upon medical practice. But this doctrine never led to any
attempt actually to analyse bodies into their supposed elements: for
composition was inferred from the resemblance of the qualities, not
from the separate exhibition of the ingredients; the supposed
analysis was, in short, a decomposition of the body into adjectives,
not into substances.

This doctrine, therefore, may be considered as a negative state,
antecedent to the very beginning of chemistry; and some progress
beyond this mere negation was made, as soon as men began to endeavor
to compound and decompound substances by the use of fire or mixture,
however erroneous might be the opinions and expectations which they
combined with their attempts. Alchemy is a step in chemistry, so far
as it implies the recognition of the work of the cupel and the
retort, as the produce of analysis and synthesis. How perplexed and
perverted were the forms in which this recognition was clothed,--how
mixed up with mythical follies and extravagancies, we have already
seen; and the share which Alchemy had in the formation of any
sounder knowledge, is not such as to justify any further notice of
that pursuit.

The result of the attempts to analyse bodies by heat, mixture, and
the like processes, was the doctrine that the first principles of
things are _three_, not four; namely, _salt_, _sulphur_, and
_mercury_; and that, of these three, all things are compounded. In
reality, the doctrine, as thus stated, contained no truth which was
of any value; for, though the chemist could extract from most bodies
portions which he called salt, {262} and sulphur, and mercury, these
names were given, rather to save the hypothesis, than because the
substances were really those usually so called: and thus the
supposed analyses proved nothing, as Boyle justly urged against
them.[1\14]

[Note 1\14: Shaw's Boyle. _Skeptical Chymist_, pp. 312, 313. &c.]

The only real advance in chemical theory, therefore, which we can
ascribe to the school of _the three principles_, as compared with
those who held the ancient dogma of the four elements, is, the
acknowledgment of the changes produced by the chemist's operations,
as being changes which were to be accounted for by the union and
separation of substantial elements, or, as they were sometimes
called, of _hypostatical principles_. The workmen of this school
acquired, no doubt, a considerable acquaintance with the results of
the kinds of processes which they pursued; they applied their
knowledge to the preparation of new medicines; and some of them, as
Paracelsus and Van Helmont, attained, in this way, to great fame and
distinction: but their merits, as regards theoretical chemistry,
consist only in a truer conception of the problem, and of the mode
of attempting its solution, than their predecessors had entertained.

This step is well marked by a word which, about the time of which we
speak, was introduced to denote the chemist's employment. It was
called the _Spagiric art_, (often misspelt _Spagyric_,) from two
Greek words, (σπάω, ἀγείρω,) which mean to _separate_ parts, and to
_unite_ them. These two processes, or in more modern language,
_analysis_ and _synthesis_, constitute the whole business of the
chemist. We are not making a fanciful arrangement, therefore, when
we mark the recognition of this object as a step in the progress of
chemistry. I now proceed to consider the manner in which the
conditions of this analysis and synthesis were further developed.




CHAPTER II.

DOCTRINE OF ACID AND ALKALI.--SYLVIUS.


AMONG the results of mixture observed by chemists, were many
instances in which two ingredients, each in itself pungent or
destructive, being put together, became mild and inoperative; each
{263} counteracting and neutralizing the activity of the other. The
notion of such opposition and neutrality is applicable to a very
wide range of chemical processes. The person who appears first to
have steadily seized and generally applied this notion is Francis de
la Boé Sylvius; who was born in 1614, and practised medicine at
Amsterdam, with a success and reputation which gave great currency
to his opinions on that art.[2\14] His chemical theories were
propounded as subordinate to his medical doctrines; and from being
thus presented under a most important practical aspect, excited far
more attention than mere theoretical opinions on the composition of
bodies could have done. Sylvius is spoken of by historians of
science, as the founder of the _iatro-chemical_ sect among
physicians; that is, the sect which considers the disorders in the
human frame as the effects of chemical relations of the fluids, and
applies to them modes of cure founded upon this doctrine. We have
here to speak, not of his physiological, but of his chemical views.

[Note 2\14: Sprengel. _Geschichte der Arzneykunde_, vol. iv.
Thomson's _History of Chemistry_ in the corresponding part is
translated from Sprengel.]

The distinction of _acid_ and _alkaline_ bodies (_acidum_,
_lixivum_) was familiar before the time of Sylvius; but he framed a
system, by considering them both as eminently acrid and yet
opposite, and by applying this notion to the human frame. Thus[3\14]
the lymph contains an acid, the bile an alkaline salt. These two
opposite acrid substances, when they are brought together,
_neutralize_ each other (_infringunt_), and are changed into an
intermediate and milder substance.

[Note 3\14: _De Methodo Medendi_, Amst. 1679. Lib. ii. cap. 28,
sects. 8 and 53.]

The progress of this doctrine, as a physiological one, is an
important part of the history of medical science in the seventeenth
century; but with that we are not here concerned. But as a chemical
doctrine, this notion of the opposition of acid and alkali, and of
its very general applicability, struck deep root, and has not been
eradicated up to our own time. Boyle, indeed, whose disposition led
him to suspect all generalities, expressed doubts with regard to
this view;[4\14] and argued that the supposition of acid and
alkaline parts in all bodies was precarious, their offices
arbitrary, and the notion of them unsettled. Indeed it was not
difficult to show, that there was no one certain criterion to which
all supposed acids conformed. Yet the general conception of such a
combination as that of acid and alkali was supposed to {264} be,
served so well to express many chemical facts, that it kept its
ground. It is found, for instance, in Lemery's _Chemistry_, which
was one of those in most general use before the introduction of the
phlogistic theory. In this work (which was translated into English
by Keill, in 1698) we find alkalies defined by their effervescing
with acids.[5\14] They were distinguished as the _mineral_ alkali
(soda), the _vegetable_ alkali (potassa), and the _volatile_ alkali
(ammonia). Again, in Macquer's _Chemistry_, which was long the
text-book in Europe during the reign of phlogiston, we find acids
and alkalies, and their union, in which they rob each other of their
characteristic properties, and form neutral salts, stated among the
leading principles of the science.[6\14]

[Note 4\14: Shaw's _Boyle_, iii. p. 432.]

[Note 5\14: Lemery, p. 25.]

[Note 6\14: Macquer, p. 19.]

In truth, the mutual relation of acids to alkalies was the most
essential part of the knowledge which chemists possessed concerning
them. The importance of this relation arose from its being the first
distinct form in which the notion of chemical attraction or affinity
appeared. For the acrid or caustic character of acids and alkalies
is, in fact, a tendency to alter the bodies they touch, and thus to
alter themselves; and the neutral character of the compounds **is
the absence of any such proclivity to change. Acids and alkalies
have a strong disposition to unite. They combine, often with
vehemence, and produce neutral salts; they exhibit, in short, a
prominent example of the chemical attraction, or affinity, by which
two ingredients are formed into a compound. The relation of _acid_
and _base_ in a salt is, to this day, one of the main grounds of all
theoretical reasonings.

The more distinct development of the notion of such chemical
attraction, gradually made its way among the chemists of the latter
part of the seventeenth and the beginning of the eighteenth century,
as we may see in the writings of Boyle, Newton, and their followers.
Beecher speaks of this attraction as a _magnetism_; but I do not
know that any writer in particular, can be pointed out as the person
who firmly established the general notion of _chemical attraction_.

But this idea of chemical attraction became both more clear and more
extensively applicable, when it assumed the form of the doctrine of
_elective_ attractions, in which shape we must now speak of it. {265}




CHAPTER III.

DOCTRINE OF ELECTIVE ATTRACTIONS. GEOFFROY. BERGMAN.


THOUGH the chemical combinations of bodies had already been referred
to attraction, in a vague and general manner, it was impossible to
explain the changes that take place, without supposing the
attraction to be greater or less, according to the nature of the
body. Yet it was some time before the necessity of such a
supposition was clearly seen. In the history of the French Academy
for 1718 (published 1719), the writer of the introductory notice
(probably Fontenelle) says, "That a body which is united to another,
for example, a solvent which has penetrated a metal, should quit it
to go and unite itself with another which we present to it, is a
thing of which the possibility had never been guessed by the most
subtle philosophers, and of which the explanation even now is not
easy." The doctrine had, in fact, been stated by Stahl, but the
assertion just quoted shows, at least, that it was not familiar. The
principle, however, is very clearly stated[7\14] in a memoir in the
same volume, by Geoffroy, a French physician of great talents and
varied knowledge, "We observe in chemistry," he says, "certain
relations amongst different bodies, which cause them to unite. These
relations have their _degrees_ and their _laws_. We observe their
different degrees in this;--that among different matters jumbled
together, which have a certain disposition to unite, we find that
one of these substances always unites constantly with a certain
other, preferably to all the rest." He then states that those which
unite by preference, have "plus de rapport," or, according to a
phrase afterwards used, more _affinity_. "And I have satisfied
myself," he adds, "that we may deduce, from these observations, the
following proposition, which is very extensively true, though I
cannot enunciate it as universal, not having been able to examine
all the possible combinations, to assure myself that I should find
no exception." The proposition which he states in this admirable
spirit of philosophical caution, is this: "In all cases where two
substances, {266} which have any disposition to combine, are united;
if there approaches them a third, which has more affinity with one
of the two, this one unites with the third and lets go the other."
He then states these affinities in the form of a Table; placing a
substance at the head of each column, and other substances in
succession below it, according to the order of their affinities for
the substance which stands at the head. He allows that the
separation is not always complete (an imperfection which he ascribes
to the glutinosity of fluids and other causes), but, with such
exceptions, he defends very resolutely and successfully his Table,
and the notions which it implies.

[Note 7\14: _Mém. Acad. Par._ 1718, p. 202.]

The value of such a tabulation was immense at the time, and is even
still very great; it enabled the chemist to trace beforehand the
results of any operation; since, when the ingredients were given, he
could see which were the strongest of the affinities brought into
play, and, consequently, what compounds would be formed. Geoffroy
himself gave several good examples of this use of his table. It was
speedily adopted into works on chemistry. For instance,
Macquer[8\14] places it at the end of his book; "taking it," as he
says, "to be of great use at the end of an elementary tract, as it
collects into one point of view, the most essential and fundamental
doctrines which are dispersed through the work."

[Note 8\14: Pref., p. 13.]

The doctrine of _Elective Attraction_, as thus promulgated,
contained so large a mass of truth, that it was never seriously
shaken, though it required further development and correction. In
particular the celebrated work of Torbern Bergman, professor at
Upsala, _On Elective Attractions_, published in 1775, introduced
into it material improvements. Bergman observed, that not only the
order of attractions, but the sum of those attractions which had to
form the new compounds, must be taken account of, in order to judge
of the result. Thus,[9\14] if we have a combination of two elements,
_P_, _s_, (potassa and vitriolic acid), and another combination,
_L_, _m_, (lime and muriatic acid,) though _s_ has a greater
affinity for _P_ than for _L_, yet the sum of the attractions of _P_
to _m_, and of _L_ to _s_, is greater than that of the original
compounds, and therefore if the two combinations are brought
together, the new compounds, _P_, _m_, and _L_, _s_, are formed.

[Note 9\14: _Elect. Attract._, p. 19.]

The Table of Elective Attractions, modified by Bergman in pursuance
of these views, and corrected according to the advanced knowledge of
the time, became still more important than before. The next step
{267} was to take into account the quantities of the elements which
combined; but this leads us into a new train of investigation, which
was, indeed, a natural sequel to the researches of Geoffroy and
Bergman.

In 1803, however, a chemist of great eminence, Berthollet, published
a work (_Essai de Statique Chimique_), the tendency of which
appeared to be to throw the subject back into the condition in which
it had been before Geoffroy. For Berthollet maintained that the
rules of chemical combination were not definite, and dependent on
the nature of the substances alone, but indefinite, depending on the
quantity present, and other circumstances. Proust answered him, and
as Berzelius says,[10\14] "Berthollet defended himself with an
acuteness which makes the reader hesitate in his judgment; but the
great mass of facts finally decided the point in favor of Proust."
Before, however, we trace the result of these researches, we must
consider Chemistry as extending her inquiries to combustion as well
as mixture, to airs as well as fluids and solids, and to weight as
well as quality. These three steps we shall now briefly treat of.

[Note 10\14: _Chem._ t. iii. p. 23.]




CHAPTER IV.

DOCTRINE OF ACIDIFICATION AND COMBUSTION.--PHLOGISTIC THEORY.


PUBLICATION _of the Theory by Beccher and Stahl._--It will be
recollected that we are tracing the history of the _progress_ only
of Chemistry, not of its errors;--that we are concerned with
doctrines only so far as they are true, and have remained part of
the received system of chemical truths. The Phlogistic Theory was
deposed and succeeded by the Theory of Oxygen. But this circumstance
must not lead us to overlook the really sound and permanent part of
the opinions which the founders of the phlogistic theory taught.
They brought together, as processes of the same kind, a number of
changes which at first appeared to have nothing in common; as
acidification, combustion, respiration. Now this classification is
true; and its importance remains undiminished, whatever are the
explanations which we adopt of the processes themselves.

The two chemists to whom are to be ascribed the merit of this step,
and the establishment of the _phlogistic theory_ which they
connected {268} with it, are John Joachim Beccher and George Ernest
Stahl; the former of whom was professor at Mentz, and physician to
the Elector of Bavaria (born 1625, died 1682); the latter was
professor at Halle, and afterwards royal physician at Berlin (born
1660, died 1734). These two men, who thus contributed to a common
purpose, were very different from each other. The first was a frank
and ardent enthusiast in the pursuit of chemistry, who speaks of
himself and his employments with a communicativeness and affection
both amusing and engaging. The other was a teacher of great talents
and influence, but accused of haughtiness and moroseness; a
character which is well borne out by the manner in which, in his
writings, he anticipates an unfavorable reception, and defies it.
But it is right to add to this that he speaks of Beccher, his
predecessor, with an ungrudging acknowledgment of obligations to
him, and a vehement assertion of his merit as the founder of the
true system, which give a strong impression of Stahl's justice and
magnanimity.

Beccher's opinions were at first promulgated rather as a correction
than a refutation of the doctrine of the three principles, salt,
sulphur, and mercury. The main peculiarity of his views consists in
the offices which he ascribes to his _sulphur_, these being such as
afterwards induced Stahl to give the name of _Phlogiston_ to this
element. Beccher had the sagacity to see that the reduction of
metals to an earthy form (_calx_), and the formation of sulphuric
acid from sulphur, are operations connected by a general analogy, as
being alike processes of combustion. Hence the metal was supposed to
consist of an earth, and of something which, in the process of
combustion, was separated from it; and, in like manner, sulphur was
supposed to consist of the sulphuric acid, which remained after its
combustion, and of the combustible part or true sulphur, which flew
off in the burning. Beccher insists very distinctly upon this
difference between his element sulphur and the "sulphur" of his
Paracelsian predecessors.

It must be considered as indicating great knowledge and talent in
Stahl, that he perceived so clearly what part of the views of
Beccher was of general truth and permanent value. Though he[11\14]
everywhere gives to Beccher the credit of the theoretical opinions
which he promulgates, ("Beccheriana sunt quæ profero,") it seems
certain that he had the merit, not only of proving them more
completely, and applying them more widely than his forerunner, but
also of conceiving them {269} with a distinctness which Beccher did
not attain. In 1697, appeared Stahl's _Zymotechnia Fundamentalis_
(the Doctrine of Fermentation), "simulque _experimentum novum_
sulphur verum arte producendi." In this work (besides other tenets
which the author considered as very important), the opinion
published by Beccher was now maintained in a very distinct
form;--namely, that the process of forming sulphur from sulphuric
acid, and of restoring the metals from their calces, are analogous,
and consist alike in the addition of some combustible element, which
Stahl termed _phlogiston_ (φλογίστον, _combustible_). The experiment
most insisted on in the work now spoken of,[12\14] was the formation
of sulphur from sulphate of potass (or of soda) by fusing the salt
with an alkali, and throwing in coals to supply phlogiston. This is
the "experimentum novum." Though Stahl published an account of this
process, he seems to have regretted his openness. "He denies not,"
he says, "that he should peradventure have dissembled this
experiment as the true foundation of the Beccherian assertion
concerning the nature of sulphur, if he had not been provoked by the
pretending arrogance of some of his contemporaries."

[Note 11\14: **Stahl, _Præf. ad Specim. Becch._ 1703.]

[Note 12\14: P. 117.]

From this time, Stahl's confidence in his theory may be traced
becoming more and more settled in his succeeding publications. It is
hardly necessary to observe here, that the explanations which his
theory gives are easily transformed into those which the more recent
theory supplies. According to modern views, the addition of oxygen
takes place in the formation of acids and of calces, and in
combustion, instead of the subtraction of phlogiston. The coal which
Stahl supposed to supply the combustible in his experiment, does in
fact absorb the liberated oxygen. In like manner, when an acid
corrodes a metal, and, according to existing theory, combines with
and oxidates it, Stahl supposed that the phlogiston separated from
the metal and combined with the acid. That the explanations of the
phlogistic theory are so generally capable of being translated into
the oxygen theory, merely by inverting the supposed transfer of the
combustible element, shows us how important a step towards the
modern doctrines the phlogistic theory really was.

The question, whether these processes were in fact addition or
subtraction, was decided by the balance, and belongs to a succeeding
period of the science. But we may observe, that both Beccher and
Stahl were aware of the increase of weight which metals undergo in
{270} calcination; although the time had not yet arrived in which
this fact was to be made one of the bases of the theory.

It has been said,[13\14] that in the adoption of the phlogistic
theory, that is, in supposing the above-mentioned processes to be
addition rather than subtraction, "of two possible roads the wrong
was chosen, as if to prove the perversity of the human mind." But we
must not forget how natural it was to suppose that some part of a
body was _destroyed_ or _removed_ by combustion; and we may observe,
that the merit of Beccher and Stahl did not consist in the selection
of one road or two, but in advancing so far as to reach this point
of separation. That, having done this, they went a little further on
the wrong line, was an error which detracted little from the merit
or value of the progress really made. It would be easy to show, from
the writings of phlogistic chemists, what important and extensive
truths their theory enabled them to express simply and clearly.

[Note 13\14: Herschel's _Introd. to Nat. Phil._ p. 300.]

That an enthusiastic temper is favorable to the production of great
discoveries in science, is a rule which suffers no exception in the
character of Beccher. In his preface[14\14] addressed "to the
benevolent reader" of his _Physica Subterranea_, he speaks of the
chemists as a strange class of mortals, impelled by an almost insane
impulse to seek their pleasure among smoke and vapor, soot and
flame, poisons and poverty. "Yet among all these evils," he says, "I
seem to myself to live so sweetly, that, may I die if I would change
places with the Persian king." He is, indeed, well worthy of
admiration, as one of the first who pursued the labors of the
furnace and the laboratory, without the bribe of golden hopes. "My
kingdom," he says, "is not of this world. I trust that I have got
hold of my pitcher by the right handle,--the true method of treating
this study. For the _Pseudochymists_ seek gold; but the _true
philosophers_, science, which is more precious than any gold."

[Note 14\14: Frankfort, 1681.]

The _Physica Subterranea_ made no converts. Stahl, in his indignant
manner, says,[15\14] "No one will wonder that it never yet obtained a
physician or a chemist as a disciple, still less as an advocate." And
again, "This work obtained very little reputation or estimation, or,
to speak ingenuously, as far as I know, none whatever." In 1671,
Beccher published a supplement to his work, in which he showed how
metal might be extracted from mud and sand. He offered to execute
{271} this at Vienna; but found that people there cared nothing about
such novelties. He was then induced, by Baron D'Isola, to go to
Holland for similar purposes. After various delays and quarrels, he
was obliged to leave Holland for fear of his creditors; and then, I
suppose, came to Great Britain, where he examined the Scottish and
Cornish mines. He is said to have died in London in 1682.

[Note 15\14: Præf. _Phys. Sub._ 1703.]

Stahl's publications appear to have excited more notice, and led to
controversy on the "so-called sulphur." The success of the
experiment had been doubted, which, as he remarks, it was foolish to
make a matter of discussion, when any one might decide the point by
experiment; and finally, it had been questioned whether the
substance obtained by this process were pure sulphur. The
originality of his doctrine was also questioned, which, as he says,
could not with any justice be impugned. He published in defence and
development of his opinion at various intervals, as the _Specimen
Beccherianum_ in 1703, the _Documentum Theoriæ Beecherianæ_, a
Dissertation _De Anatomia Sulphuris Artificialis_; and finally,
_Casual Thoughts on the so-called Sulphur_, in 1718, in which he
gave (in German) both a historical and a systematic view of his
opinions on the nature of salts and of his Phlogiston.

_Reception and Application of the Theory._--The theory that the
formation of sulphuric acid, and the restoration of metals from
their calces, are analogous processes, and consist in the addition
of _phlogiston_, was soon widely received; and the Phlogistic School
was thus established. From Berlin, its original seat, it was
diffused into all parts of Europe. The general reception of the
theory may be traced, not only in the use of the term "phlogiston,"
and of the explanations which it implies; but in the adoption of a
nomenclature founded on those explanations, which, though not very
extensive, is sufficient evidence of the prevalence of the theory.
Thus when Priestley, in 1774, discovered oxygen, and when Scheele, a
little later, discovered chlorine, these gases were termed
_dephlogisticated air_, and _dephlogisticated marine acid_; while
azotic acid gas, having no disposition to combustion, was supposed
to be saturated with phlogiston, and was called _phlogisticated air_.

This phraseology kept its ground, till it was expelled by the
antiphlogistic, or oxygen theory. For instance. Cavendish's papers
on the chemistry of the airs are expressed in terms of it, although
his researches led him to the confines of the new theory. We must
now give an account of such researches, and of the consequent
revolution in the science. {272}




CHAPTER V.

CHEMISTRY OF GASES.--BLACK. CAVENDISH.


THE study of the properties of aëriform substances, or Pneumatic
Chemistry, as it was called, occupied the chemists of the eighteenth
century, and was the main occasion of the great advances which the
science made at that period. The most material general truths which
came into view in the course of these researches, were, that gases
were to be numbered among the constituent elements of solid and
fluid bodies; and that, in these, as in all other cases of
composition, the compound was equal to the sum of its elements. The
latter proposition, indeed, cannot be looked upon as a discovery,
for it had been frequently acknowledged, though little applied; in
fact, it could not be referred to with any advantage, till the
aëriform elements, as well as others, were taken into the account.
As soon as this was done, it produced a revolution in chemistry.

[2nd Ed.] [Though the view of the mode in which gaseous elements
become fixed in bodies and determine their properties, had great
additional light thrown upon it by Dr. Black's discoveries, as we
shall see, the notion that solid bodies involve such gaseous
elements was not new at that period. Mr. Vernon Harcourt has
shown[16\14] that Newton and Boyle admitted into their speculations
airs of various kinds, capable of fixation in bodies. I have, in the
succeeding chapter (chap. vi.), spoken of the views of Rey, Hooke,
and Mayow, connected with the function of airs in chemistry, and
forming a prelude to the Oxygen Theory.]

[Note 16\14: _Phil. Mag._ 1846.]

Notwithstanding these preludes, the credit of the first great step
in pneumatic chemistry is, with justice, assigned to Dr. Black,
afterwards professor at Edinburgh, but a young man of the age of
twenty-four at the time when he made his discovery.[17\14] He found
that the difference between caustic lime and common limestone arose
from this, that the latter substance consists of the former,
combined with a certain air, which, being thus fixed in the solid
body, he called _fixed air_ (carbonic {273} acid gas). He found,
too, that magnesia, caustic potash, and caustic soda, would combine
with the same air, with similar results. This discovery consisted,
of course, in a new interpretation of observed changes. Alkalies
appeared to be made caustic by contact with quicklime: at first
Black imagined that they underwent this change by acquiring igneous
matter from the quicklime; but when he perceived that the lime
gained, not lost, in magnitude as it became mild, he rightly
supposed that the alkalies were rendered caustic by imparting their
air to the lime. This discovery was announced in Black's inaugural
dissertation, pronounced in 1755, on the occasion of his taking his
degree of Doctor in the University of Edinburgh.

[Note 17\14: Thomson's _Hist. Chem._ i. 317.]

The chemistry of airs was pursued by other experimenters. The
Honorable Henry Cavendish, about 1765, invented an apparatus, in
which aërial fluids are confined by water, so that they can be
managed and examined. This hydro-pneumatic apparatus, or as it is
sometimes called, _the pneumatic trough_, from that time was one of
the most indispensable parts of the chemist's apparatus.
Cavendish,[18\14] in 1766, showed the identity of the properties of
fixed air derived from various sources; and pointed out the peculiar
qualities of _inflammable air_ (afterwards called hydrogen gas),
which, being nine times lighter than common air, soon attracted
general notice by its employment for raising balloons. The promise
of discovery which this subject now offered, attracted the confident
and busy mind of Priestley, whose _Experiments and Observations on
different kinds of Air_ appeared in 1744-79. In these volumes, he
describes an extraordinary number of trials of various kinds; the
results of which were, the discovery of new kinds of air, namely,
_phlogisticated air_ (azotic gas), _nitrous air_ (nitrous gas), and
_dephlogisticated air_ (oxygen gas).

[Note 18\14: _Phil. Trans._ 1766.]

But the discovery of new substances, though valuable in supplying
chemistry with materials, was not so important as discoveries
respecting their modes of composition. Among such discoveries, that of
Cavendish, published in the _Philosophical Transactions_ for 1784, and
disclosing the composition of water by the union of two gases, oxygen
and hydrogen, must be considered as holding a most distinguished
place. He states,[19\14] that his "experiments were made principally
with a view to find out the cause of the diminution which common air
is well known to suffer, by all the various ways in which it is
phlogisticated." And, after describing various unsuccessful attempts,
he finds {274} that when inflammable air is used in this
phlogistication (or burning), the diminution of the common air is
accompanied by the formation of a dew in the apparatus.[20\14] And
thus he infers[21\14] that "almost all the inflammable air, and
one-fifth of the common air, are turned into pure water."

[Note 19\14: _Phil. Trans._ 1784, p. 119.]

[Note 20\14: _Phil. Trans._ 1784, p. 128.]

[Note 21\14: Ib. p. 129.]

Lavoisier, to whose researches this result was, as we shall soon
see, very important, was employed in a similar attempt at the same
time (1783), and had already succeeded,[22\14] when he learned from
Dr. Blagden, who was present at the experiment, that Cavendish had
made the discovery a few months sooner. Monge had, about the same
time, made the same experiments, and communicated the result to
Lavoisier and Laplace immediately afterwards. The synthesis was soon
confirmed by a corresponding analysis. Indeed the discovery
undoubtedly lay in the direct path of chemical research at the time.
It was of great consequence in the view it gave of experiments in
composition; for the small quantity of water produced in many such
processes, had been quite overlooked; though, as it now appeared,
this water offered the key to the whole interpretation of the change.

[Note 22\14: _A. P._ 1781, p. 472]

Though some objections to Mr. Cavendish's view were offered by
Kirwan,[23\14] on the whole they were generally received with assent
and admiration. But the bearing of these discoveries upon the new
theory of Lavoisier, who rejected phlogiston, was so close, that we
cannot further trace the history of the subject without proceeding
immediately to that theory.

[Note 23\14: _P. T._ 1784, p. 154.]

[2nd Ed.] [I have elsewhere stated,[24\14]--with reference to recent
attempts to deprive Cavendish of the credit of his discovery of the
composition of water, and to transfer it to Watt,--that Watt not
only did not anticipate, but did not fully appreciate the discovery
of Cavendish and Lavoisier; and I have expressed my concurrence with
Mr. Vernon Harcourt's views, when he says,[25\14] that "Cavendish
pared off from the current hypotheses their theory of combustion,
and their affinities of imponderable for ponderable matter, as
complicating chemical with physical considerations; and he then
corrected and adjusted them with admirable skill to the actual
phenomena, not binding the facts to the theory, but adapting the
theory to the facts."

[Note 24\14: _Philosophy_, b. vi. c. 4.]

[Note 25\14: _Address to the British Association_, 1839.]

I conceive that the discussion which the subject has recently
received, has left no doubt on the mind of any one who has perused
the {275} documents, that Cavendish is justly entitled to the honor
of this discovery, which in his own time was never contested. The
publication of his Journals of Experiments[26\14] shows that he
succeeded in establishing the point in question in July, 1781. His
experiments are referred to in an abstract of a paper of
Priestley's, made by Dr. Maty, the secretary of the Royal Society,
in June, 1783. In June, 1783, also, Dr. Blagden communicated the
result of Cavendish's experiments to Lavoisier, at Paris. Watt's
letter, containing his hypothesis that "water is composed of
dephlogisticated air and phlogiston deprived of part of their latent
or elementary heat; and that phlogisticated or pure air is composed
of water deprived of its phlogiston and united to elementary heat
and light," was not read till Nov. 1783; and even if it could have
suggested such an experiment as Cavendish's (which does not appear
likely), is proved, by the dates, to have had no share in doing so.

[Note 26\14: _Appendix_ to Mr. V. Harcourt's _Address_]

Mr. Cavendish's experiment was suggested by an experiment in which
Warltire, a lecturer on chemistry at Birmingham, exploded a mixture
of hydrogen and common air in a close vessel, in order to determine
whether heat were ponderable.]




CHAPTER VI.

EPOCH OF THE THEORY OF OXYGEN.--LAVOISIER.


_Sect._ 1.--_Prelude to the Theory.--Its Publication._

WE arrive now at a great epoch in the history of Chemistry. Few
revolutions in science have immediately excited so much general
notice as the introduction of the theory of oxygen. The simplicity
and symmetry of the modes of combination which it assumed; and,
above all, the construction and universal adoption of a nomenclature
which applied to all substances, and which seemed to reveal their
inmost constitution by their name, naturally gave it an almost
irresistible sway over men's minds. We must, however,
dispassionately trace the course of its introduction. {276}

Antoine Laurent Lavoisier, an accomplished French chemist, had
pursued, with zeal and skill, researches such as those of Black,
Cavendish, and Priestley, which we have described above. In 1774, he
showed that, in the calcination of metals in air, the metal acquires
as much weight as the air loses. It might appear that this discovery
at once overturned the view which supposed the metal to be phlogiston
_added_ to the calx. Lavoisier's contemporaries were, however, far
from allowing this; a greater mass of argument was needed to bring
them to this conclusion. Convincing proofs of the new opinion were,
however, rapidly supplied. Thus, when Priestley had discovered
dephlogisticated air, in 1774, Lavoisier showed, in 1776, that fixed
air consisted of charcoal and the dephlogisticated or pure air; for
the mercurial calx which, heated by itself, gives out pure air, gives
out, when heated with charcoal, fixed air,[27\14] which has,
therefore, since been called _carbonic acid gas_.

[Note 27\14: _Mém. Ac. Par._ 1775.]

Again, Lavoisier showed that the atmospheric air consists of pure or
vital air, and of an _unvital_ air, which he thence called _azot_.
The vital air he found to be the agent in combustion, acidification,
calcination, respiration; all of these processes were analogous: all
consisted in a decomposition of the atmospheric air, and a fixation
of the pure or vital portion of it.

But he thus arrived at the conclusion, that this pure air was added,
in all the cases in which, according to the received theory,
_phlogiston_ was subtracted, and _vice versâ_. He gave the
name[28\14] of _oxygen_ (_principe oxygène_) to "the substance which
thus unites itself with metals to form their calces, and with
combustible substances to form acids."

[Note 28\14: _Mém. Ac. Par._ 1781, p. 448.]

A new theory was thus produced, which would account for all the
facts which the old one would explain, and had besides the evidence
of the balance in its favor. But there still remained some apparent
objections to be removed. In the action of dilute acids on metals,
inflammable air was produced. Whence came this element? The
discovery of the decomposition of water sufficiently answered this
question, and converted the objection into an argument on the side
of the theory: and thus the decomposition of water was, in fact, one
of the most critical events for the fortune of the Lavoisierian
doctrine, and one which, more than any other, decided chemists in
its favor. In succeeding years, Lavoisier showed the consistency of
his theory with {277} all that was discovered concerning the
composition of alcohol, oil, animal and vegetable substances, and
many other bodies.

It is not necessary for us to consider any further the evidence for
this theory, but we must record a few circumstances respecting its
earlier history. Rey, a French physician, had in 1630, published a
book, in which he inquires into the grounds of the increase of the
weight of metals by calcination.[29\14] He says, "To this question,
then, supported on the grounds already mentioned, I answer, and
maintain with confidence, that the increase of weight arises from
the air, which is condensed, rendered heavy and adhesive, by the
heat of the furnace." Hooke and Mayow had entertained the opinion
that the air contains a "nitrous spirit," which is the supporter of
combustion. But Lavoisier disclaimed the charge of having derived
anything from these sources; nor is it difficult to understand how
the received generalizations of the phlogistic theory had thrown all
such narrower explanations into obscurity. The merit of Lavoisier
consisted in his combining the generality of Stahl with the verified
conjectures of Rey and Mayow.

[Note 29\14: Thomson, _Hist. Chem._ ii. 95.]

No one could have a better claim, by his early enthusiasm for
science, his extensive knowledge, and his zealous labors, to hope
that a great discovery might fall to his share, than Lavoisier. His
father,[30\14] a man of considerable fortune, had allowed him to
make science his only profession; and the zealous philosopher
collected about him a number of the most active physical inquirers
of his time, who met and experimented at his house one day in the
week. In this school, the new chemistry was gradually formed. A few
years after the publication of Priestley's first experiments,
Lavoisier was struck with the presentiment of the theory which he
was afterwards to produce. In 1772, he deposited[31\14] with the
secretary of the Academy, a note which contained the germ of his
future doctrines. "At that time," he says, in explaining this step,
"there was a kind of rivalry between France and England in science,
which gave importance to new experiments, and which sometimes was
the cause that the writers of the one or other of the nations
disputed the discovery with the real author." In 1777, the editor of
the Memoirs of the Academy speaks of his theory as overturning that
of Stahl; but the general acceptance of the new opinion did not take
place till later. {278}

[Note 30\14: _Biogr. Univ._ (Cuvier.)]

[Note 31\14: Thomson, ii. 99.]


_Sect._ 2.--_Reception and Confirmation of the Theory of Oxygen._

THE Oxygen Theory made its way with extraordinary rapidity among the
best philosophers.[32\14] In 1785, that is, soon after Cavendish's
synthesis of water had removed some of the most formidable
objections to it, Berthollet, already an eminent chemist, declared
himself a convert. Indeed it was so soon generally adopted in
France, that Fourcroy promulgated its doctrines under the name of
"La Chimie Française," a title which Lavoisier did not altogether
relish. The extraordinary eloquence and success of Fourcroy as a
lecturer at the Jardin des Plantes, had no small share in the
diffusion of the oxygen theory; and the name of "the apostle of the
new chemistry" which was at first given him in ridicule, was justly
held by him to be a glorious distinction.[33\14]

[Note 32\14: Thomson, ii. 130.]

[Note 33\14: Cuvier, _Eloges_, i. p. 20.]

Guyton de Morveau, who had at first been a strenuous advocate of the
phlogistic theory, was invited to Paris, and brought over to the
opinions of Lavoisier; and soon joined in the formation of the
nomenclature founded upon the theory. This step, of which we shall
shortly speak, fixed the new doctrine, and diffused it further.
Delametherie alone defended the phlogistic theory with vigor, and
indeed with violence. He was the editor of the _Journal de
Physique_, and to evade the influence which this gave him, the
antiphlogistians[34\14] established, as the vehicle of their
opinions, another periodical, the _Annales de Chimie_.

[Note 34\14: Thomson, ii. 133.]

In England, indeed, their success was not so immediate.
Cavendish,[35\14] in his Memoir of 1784, speaks of the question
between the two opinions as doubtful. "There are," he says, "several
Memoirs of M. Lavoisier, in which he entirely discards phlogiston; and
as not only the foregoing experiments, but most other phenomena of
nature, seem explicable as well, or nearly as well, upon this as upon
the commonly believed principle of phlogiston," Cavendish proceeds to
explain his experiments according to the new views, expressing no
decided preference, however, for either system. But Kirwan, another
English chemist, contested the point much more resolutely. His theory
identified inflammable air, or hydrogen, with phlogiston; and in this
view, he wrote a work which was intended as a confutation of {279} the
essential part of the oxygen theory. It is a strong proof of the
steadiness and clearness with which the advocates of the new system
possessed their principles, that they immediately translated this
work, adding, at the end of each chapter, a refutation of the
phlogistic doctrines which it contained. Lavoisier, Berthollet, De
Morveau, Fourcroy, and Monge, were the authors of this curious
specimen of scientific polemics. It is also remarkable evidence of the
candor of Kirwan, that notwithstanding the prominent part he had taken
in the controversy, he allowed himself at last to be convinced. After
a struggle of ten years, he wrote[36\14] to Berthollet in 1796, "I lay
down my arms, and abandon the cause of phlogiston." Black followed the
same course. Priestley alone, of all the chemists of great name, would
never assent to the new doctrines, though his own discoveries had
contributed so much to their establishment. "He saw," says
Cuvier,[37\14] "without flinching, the most skilful defenders of the
ancient theory go over to the enemy in succession; and when Kirwan
had, almost the last of all, abjured phlogiston, Priestley remained
alone on the field of battle, and threw out a new challenge, in a
memoir addressed to the principal French chemists." It happened,
curiously enough, that the challenge was accepted, and the arguments
answered by M. Adet, who was at that time (1798,) the French
ambassador to the United States, in which country Priestley's work was
published. Even in Germany, the birth-place and home of the phlogistic
theory, the struggle was not long protracted. There was, indeed, a
controversy, the older philosophers being, as usual, the defenders of
the established doctrines; but in 1792, Klaproth repeated, before the
Academy of Berlin, all the fundamental experiments; and "the result
was a full conviction on the part of Klaproth and the Academy, that
the Lavoisierian theory was the true one."[38\14] Upon the whole, the
introduction of the Lavoisierian theory in the scientific world, when
compared with the great revolution of opinion to which it comes
nearest in importance, the introduction of the Newtonian theory,
shows, by the rapidity and temper with which it took place, a great
improvement, both in the means of arriving at truth, and in the spirit
with which they were used.

[Note 35\14: _Phil. Trans._ 1784, p. 150.]

[Note 36\14: Pref. to Fourcroy's _Chemistry_, xiv.]

[Note 37\14: Cuvier, _Eloge de Priestley_, p. 208.]

[Note 38\14: Thomson, vol. ii. p. 136.]

Some English writers[39\14] have expressed an opinion that there was
{280} little that was original in the new doctrines. But if they
were so obvious, what are we to say of eminent chemists, as Black
and Cavendish, who hesitated when they were presented, or Kirwan and
Priestley, who rejected them? This at least shows that it required
some peculiar insight to see the evidence of these truths. To say
that most of the materials of Lavoisier's theory existed before him,
is only to say that his great merit was, that which must always be
the great merit of a new theory, his generalization. The effect
which the publication of his doctrines produced, shows us that he
was the first person who, possessing clearly the idea of
quantitative composition, applied it steadily to a great range of
well-ascertained facts. This is, as we have often had to observe,
precisely the universal description of an inductive discoverer. It
has been objected, in like manner, to the originality of Newton's
discoveries, that they were contained in those of Kepler. They were
so, but they needed a Newton to find them there. The originality of
the theory of oxygen is proved by the conflict, short as it was,
which accompanied its promulgation; its importance is shown by the
changes which it soon occasioned in every part of the science.

[Note 39\14: Brande, _Hist. Diss._ in _Enc, Brit._ p. 182. Lunn,
_Chem._ in _Enc. Met._ p. 596.]

Thus Lavoisier, far more fortunate than most of those who had, in
earlier ages, produced revolutions in science, saw his theory
accepted by all the most eminent men of his time, and established
over a great part of Europe within a few years from its first
promulgation. In the common course of events, it might have been
expected that the later years of his life would have been spent amid
the admiration and reverence which naturally wait upon the patriarch
of a new system of acknowledged truths. But the times in which he
lived allowed no such euthanasia to eminence of any kind. The
democracy which overthrew the ancient political institutions of
France, and swept away the nobles of the land, was not, as might
have been expected, enthusiastic in its admiration of a great
revolution in science, and forward to offer its homage to the
genuine nobility of a great discoverer. Lavoisier was thrown into
prison on some wretched charge of having, in the discharge of a
public office which he had held, adulterated certain tobacco; but in
reality, for the purpose of confiscating his property.[40\14] In his
imprisonment, his philosophy was his resource; and he employed
himself in the preparation of his papers for printing. When he was
brought before the revolutionary tribunal, he begged for a respite
of a few days, in order to complete some researches, the results of
which {281} were, he said, important to the good of humanity. The
brutish idiot, whom the state of the country at that time had placed
in the judgment-seat, told him that the republic wanted no sçavans.
He was dragged to the guillotine, May the 8th, 1794, and beheaded,
in the fifty-second year of his age; a melancholy proof that, in
periods of political ferocity, innocence and merit, private virtues
and public services, amiable manners and the love of friends,
literary fame and exalted genius, are all as nothing to protect
their possessor from the last extremes of violence and wrong,
inflicted under judicial forms.

[Note 40\14: _Biog. Univ._ (Cuvier.)]


_Sect._ 3.--_Nomenclature of the Oxygen Theory._

AS we have already said, a powerful instrument in establishing and
diffusing the new chemical theory, was a Systematic Nomenclature
founded upon it, and applicable to all chemical compounds, which was
soon constructed and published by the authors of the theory. Such a
nomenclature made its way into general use the more easily, in that
the want of such a system had already been severely felt; the names
in common use being fantastical, arbitrary, and multiplied beyond
measure. The number of known substances had become so great, that a
list of names with no regulative principle, founded on accident,
caprice, and error, was too cumbrous and inconvenient to be
tolerated. Even before the currency which Lavoisier's theory
obtained, these evils had led to attempts towards a more convenient
set of names. Bergman and Black had constructed such lists; and
Guyton de Morveau, a clever and accomplished lawyer of Dijon, had
formed a system of nomenclature in 1782, before he had become a
convert to Lavoisier's theory, in which task he had been exhorted
and encouraged by Bergman and Macquer. In this system,[41\14] we do
not find most of the characters of the method which was afterwards
adopted. But a few years later, Lavoisier, De Morveau, Berthollet
and Fourcroy, associated themselves for the purpose of producing a
nomenclature which should correspond to the new theoretical views.
This appeared in 1787, and soon made its way into general use. The
main features of this system are, a selection of the simplest
radical words, by which substances are designated, and a systematic
distribution of terminations, to express their relations. Thus,
sulphur, combined with oxygen in two different proportions, forms
two acids, the {282} sulphur_ous_ and the sulphur_ic_; and these
acids form, with earthy or alkaline bases, sulph_ides_ and
sulph_ates_; while sulphur directly combined with another element,
forms a sulph_uret_. The term _oxyd_ (now usually written _oxide_)
expressed a lower degree of combination with oxygen than the acids.
The _Méthode de Nomenclature Chimique_ was published in 1787; and in
1789, Lavoisier published a treatise on chemistry in order further
to explain this method. In the preface to this volume, he apologizes
for the great amount of the changes, and pleads the authority of
Bergman, who had exhorted De Morveau "to spare no improper names;
those who are learned will always be learned, and those who are
ignorant will thus learn sooner." To this maxim they so far
conformed, that their system offers few anomalies; and though the
progress of discovery, and the consequent changes of theoretical
opinion, which have since gone on, appear now to require a further
change of nomenclature, it is no small evidence of the skill with
which this scheme was arranged, that for half a century it was
universally used, and felt to be far more useful and effective than
any nomenclature in any science had ever been before.

[Note 41\14: _Journal de Physique_, 1782, p. 370.]




CHAPTER VII.

APPLICATION AND CORRECTION OF THE OXYGEN THEORY.


SINCE a chemical theory, as far as it is true, must enable us to
obtain a true view of the intimate composition of all bodies
whatever, it will readily be supposed that the new chemistry led to
an immense number of analyses and researches of various kinds. These
it is not necessary to dwell upon; nor will I even mention the names
of any of the intelligent and diligent men who have labored in this
field. Perhaps one of the most striking of such analyses was Davy's
decomposition of the earths and alkalies into metallic bases and
oxygen, in 1807 and 1808; thus extending still further that analogy
between the earths and the calces of the metals, which had had so
large a share in the formation of chemical theories. This discovery,
however, both in the means by which it was made, and in the views to
which it led, bears upon subjects hereafter to be treated of.

The Lavoisierian theory also, wide as was the range of truth which
it embraced, required some limitation and correction. I do not now
{283} speak of some erroneous opinions entertained by the author of
the theory; as, for instance, that the heat produced in combustion,
and even in respiration, arose from the conversion of oxygen gas to
a solid consistence, according to the doctrine of latent heat. Such
opinions not being necessarily connected with the general idea of
the theory, need not here be considered. But the leading
generalization of Lavoisier, that acidification was _always_
combination with oxygen, was found untenable. The point on which the
contest on this subject took place was the constitution of the
_oxymuriatic_ and _muriatic_ acids;--as they had been termed by
Berthollet, from the belief that muriatic acid contained oxygen, and
oxymuriatic a still larger dose of oxygen. In opposition to this, a
new doctrine was put forward in 1809 by Gay-Lussac and Thenard in
France, and by Davy in England;--namely, that oxymuriatic acid was a
simple substance, which they termed _chlorine_, and that muriatic
acid was a combination of chlorine with hydrogen, which therefore
was called _hydrochloric acid_. It may be observed, that the point
in dispute in the controversy on this subject was nearly the same
which had been debated in the course of the establishment of the
oxygen theory; namely, whether in the formation of muriatic acid
from chlorine, oxygen is subtracted, or hydrogen added, and the
water concealed.

In the course of this dispute, it was allowed on both sides, that
the combination of dry muriatic acid and ammonia afforded an
_experimentum crucis_; since, if water was produced from these
elements, oxygen must have existed in the acid. Davy being at
Edinburgh in 1812, this experiment was made in the presence of
several eminent philosophers; and the result was found to be, that
though a slight dew appeared in the vessel, there was not more than
might be ascribed to unavoidable imperfection in the process, and
certainly not so much as the old theory of muriatic acid required.
The new theory, after this period, obtained a clear superiority in
the minds of philosophical chemists, and was further supported by
new analogies.[42\14]

[Note 42\14: Paris, _Life of Davy_, i. 337.]

For, the existence of one _hydracid_ being thus established, it was
found that other substances gave similar combinations; and thus
chemists obtained the _hydriodic_, _hydrofluoric_, and _hydrobromic_
acids. These acids, it is to be observed, form salts with bases, in
the same manner as the oxygen acids do. The analogy of the muriatic
and fluoric compounds was first clearly urged by a philosopher who
was {284} not peculiarly engaged in chemical research, but who was
often distinguished by his rapid and happy generalizations, M.
Ampère. He supported this analogy by many ingenious and original
arguments, in letters written to Davy, while that chemist was
engaged in his researches on fluor spar, as Davy himself
declares.[43\14]

[Note 43\14: Paris, _Life of Davy_, i. 370.]

Still further changes have been proposed, in that classification of
elementary substances to which the oxygen theory led. It has been
held by Berzelius and others, that other elements, as, for example,
sulphur, form _salts_ with the alkaline and earthy metals, rather
than sulphurets. The character of these _sulpho-salts_, however, is
still questioned among chemists; and therefore it does not become us
to speak as if their place in history were settled. Of course, it
will easily be understood that, in the same manner in which the
oxygen theory introduced its own proper nomenclature, the overthrow
or material transformation of the theory would require a change in
the nomenclature; or rather, the anomalies which tended to disturb
the theory, would, as they were detected, make the theoretical terms
be felt as inappropriate, and would suggest the necessity of a
reformation in that respect. But the discussion of this point
belongs to a step of the science which is to come before us
hereafter.

It may be observed, that in approaching the limits of this part of
our subject, as we are now doing, the doctrine of the combination of
_acids_ and _bases_, of which we formerly traced the rise and
progress, is still assumed as a fundamental relation by which other
relations are tested. This remark connects the stage of chemistry
now under our notice with its earliest steps. But in order to point
out the chemical bearing of the next subjects of our narrative, we
may further observe, that _metals_, _earths_, _salts_, are spoken of
as known _classes_ of substances; and in like manner the
newly-discovered elements, which form the last trophies of
chemistry, have been distributed into such classes according to
their analogies; thus _potassium_, _sodium_, _barium_, have been
asserted to be metals; _iodine_, _bromine_, _fluorine_, have been
arranged as analogical to _chlorine_. Yet there is something vague
and indefinite in the boundaries of such classifications and
analogies; and it is precisely where this vagueness falls, that the
science is still obscure or doubtful. We are led, therefore, to see
the dependence of Chemistry upon Classification; and it is to
Sciences of Classification which we shall next proceed; as soon as
we have noticed the most general views {285} which have been given
of chemical relations, namely, the views of the electro-chemists.

But before we do this, we must look back upon a law which obtains in
the combination of elements, and which we have hitherto not stated;
although it appears, more than any other, to reveal to us the
intimate constitution of bodies, and to offer a basis for future
generalizations. I speak of the _Atomic Theory_, as it is usually
termed; or, as we might rather call it, the Doctrine of Definite,
Reciprocal, and Multiple Proportions.




CHAPTER VIII.

THEORY OF DEFINITE, RECIPROCAL, AND MULTIPLE PROPORTIONS.


_Sect._ 1.--_Prelude to the Atomic Theory, and its Publication by
Dalton._

THE general laws of chemical combination announced by Mr. Dalton are
truths of the highest importance in the science, and are now nowhere
contested; but the view of matter as constituted of _atoms_, which
he has employed in conveying those laws, and in expressing his
opinion of their cause, is neither so important nor so certain. In
the place which I here assign to his discovery, as one of the great
events of the history of chemistry, I speak only of the _law of
phenomena_, the rules which govern the quantities in which elements
combine.

This law may be considered as consisting of three parts, according
to the above description of it;--that elements combine in _definite_
proportions;--that these determining proportions operate
_reciprocally_;--and that when, between the same elements, several
combining proportions occur, they are related as _multiples_.

That elements combine in certain definite proportions of quantity,
and in no other, was implied, as soon as it was supposed that
chemical compounds had any definite properties. Those who first
attempted to establish regular formulæ[44\14] for the constitution
of salts, minerals, and {286} other compounds, assumed, as the basis
of this process, that the elements in different specimens had the
same proportion. Wenzel, in 1777, published his _Lehre von der
Verwandschaft der Körper_; or, _Doctrine of the Affinities of
Bodies_; in which he gave many good and accurate analyses. His work,
it is said, never grew into general notice. Berthollet, as we have
already stated, maintained that chemical compounds were not
definite; but this controversy took place at a later period. It
ended in the establishment of the doctrine, that there is, for each
combination, only one proportion of the elements, or at most only
two or three.

[Note 44\14: Thomson, _Hist. Chem._ vol. ii. p. 279.]

Not only did Wenzel, by his very attempt, presume the first law of
chemical composition, the definiteness of the proportions, but he
was also led, by his results, to the second rule, that they are
reciprocal. For he found that when two _neutral_ salts decompose
each other, the resulting salts are also neutral. The neutral
character of the salts shows that they are definite compounds; and
when the two elements of the one salt, _P_ and _s_, are presented to
those of the other, _B_ and _n_, if _P_ be in such quantity as to
combine definitely with _n_, _B_ will also combine definitely with
_s_.[45\14]

[Note 45\14: I am told that Wenzel (whose book I have not seen),
though he adduces many cases in which double decomposition gives
neutral salts, does not express the proposition in a general form,
nor use letters in expressing it.]

Views similar to those of Wenzel were also published by Jeremiah
Benjamin Richter[46\14] in 1792, in his _Anfangsgründe der
Stöchyometrie, oder Messkunst Chymischer Elemente_, (_Principles of
the Measure of Chemical Elements_) in which he took the law, just
stated, of reciprocal proportions, as the basis of his researches,
and determined the numerical quantities of the common bases and
acids which would saturate each other. It is clear that, by these
steps, the two first of our three rules may be considered as fully
developed. The change of general views which was at this time going
on, probably prevented chemists from feeling so much interest as
they might have done otherwise, in these details; the French and
English chemists, in particular, were fully employed with their own
researches and controversies.

[Note 46\14: Thomson, _Hist. Chem._ vol. ii. p. 283.]

Thus the rules which had already been published by Wenzel and
Richter had attracted so little notice, that we can hardly consider
Mr. Dalton as having been anticipated by those writers, when, in
1803, he began to communicate his views on the chemical constitution
of {287} bodies; these views being such as to include both these two
rules in their most general form, and further, the rule, at that
time still more new to chemists, of _multiple_ proportions. He
conceived bodies as composed of atoms of their constituent elements,
grouped, either one and one, or one and two, or one and three, and
so on. Thus, if _C_ represent an atom of carbon and _O_ one of
oxygen, _O C_ will be an atom of _carbonic oxide_, and _O C O_ an
atom of _carbonic acid_; and hence it follows, that while both these
bodies have a definite quantity of oxygen to a given quantity of
carbon, in the latter substance this quantity is _double_ of what it
is in the former.

The consideration of bodies as consisting of compound atoms, each of
these being composed of elementary atoms, naturally led to this law
of multiple proportions. In this mode of viewing bodies, Mr. Dalton
had been preceded (unknown to himself) by Mr. Higgins, who, in 1789,
published[47\14] his _Comparative View of the Phlogistic and
Antiphlogistic Theories_. He there says,[48\14] "That in volatile
vitriolic acid, a single ultimate particle of sulphur is united only
to a single particle of dephlogisticated air; and that in perfect
vitriolic acid, every single particle of sulphur is united to two of
dephlogisticated air, being the quantity necessary to saturation;"
and he reasons in the same manner concerning the constitution of
water, and the compounds of nitrogen and oxygen. These observations
of Higgins were, however, made casually, and not followed out, and
cannot affect Dalton's claim to original merit.

[Note 47\14: Turner's _Chem._ p. 217.]

[Note 48\14: P. 36 and 37.]

Mr. Dalton's generalization was first suggested[49\14] during his
examination of olefiant gas and carburetted hydrogen gas; and was
asserted generally, on the strength of a few facts, being, as it
were, irresistibly recommended by the clearness and simplicity which
the notion possessed. Mr. Dalton himself represented the compound
atoms of bodies by symbols, which professed to exhibit the
arrangement of the elementary atoms in space as well as their
numerical proportion; and he attached great importance to this part
of his scheme. It is clear, however, that this part of his doctrine
is not essential to that numerical comparison of the law with facts,
on which its establishment rests. These hypothetical configurations
of atoms have no value till they are confirmed by corresponding
facts, such as the optical or crystalline properties of bodies may
perhaps one day furnish. {288}

[Note 49\14: Thomson, vol. ii. p. 291.]


_Sect._ 2.--_Reception and Confirmation of the Atomic Theory._

IN order to give a sketch of the progress of the Atomic Theory into
general reception, we cannot do better than borrow our information
mainly from Dr. Thomson, who was one of the earliest converts and
most effective promulgators of the doctrine. Mr. Dalton, at the time
when he conceived his theory, was a teacher of mathematics at
Manchester, in circumstances which might have been considered
narrow, if he himself had been less simple in his manner of life,
and less moderate in his worldly views. His experiments were
generally made with apparatus of which the simplicity and cheapness
corresponded to the rest of his habits. In 1804, he was already in
possession of his atomic theory, and explained it to Dr. Thomson,
who visited him at that time. It was made known to the chemical
world in Dr. Thomson's _Chemistry_, in 1807; and in Dalton's own
_System of Chemistry_ (1808) the leading ideas of it were very
briefly stated. Dr. Wollaston's memoir, "on superacid and subacid
salts," which appeared in the _Philosophical Transactions_ for 1808,
did much to secure this theory a place in the estimation of
chemists. Here the author states, that he had observed, in various
salts, the quantities of acid combined with the base in the neutral
and in the superacid salts to be as one to two: and he says that,
thinking it likely this law might obtain generally in such
compounds, it was his design to have pursued this subject, with the
hope of discovering the cause to which so regular a relation may be
ascribed. But he adds, that this appears to be superfluous after the
publication of Dalton's theory by Dr. Thomson, since all such facts
are but special cases of the general law. We cannot but remark here,
that the scrupulous timidity of Wollaston was probably the only
impediment to his anticipating Dalton in the publication of the rule
of multiple proportions; and the forwardness to generalize, which
belongs to the character of the latter, justly secured him, in this
instance, the name of the discoverer of this law. The rest of the
English chemists soon followed Wollaston and Thomson, though Davy
for some time resisted. They objected, indeed, to Dalton's
assumption of atoms, and, to avoid this hypothetical step, Wollaston
used the phrase _chemical equivalents_, and Davy the word
_proportions_, for the numbers which expressed Dalton's atomic
weights. We may, however, venture to say that the term "atom" is the
most convenient, and it need not be understood as claiming our
assent to the hypothesis of indivisible molecules. {289}

As Wollaston and Dalton were thus arriving independently at the same
result in England, other chemists, in other countries, were, unknown
to each other, travelling towards the same point.

In 1807, Berzelius,[50\14] intending to publish a system of
chemistry, went through several works little read, and among others
the treatises of Richter. He was astonished, he tells us, at the
light which was there thrown upon composition and decomposition, and
which had never been turned to profit. He was led to a long train of
experimental research, and, when he received information of Dalton's
ideas concerning multiple proportions, he found, in his own
collection of analyses, a full confirmation of this theory.

[Note 50\14: Berz. _Chem._ B. iii. p. 27.]

Some of the Germans, indeed, appear discontented with the partition
of reputation which has taken place with respect to the Theory of
Definite Proportions. One[51\14] of them says, "Dalton has only done
this;--he has wrapt up the good Richter (whom he knew; compare
Schweigger, T, older series, vol. x., p. 381;) in a ragged suit,
patched together of atoms; and now poor Richter comes back to his
own country in such a garb, like Ulysses, and is not recognized." It
is to be recollected, however, that Richter says nothing of multiple
proportions.

[Note 51\14: Marx. _Gesch. der Cryst._ p. 202.]

The general doctrine of the atomic theory is now firmly established
over the whole of the chemical world. There remain still several
controverted points, as, for instance, whether the atomic weights of
all elements are exact multiples of the atomic weight of hydrogen.
Dr. Prout advanced several instances in which this appeared to be
true, and Dr. Thomson has asserted the law to be of universal
application. But, on the other hand, Berzelius and Dr. Turner
declare that this hypothesis is at variance with the results of the
best analyses. Such controverted points do not belong to our
history, which treats only of the progress of scientific truths
already recognized by all competent judges.

Though Dalton's discovery was soon generally employed, and
universally spoken of with admiration, it did not bring to him
anything but barren praise, and he continued in the humble
employment of which we have spoken, when his fame had filled Europe,
and his name become a household word in the laboratory. After some
years he was appointed a corresponding member of the Institute of
France; which may be considered as a European recognition of the
importance {290} of what he had done; and, in 1826, two medals for
the encouragement of science having been placed at the disposal of
the Royal Society by the King of England, one of them was assigned
to Dalton, "for his development of the atomic theory." In 1833, at
the meeting of the British Association for the Advancement of
Science, which was held in Cambridge, it was announced that the King
had bestowed upon him a pension of 150_l._; at the preceding meeting
at Oxford, that university had conferred upon him the degree of
Doctor of Laws, a step the more remarkable, since he belonged to the
sect of Quakers. At all the meetings of the British Association he
has been present, and has always been surrounded by the reverence
and admiration of all who feel any sympathy with the progress of
science. May he long remain among us thus to remind us of the vast
advance which Chemistry owes to him!

[2nd Ed.] [Soon after I wrote these expressions of hope, the period
of Dalton's sojourn among us terminated. He died on the 27th of
July, 1844, aged 78.

His fellow-townsmen, the inhabitants of Manchester, who had so long
taken a pride in his residence among them, soon after his death came
to a determination to perpetuate his memory by establishing in his
honor a Professor of Chemistry at Manchester.]


_Sect._ 3.--_The Theory of Volumes.--Gay-Lussac._

THE atomic theory, at the very epoch of its introduction into
France, received a modification in virtue of a curious discovery
then made. Soon after the publication of Dalton's system, Gay-Lussac
and Humboldt found a rule for the combination of substances, which
includes that of Dalton as far as it goes, but extends to
combinations of gases only. This law is the _theory of volumes_;
namely, that gases unite together _by volume_ in very simple and
definite proportions. Thus water is composed exactly of 100 measures
of oxygen and 200 measures of hydrogen. And since these simple
ratios 1 and 1, 1 and 2, 1 and 3, alone prevail in such
combinations, it may easily be shown that laws like Dalton's law of
multiple proportions, must obtain in such cases as he considered.

[2nd Ed.] [M. Schröder, of Mannheim, has endeavored to extend to
solids a law in some degree resembling Gay-Lussac's law of the
volumes of gases. According to him, the volumes of the chemical
equivalents {291} of simple substances and their compounds are as
whole numbers.[52\14] MM. Kopp, Playfair, and Joule have labored in
the same field.]

[Note 52\14: _Die molecular-volume der Chemischen Verbindungen in
festen und flüssingen Zustande_, 1843.]

I cannot now attempt to trace other bearings and developments of
this remarkable discovery. I hasten on to the last generalization of
chemistry; which presents to us chemical forces under a new aspect,
and brings us back to the point from which we departed in commencing
the history of this science.




CHAPTER IX.

EPOCH OF DAVY AND FARADAY.


_Sect._ 1.--_Promulgation of the Electro-chemical Theory by Davy._

THE reader will recollect that the History of Chemistry, though
highly important and instructive in itself, has been an interruption
of the History of Electro-dynamic Research:--a necessary
interruption, however; for till we became acquainted with Chemistry
in general, we could not follow the course of Electro-chemistry: we
could not estimate its vast yet philosophical theories, nor even
express its simplest facts. We have now to endeavor to show what has
thus been done, and by what steps;--to give a fitting view of the
Epoch of Davy and Faraday.

This is, doubtless, a task of difficulty and delicacy. We cannot
execute it at all, except we suppose that the great truths, of which
the discovery marks this epoch, have already assumed their definite
and permanent form. For we do not learn the just value and right
place of imperfect attempts and partial advances in science, except
by seeing to what they lead. We judge properly of our trials and
guesses only when we have gained our point and guessed rightly. We
might personify philosophical theories, and might represent them to
ourselves as figures, all pressing eagerly onwards in the same {292}
direction, whom we have to pursue: and it is only in proportion as
we ourselves overtake those figures in the race, and pass beyond
them, that we are enabled to look back upon their faces; to discern
their real aspects, and to catch the true character of their
countenances. Except, therefore, I were of opinion that the great
truths which Davy brought into sight have been firmly established
and clearly developed by Faraday, I could not pretend to give the
history of this striking portion of science. But I trust, by the
view I have to offer of these beautiful trains of research and their
result, to justify the assumption on which I thus proceed.

I must, however, state, as a further appeal to the reader's
indulgence, that, even if the great principles of electro-chemistry
have now been brought out in their due form and extent, the
discovery is but a very few years, I might rather say a few months,
old, and that this novelty adds materially to the difficulty of
estimating previous attempts from the point of view to which we are
thus led. It is only slowly and by degrees that the mind becomes
sufficiently imbued with those new truths, of which the office is,
to change the face of a science. We have to consider familiar
appearances under a new aspect; to refer old facts to new
principles; and it is not till after some time, that the struggle
and hesitation which this employment occasions, subsides into a
tranquil equilibrium. In the newly acquired provinces of man's
intellectual empire, the din and confusion of conquest pass only
gradually into quiet and security. We have seen, in the history of
all capital discoveries, how hardly they have made their way, even
among the most intelligent and candid philosophers of the antecedent
schools: we must, therefore, not expect that the metamorphosis of
the theoretical views of chemistry which is now going on, will be
effected without some trouble and delay.

I shall endeavor to diminish the difficulties of my undertaking, by
presenting the earlier investigations in the department of which I
have now to speak, as much as possible according to the most
deliberate view taken of them by the great discoverers themselves,
Davy and Faraday; since these philosophers are they who have taught
us the true import of such investigations.

There is a further difficulty in my task, to which I might
refer;--the difficulty of speaking, without error and without
offence, of men now alive, or who were lately members of social
circles which exist still around us. But the scientific history in
which such persons play a part, is so important to my purpose, that
I do not hesitate to incur {293} the responsibility which the
narration involves; and I have endeavored earnestly, and I hope not
in vain, to speak as if I were removed by centuries from the
personages of my story.

The phenomena observed in the Voltaic apparatus were naturally the
subject of many speculations as to their cause, and thus gave rise
to "Theories of the Pile." Among these phenomena there was one class
which led to most important results: it was discovered by Nicholson
and Carlisle, in 1800, that water was _decomposed_ by the pile of
Volta; that is, it was found that when the wires of the pile were
placed with their ends near each other in the fluid, a stream of
bubbles of air arose from each wire, and these airs were found on
examination to be oxygen and hydrogen: which, as we have had to
narrate, had already been found to be the constituents of water.
This was, as Davy says,[53\14] the true origin of all that has been
done in electro-chemical science. It was found that other substances
also suffered a like decomposition under the same circumstances.
Certain metallic solutions were decomposed, and an alkali was
separated on the negative plates of the apparatus. Cruickshank, in
pursuing these experiments, added to them many important new
results; such as the decomposition of muriates of magnesia, soda,
and ammonia by the pile; and the general observation that the
alkaline matter always appeared at the _negative_, and the acid at
the _positive_, pole.

[Note 53\14: _Phil. Trans._ 1826, p. 386.]

Such was the state of the subject when one who was destined to do so
much for its advance, first contributed his labors to it. Humphry
Davy was a young man who had been apprenticed to a surgeon at
Penzance, and having shown an ardent love and a strong aptitude for
chemical research, was, in 1798, made the superintendent of a
"Pneumatic Institution," established at Bristol by Dr. Beddoes, for
the purpose of discovering medical powers of factitious airs.[54\14]
But his main attention was soon drawn to galvanism; and when, in
consequence of the reputation he had acquired, he was, in 1801,
appointed lecturer at the Royal Institution in London (then recently
established), he was soon put in possession of a galvanic apparatus
of great power; and with this he was not long in obtaining the most
striking results.

[Note 54\14: Paris, _Life of Davy_, i. 58.]

His first paper on the subject[55\14] is sent from Bristol, in
September, 1800; and describes experiments, in which he had found
that the decompositions observed by Nicholson and Carlisle go on,
although the {294} water, or other substance in which the two wires
are plunged, be separated into two portions, provided these portions
are connected by muscular or other fibres. This use of muscular
fibres was, probably, a remnant of the original disposition, or
accident, by which galvanism had been connected with physiology, as
much as with chemistry. Davy, however, soon went on towards the
conclusion, that the phenomena were altogether chemical in their
nature. He had already conjectured,[56\14] in 1802, that all
decompositions might be _polar_; that is, that in all cases of
chemical decomposition, the elements might be related to each other
as electrically _positive_ and _negative_; a thought which it was
the peculiar glory of his school to confirm and place in a distinct
light. At this period such a view was far from obvious; and it was
contended by many, on the contrary, that the elements which the
voltaic apparatus brought to view, were not liberated from
combinations, but generated. In 1806, Davy attempted the solution of
this question; he showed that the ingredients which had been
supposed to be produced by electricity, were due to impurities in
the water, or to the decomposition of the vessel; and thus removed
all preliminary difficulties. And then he says,[57\14] "referring to
my experiments of 1800, 1801, and 1802, and to a number of new
facts, which showed that inflammable substances and oxygen, alkalies
and acids, and oxidable and noble metals, were in electrical
relations of positive and negative, I drew the conclusion, _that the
combinations and decompositions by electricity were referrible to
the law of electrical attractions and repulsions_," and advanced the
hypothesis, "_that chemical and electrical attractions were produced
by the same cause, acting in the one case on particles, in the other
on masses; . . . and that the same property, under different
modifications, was the cause of all the phenomena exhibited by
different voltaic combinations._"

[Note 55\14: Nicholson's _Journal_, 4to. iv. 275.]

[Note 56\14: _Phil. Trans._ 1826.]

[Note 57\14: Ib. 1826, p. 389.]

Although this is the enunciation, in tolerably precise terms, of the
great discovery of his epoch, it was, at the period of which we
speak, conjectured rather than proved; and we shall find that
neither Davy nor his followers, for a considerable period,
apprehended it with that distinctness which makes a discovery
complete. But in a very short time afterwards, Davy drew great
additional notice to his researches by effecting, in pursuance, as
it appeared, of his theoretical views, the decomposition of potassa
into a metallic base and oxygen. This was, as he truly said, in the
memorandum written in his journal at the {295} instant, "a capital
experiment." This discovery was soon followed by that of the
decomposition of soda; and shortly after, of other bodies of the
same kind; and the interest and activity of the whole chemical world
were turned to the subject in an intense degree.

At this period, there might be noticed three great branches of
speculation on this subject; _the theory of the pile_, _the theory
of electrical decomposition_, and **_the theory of the identity of
chemical and electrical forces_; which last doctrine, however, was
found to include the other two, as might have been anticipated from
the time of its first suggestion.

It will not be necessary to say much on the theories of the voltaic
pile, as separate from other parts of the subject. The
_contact-theory_, which ascribed the action to the contact of
different metals, was maintained by Volta himself; but gradually
disappeared, as it was proved (by Wollaston[58\14] especially,) that
the effect of the pile was inseparably connected with oxidation or
other chemical changes. The theories of electro-chemical
decomposition were numerous, and especially after the promulgation
of Davy's _Memoir_ in 1806; and, whatever might be the defects under
which these speculations for a long time labored, the subject was
powerfully urged on in the direction in which truth lay, by Davy's
discoveries and views. That there remained something still to be
done, in order to give full evidence and consistency to the theory,
appears from this;--that some of the most important parts of Davy's
results struck his followers as extraordinary paradoxes;--for
instance, the fact that the decomposed elements are transferred from
one part of the circuit to another, in a form which escapes the
cognizance of our senses, through intervening substances for which
they have a strong affinity. It was found afterwards that the
circumstance which appeared to make the process so wonderful, was,
in fact, the condition of its going on at all. Davy's expressions
often seem to indicate the most exact notions: for instance, he
says, "It is very natural to suppose that the repellent and
attractive energies are communicated from one particle to another of
the same kind, so as to establish a conducting _chain_ in the fluid;
and that the locomotion takes place in consequence;"[59\14] and yet
at other times he speaks of the element as _attracted_ and
_repelled_ by the metallic surfaces which form the _poles_;--a
different, and, as it appeared afterwards, an untenable view. Mr.
Faraday, who supplied what was wanting, justly notices this
vagueness. {296} He says,[60\14] that though, in Davy's celebrated
Memoir of 1806, the points established are of the utmost value, the
mode of action by which the effects take place is stated very
generally; so generally, indeed, that probably a dozen precise
schemes of electro-chemical action might be drawn up, differing
essentially from each other, yet all agreeing with the statement
there given." And at a period a little later, being reproached by
Davy's brother with injustice in this expression, he substantiated
his assertion by an enumeration of twelve such schemes which had
been published.

[Note 58\14: _Phil. Trans._ 1801, p. 427.]

[Note 59\14: Paris, i. 154.]

[Note 60\14: _Researches_, 482.]

But yet we cannot look upon this Memoir of 1806, otherwise than as a
great event, perhaps the most important event of the epoch now under
review. And as such it was recognized at once all over Europe. In
particular, it received the distinguished honor of being crowned by
the Institute of France, although that country and England were then
engaged in fierce hostility. Buonaparte had proposed a prize of
sixty thousand francs "to the person who by his experiments and
discoveries should advance the knowledge of electricity and
galvanism, as much as Franklin and Volta did;" and "of three
thousand francs for the best experiment which should be made in the
course of each year on the galvanic fluid;" the latter prize was, by
the First Class of the Institute, awarded to Davy.

From this period he rose rapidly to honors and distinctions, and
reached a height of scientific fame as great as has ever fallen to
the lot of a discoverer in so short a time. I shall not, however,
dwell on such circumstances, but confine myself to the progress of
my subject.


_Sect._ 2.--_Establishment of the Electro-chemical Theory by Faraday._

THE defects of Davy's theoretical views will be seen most clearly by
explaining what Faraday added to them. Michael Faraday was in every
way fitted and led to become Davy's successor in his great career of
discovery. In 1812, being then a bookseller's apprentice, he
attended the lectures of Davy, which at that period excited the
highest admiration.[61\14] "My desire to escape from trade," Mr.
Faraday says, "which I thought vicious and selfish, and to enter
into the service of science, which I imagined made its pursuers
amiable and liberal, induced me at last to take the bold and simple
step of writing to Sir H. Davy." He was favorably received, and, in
the next year, became {297} Davy's assistant at the Institution; and
afterwards his successor. The Institution which produced such
researches as those of these two men, may well be considered as a
great school of exact and philosophical chemistry. Mr. Faraday, from
the beginning of his course of inquiry, appears to have had the
consciousness that he was engaged on a great connected work. His
_Experimental Researches_, which appeared in a series of Memoirs in
the _Philosophical Transactions_, are divided into short paragraphs,
numbered into a continued order from 1 up to 1160, at the time at
which I write;[62\14] and destined, probably, to extend much
further. These paragraphs are connected by a very rigorous method of
investigation and reasoning which runs through the whole body of
them. Yet this unity of purpose was not at first obvious. His first
two Memoirs were upon subjects which we have already treated of (B.
xiii. c. 5 and c. 8), Voltaic Induction, and the evolution of
Electricity from Magnetism. His "Third Series" has also been already
referred to. Its object was, as a preparatory step towards further
investigation, to show the identity of voltaic and animal
electricity with that of the electrical machine; and as machine
electricity differs from other kinds in being successively in a
state of tension and explosion, instead of a continued current, Mr.
Faraday succeeded in identifying it with them, by causing the
electrical discharge to pass through a bad conductor into a
discharging-train of vast extent; nothing less, indeed, than the
whole fabric of the metallic gas-pipes and water-pipes of London. In
this Memoir[63\14] it is easy to see already traces of the general
theoretical views at which he had arrived; but these are not
expressly stated till his "Fifth Series;" his intermediate Fourth
Series being occupied by another subsidiary labor on the conditions
of conduction. At length, however, in the Fifth Series, which was
read to the Royal Society in June, 1833, he approaches the theory of
electro-chemical decomposition. Most preceding theorists, and Davy
amongst the number, had referred this result to _attractive powers_
residing in the _poles_ of the apparatus; and had even pretended to
compare the intensity of this attraction at different distances from
the poles. By a number of singularly beautiful and skilful
experiments, Mr. Faraday shows that the phenomena can with no
propriety be {298} ascribed to the attraction of the poles.[64\14]
"As the substances evolved in cases of electro-chemical
decomposition may be made to appear against air,[65\14] which,
according to common language, is not a conductor, nor is decomposed;
or against water,[66\14] which is a conductor, and can be
decomposed; as well as against the metal poles, which are excellent
conductors, but undecomposable; there appears but little reason to
consider this phenomenon generally as due to the attraction or
attractive powers of the latter, when used in the ordinary way,
since similar attractions can hardly be imagined in the former
instances."

[Note 61\14: Paris, ii. 3.]

[Note 62\14: December, 1835. (At present, when I am revising the
second edition, September, 1846, Dr. Faraday has recently published
the "Twenty-first Series" of his _Researches_ ending with paragraph
2453.)]

[Note 63\14: _Phil. Trans._ 1833.]

[Note 64\14: _Researches_, Art. 497]

[Note 65\14: _Researches_, Arts. 465, 469.]

[Note 66\14: 495.]

Faraday's opinion, and, indeed, the only way of expressing the
results of his experiments, was, that the chemical elements, in
obedience to the direction of the voltaic currents established in
the decomposing substance, were evolved, or, as he prefers to say,
_ejected_ at its extremities.[67\14] He afterwards states that the
influence which is present in the electric current may be
described[68\14] as _an axis of power, having_ [at each point]
_contrary forces exactly equal in amount in contrary directions_.

[Note 67\14: 493.]

[Note 68\14: 517.]

Having arrived at this point, Faraday rightly wished to reject the
term _poles_, and other words which could hardly be used without
suggesting doctrines now proved to be erroneous. He considered, in
the case of bodies electrically decomposed, or, as he termed them,
_electrolytes_, the elements as travelling in two opposite
directions; which, with reference to the direction of terrestrial
magnetism, might be considered as naturally east and west; and he
conceived elements as, in this way, arriving at the doors or outlets
at which they finally made their separate appearance. The doors he
called _electrodes_, and, separately, the _anode_ and the
_cathode_;[69\14] and the elements which thus travel he termed the
_anïon_ and the _catïon_ (or _cathïon_).[70\14] By means of this
nomenclature he was able to express his general results with much
more distinctness and facility.

[Note 69\14: 663.]

[Note 70\14: The analogy of the Greek derivation requires _catïon_;
but to make the relation to _cathode_ obvious to the English reader,
and to avoid a violation of the habits of English pronunciation, I
should prefer _cathïon_.]

But this general view of the electrolytical process required to be
pursued further, in order to explain the nature of the action. The
identity of electrical and chemical forces, which had been hazarded
as {299} a conjecture by Davy, and adopted as the basis of chemistry
by Berzelius, could only be established by exact measures and
rigorous proofs. Faraday had, in his proof of the identity of
voltaic and electric agency, attempted also to devise such a measure
as should give him a comparison of their quantity; and in this way
he proved that[71\14] a voltaic group of two small wires of platinum
and zinc, placed near each other, and immersed in dilute acid for
three seconds, yields as much electricity as the electrical battery,
charged by ten turns of a large machine; and this was established
both by its momentary electro-magnetic effect, and by the amount of
its chemical action.[72\14]

[Note 71\14: _Researches_, Art. 371.]

[Note 72\14: 537.]

It was in his "Seventh Series," that he finally established a
principle of definite measurement of the amount of electrolytical
action, and described an instrument which he termed[73\14] a
_volta-electrometer_. In this instrument the amount of action was
measured by the quantity of water decomposed: and it was necessary,
in order to give validity to the mensuration, to show (as Faraday
did show) that neither the size of the electrodes, nor the intensity
of the current, nor the strength of the acid solution which acted on
the plates of the pile, disturbed the accuracy of this measure. He
proved, by experiments upon a great variety of substances, of the
most different kinds, that the electro-chemical action is definite
in amount according to the measurement of the new instrument.[74\14]
He had already, at an earlier period,[75\14] asserted, that _the
chemical power of a current of electricity is in direct proportion
to the absolute quantity of electricity which passes_; but the
volta-electrometer enabled him to fix with more precision the
meaning of this general proposition, as well as to place it beyond
doubt.

[Note 73\14: 739.]

[Note 74\14: Arts. 758, 814.]

[Note 75\14: 377.]

The vast importance of this step in chemistry soon came into view.
By the use of the volta-electrometer, Faraday obtained, for each
elementary substance, a number which represented the relative amount
of its decomposition, and which might properly[76\14] be called its
"electro-chemical equivalent." And the question naturally occurs,
whether these numbers bore any relation to any previously
established chemical measures. The answer is remarkable. _They were
no other than the atomic weights of the Daltonian theory_, which
formed the climax of the previous ascent of chemistry; and thus
here, as everywhere in {300} the progress of science, the
generalizations of one generation are absorbed in the wider
generalizations of the next.

[Note 76\14: 792.]

But in order to reach securely this wider generalization, Faraday
combined the two branches of the subject which we have already
noticed;--the _theory of electrical decomposition_ with the _theory
of the pile_. For his researches on the origin of activity of the
voltaic circuit (his Eighth Series), led him to see more clearly
than any one before him, what, as we have said, the most sagacious
of preceding philosophers had maintained, that the current in the
pile was due to the mutual chemical action of its elements. He was
led to consider the processes which go on in the _exciting-cell_ and
in the decomposing place as of the same kind, but opposite in
direction. The chemical _composition_ of the fluid with the zinc, in
the common apparatus, produces, when the circuit is completed, a
current of electric influence in the wire; and this current, if it
pass through an electrolyte, manifests itself by _decomposition_,
overcoming the chemical affinity which there resists it. An
electrolyte cannot conduct without being decomposed. The forces at
the point of composition and the point of decomposition are of the
same kind, and are opposed to each other by means of the
conducting-wire; the wire may properly be spoken of[77\14] as
_conducting chemical affinity_: it allows two forces of the same
kind to oppose one another;[78\14] electricity is only another mode
of the exertion of chemical forces;[79\14] and we might express all
the circumstances of the voltaic pile without using any other term
than chemical affinity, though that of electricity may be very
convenient.[80\14] Bodies are held together by a definite power,
which, when it ceases to discharge that office, may be thrown into
the condition of an electric current.[81\14]

[Note 77\14: Researches Art. 918.]

[Note 78\14: 910.]

[Note 79\14: 915.]

[Note 80\14: 917.]

[Note 81\14: 855.]

Thus the great principle of the identity of electrical and chemical
action was completely established. It was, as Faraday with great
candor says,[82\14] a confirmation of the general views put forth by
Davy, in 1806, and might be expressed in his terms, that "chemical
and electrical attractions are produced by the same cause;" but it
is easy to see that neither was the full import of these expressions
understood nor were the quantities to which they refer conceived as
measurable quantities, nor was the assertion anything but a
sagacious conjecture, till Faraday gave the interpretation, measure,
and proof, of which we have spoken. The evidence of the
incompleteness of the views of his predecessor we have already
adduced, in speaking of his vague and {301} inconsistent theoretical
account of decomposition. The confirmation of Davy's discoveries by
Faraday is of the nature of Newton's confirmation of the views of
Borelli and Hooke respecting gravity, or like Young's confirmation
of the undulatory theory of Huyghens.

[Note 82\14: 965.]

We must not omit to repeat here the moral which we wish to draw from
all great discoveries, that they depend upon the combination of
_exact facts_ with _clear ideas_. The former of these conditions is
easily illustrated in the case of Davy and Faraday, both admirable
and delicate experimenters. Davy's rapidity and resource in
experimenting were extraordinary,[83\14] and extreme elegance and
ingenuity distinguish almost every process of Faraday. He had
published, in 1829, a work on _Chemical Manipulation_, in which
directions are given for performing in the neatest manner all
chemical processes. Manipulation, as he there truly says, is to the
chemist like the external senses to the mind;[84\14] and without the
supply of fit materials which such senses only can give, the mind
can acquire no real knowledge.

[Note 83\14: Paris, i. 145.]

[Note 84\14: _Pref._ p. ii.]

But still the operations of the mind as well as the information of the
senses, ideas as well as facts, are requisite for the attainment of
any knowledge; and all great steps in science require a peculiar
distinctness and vividness of thought in the discoverer. This it is
difficult to exemplify in any better way than by the discoveries
themselves. Both Davy and Faraday possessed this vividness of mind;
and it was a consequence of this endowment, that Davy's **lectures
upon chemistry, and Faraday's upon almost any subject of physical
philosophy, were of the most brilliant and captivating character. In
discovering the nature of voltaic action, the essential intellectual
requisite was to have a distinct conception of that which Faraday
expressed by the remarkable phrase,[85\14] "_an axis of power having
equal and opposite forces_;" and the distinctness of this idea in
Faraday's mind shines forth in every part of his writings. Thus he
says, the force which determines the decomposition of a body is _in_
the body, not in the poles.[86\14] But for the most part he can of
course only convey this fundamental idea by illustrations. Thus[87\14]
he represents the voltaic circuit by a double circle, studded with the
elements of the circuit, and shows how the _anïons_ travel round it in
one direction, and the _cathïons_ in the opposite. He considers[88\14]
the powers at the two places of action as balancing against each other
through the medium of the conductors, in a manner {302} analogous to
that in which mechanical forces are balanced against each other by the
intervention of the lever. It is impossible to him[89\14] to resist
the idea, that the voltaic current must be preceded by a state of
tension in its interrupted condition, which is relieved when the
circuit is completed. He appears to possess the idea of this kind of
force with the same eminent distinctness with which Archimedes in the
ancient, and Stevinus in the modern history of science, possessed the
idea of pressure, and were thus able to found the science of
mechanics.[90\14] And when he cannot obtain these distinct modes of
conception, he is dissatisfied, and conscious of defect. Thus in the
relation between magnetism and electricity,[91\14] "there appears to
be a link in the chain of effects, a wheel in the physical mechanism
of the action, as yet unrecognized." All this variety of expression
shows how deeply seated is the thought. This conception of Chemical
Affinity as a peculiar influence of force, which, acting in opposite
directions, combines and resolves bodies;--which may be liberated and
thrown into the form of a voltaic current, and thus be transferred to
remote points, and applied in various ways; is essential to the
understanding, as it was to the making, of these discoveries.

[Note 85\14: Art. 517.]

[Note 86\14: Art. 661.]

[Note 87\14: **963.]

[Note 88\14: 917.]

[Note 89\14: Art. 950.]

[Note 90\14: 990.]

[Note 91\14: 1114.]

By those to whom this conception has been conveyed, I venture to
trust that I shall be held to have given a faithful account of this
important event in the history of science. We may, before we quit
the subject, notice one or two of the remarkable subordinate
features of Faraday's discoveries.


_Sect._ 3.--_Consequences of Faraday's Discoveries._

FARADAY'S volta-electrometer, in conjunction with the method he had
already employed, as we have seen, for the comparison of voltaic and
common electricity, enabled him to measure the actual quantity of
electricity which is exhibited, in given cases, in the form of
chemical affinity. His results appeared in numbers of that enormous
amount which so often comes before us in the expression of natural
laws. One grain of water[92\14] will require for its decomposition
as much electricity as would make a powerful flash of lightning. By
further calculation, he finds this quantity to be not less than
800,000 charges of his Leyden battery;[93\14] and this is, by his
theory of the identity of the combining with the decomposing force,
the quantity of electricity {303} which is naturally associated with
the elements of the grain of water, endowing them with their mutual
affinity.

[Note 92\14: **853.]

[Note 93\14: 861.]

Many of the subordinate facts and laws which were brought to light
by these researches, clearly point to generalizations, not included
in that which we have had to consider, and not yet discovered: such
laws do not properly belong to our main plan, which is to make our
way _up to_ the generalizations. But there is one which so evidently
promises to have an important bearing on future chemical theories,
that I will briefly mention it. The class of bodies which are
capable of electrical decomposition is limited by a very remarkable
law: they are such binary compounds only as consist of _single_
proportionals of their elementary principles. It does not belong to
us here to speculate on the possible import of this curious law;
which, if not fully established, Faraday has rendered, at least,
highly probable:[94\14] but it is impossible not to see how closely
it connects the Atomic with the Electro-chemical Theory; and in the
connexion of these two great members of Chemistry, is involved the
prospect of its reaching wider generalizations, and principles more
profound than we have yet caught sight of.

[Note 94\14: Art. 697.]

As another example of this connexion, I will, finally, notice that
Faraday has employed his discoveries in order to decide, in some
doubtful cases, what is the true chemical equivalent;[95\14] "I have
such conviction," he says, "that the power which governs
electro-decomposition and ordinary chemical attractions is the same;
and such confidence in the overruling influence of those natural
laws which render the former definite, as to feel no hesitation in
believing that the latter must submit to them too. Such being the
case, I can have no doubt that, assuming hydrogen as 1, and
dismissing small fractions for the simplicity of expression, the
equivalent number or atomic weight of oxygen is 8, of chlorine 36,
of bromine 78·4, of lead 103·5, of tin 59, &c.; notwithstanding that
a very high authority doubles several of these numbers."

[Note 95\14: 851.]


_Sect._ 4.--_Reception of the Electro-chemical Theory._

THE epoch of establishment of the electro-chemical theory, like
other great scientific epochs, must have its sequel, the period of
its reception and confirmation, application and extension. In that
period we {304} are living, and it must be the task of future
historians to trace its course.

We may, however, say a word on the reception which the theory met
with, in the forms which it assumed, anterior to the labors of
Faraday. Even before the great discovery of Davy, Grotthuss, in
1805, had written upon the theory of electro-chemical decomposition;
but he and, as we have seen, Davy, and afterwards other writers, as
Riffault and Chompré, in 1807, referred the effects to the
poles.[96\14] But the most important attempt to appropriate and
employ the generalization which these discoveries suggested, was
that of Berzelius; who adopted at once the view of the identity, or
at least the universal connexion, of electrical relations with
chemical affinity. He considered,[97\14] that in all chemical
combinations the elements may be considered as electro-positive and
electro-negative; and made this opposition the basis of his chemical
doctrines; in which he was followed by a large body of the chemists
of Germany. He held too that the heat and light, evolved during
cases of powerful combination, are the consequence of the electric
discharge which is at that moment taking place: a conjecture which
Faraday at first spoke of with praise.[98\14] But at a later period
he more sagely says,[99\14] that the flame which is produced in such
cases exhibits but a small portion of the electric power which
really acts. "These therefore may not, cannot, be taken as evidences
of the nature of the action; but are merely incidental results,
incomparably small in relation to the forces concerned, and
supplying no information of the way in which the particles are
active on each other, or in which their forces are finally
arranged." And comparing the evidence which he himself had given of
the principle on which Berzelius's speculations rested, with the
speculations themselves, Faraday justly conceived, that he had
transferred the doctrine from the domain of what he calls _doubtful
knowledge_, to that of inductive certainty.

[Note 96\14: Faraday (_Researches_, Art. 481, 492).]

[Note 97\14: _Ann. Chim._ lxxxvi. 146, for 1813.]

[Note 98\14: _Researches_, Art. 870]

[Note 99\14: 960.]

Now that we are arrived at the starting-place, from which this
well-proved truth, the identity of electric and chemical forces,
must make its future advances, it would be trifling to dwell longer
on the details of the diffusion of that doubtful knowledge which
preceded this more certain science. Our history of chemistry is,
therefore, here at an end. I have, as far as I could, executed my
task; which was, to mark all the {305} great steps of its advance,
from the most unconnected facts and the most imperfect speculations,
to the highest generalization at which chemical philosophers have
yet arrived.

Yet it will appear to our purpose to say a few words on the
connexion of this science with those of which we are next to treat;
and that I now proceed to do.




CHAPTER X.

TRANSITION FROM THE CHEMICAL TO THE CLASSIFICATORY SCIENCES.


IT is the object and the boast of chemistry to acquire a knowledge
of bodies which is more exact and constant than any knowledge
borrowed from their sensible qualities can be; since it penetrates
into their intimate constitution, and discloses to us the invariable
laws of their composition. But yet it will be seen, on a little
reflection, that such knowledge could not have any existence, if we
were not also attentive to their sensible qualities.

The whole fabric of chemistry rests, even at the present day, upon
the opposition of acids and bases: an acid was certainly at first
known by its sensible qualities, and how otherwise, even now, do we
perceive its quality? It was a great discovery of modern times that
earths and alkalies have for their bases metals: but what are
_metals_? or how, except from lustre, hardness, weight, and the
like, do we recognize a body as a metal? And how, except by such
characters, even before its analysis, was it known to be an earth or
an alkali? We must suppose some classification established, before
we can make any advance by experiment or observation.

It is easy to see that all attempts to avoid this difficulty by
referring to processes and analogies, as well as to substances,
bring us back to the same point in a circle of fallacies. If we say
that an acid and alkali are known by combining with each other, we
still must ask, What is the criterion that they have _combined_? If
we say that the distinctive qualities of metals and earths are, that
metals become earths by oxidation, we must still inquire how we
recognize the process of _oxidation_? We have seen how important a
part combustion plays in the history of chemical speculation; and we
may usefully form such classes of {306} bodies as _combustibles_ and
_supporters of combustion_. But even _combustion_ is not capable of
being infallibly known, for it passes by insensible shades into
oxidation. We can find no basis for our reasonings, which does not
assume a classification of obvious facts and qualities.

But any classification of substances on such grounds, appears, at
first sight, to involve us in vagueness, ambiguity, and
contradiction. Do we really take the sensible qualities of an acid
as the criterion of its being an acid?--for instance, its sourness?
Prussic acid, arsenious acid, are not sour. "I remember," says Dr.
Paris,[100\14] "a chemist having been exposed to much ridicule from
speaking of a _sweet_ acid,--why not?" When Davy had discovered
potassium, it was disputed whether it was a metal; for though its
lustre and texture are metallic, it is so light as to swim on water.
And if potassium be allowed to be a metal, is silicium one, a body
which wants the metallic lustre, and is a non-conductor of
electricity? It is clear that, at least, the _obvious_ application
of a classification by physical characters, is attended with endless
perplexity.

[Note 100\14: _Life of Davy_, i. 263.]

But since we cannot even begin our researches without assuming a
classification, and since the forms of such a classification which
first occur, end in apparent confusion, it is clear that we must
look to our philosophy for a solution of this difficulty; and must
avoid the embarrassments and contradictions of casual and
unreflective classification, by obtaining a consistent and
philosophical arrangement. We must employ external characters and
analogies in a connected and systematic manner; we must have
_Classificatory Sciences_, and these must have a bearing even on
Chemistry.

Accordingly, the most philosophical chemists now proceed upon this
principle. "The method which I have followed," says M. Thenard, in
his _Traité de Chimie_, published in 1824, "is, to unite in one
group all analogous bodies; and the advantage of this method, which
is that employed by naturalists, is very great, especially in the
study of the metals and their compounds."[101\14] In this, as in all
good systems of chemistry, which have appeared since the
establishment of the phlogistic theory, combustion, and the
analogous processes, are one great element in the arrangement, while
the difference of metallic and non-metallic, is another element.
Thus Thenard, in the first place, speaks of Oxygen; in the next
place, of the Non-metallic Combustibles, as Hydrogen, Carbon,
Sulphur, Chlorine; and in the next place, of Metals. But the Metals
are again divided into six Sections, with reference, {307}
principally, to their facility of combination with oxygen. Thus, the
First Section is the Metals of the Earths; the Second, the Metals of
the Alkalies; the Third, the Easily Oxidable Metals, as Iron; the
Fourth, Metals Less Oxidable, as Copper and Lead; the Fifth Section
contains only Mercury and Osmium; and the Sixth, what were at an
earlier period termed the _Noble_ Metals, Gold, Silver, Platinum,
and others.

[Note 101\14: Pref., p. viii.]

How such principles are to be applied, so as to produce a definite
and consistent arrangement, will be explained in speaking of the
philosophy of the Classificatory Sciences; but there are one or two
peculiarities in the classes of bodies thus recognized by modern
chemistry, which it may be useful to notice.

1. The distinction of Metallic and Non-metallic is still employed,
as of fundamental importance. The discovery of new metals is so much
connected with the inquiries concerning chemical elements, that we
may notice the general progress of such discoveries. _Gold_,
_Silver_, _Iron_, _Copper_, _Quicksilver_, _Lead_, _Tin_, were known
from the earliest antiquity. In the beginning of the sixteenth
century, mine-directors, like George Agricola, had advanced so far
in practical metallurgy, that they had discovered the means of
extracting three additional metals, _Zinc_, _Bismuth_, _Antimony_.
After this, there was no new metal discovered for a century, and
then such discoveries were made by the theoretical chemists, a race
of men who had not existed before Beccher and Stahl. Thus _Arsenic_
and _Cobalt_ were made known by Brandt, in the middle of the
eighteenth century, and we have a long list of similar discoveries
belonging to the same period; _Nickel_, _Manganese_, and _Tungsten_,
which were detected by Cronstedt, Gahn, and Scheele, and Delhuyart,
respectively; metals of a very different kind, _Tellurium_ and
_Molybdenum_, which were brought to light by Müller, Scheele,
Bergman, and Hielm; _Platinum_, which was known as early as 1741,
but with the ore of which, in 1802 and 1803, the English chemists,
Wollaston and Tennant, found that no less than four other new metals
(_Palladium_, _Rhodium_, _Iridium_ and _Osmium_) were associated.
Finally, (omitting some other new metals,) we have another period of
discovery, opened in 1807, by Davy's discovery of _Potassium_, and
including the resolution of all, or almost all, the alkalies and
earths into metallic bases.

[2nd Ed.] [The next few years made some, at least some conjectural,
additions to the list of simple substances, detected by a more
minute scrutiny of known substances. _Thorium_ was discovered by
Berzelius in 1828; and _Vanadium_ by Professor Sefström in 1830. A
{308} metal named _Cerium_, was discovered in 1803, by Hisinger and
Berzelius, in a rare Swedish mineral known by the name of Cerit.
Mosander more recently has found combined with Cerium, other new
metals which he has called _Lanthanium_, _Didymium_, _Erbium_, and
_Terbium_: M. Klaus has found a new metal, _Ruthenium_, in the ore
of Platinum; and Rose has discovered in Tantalite two other new
metals, which he has announced under the names of _Pelopium_ and
_Niobium_. Svanberg is said to have discovered a new earth in
Eudialyt, which is supposed to have, like the rest, a new radical.
If these last discoveries be confirmed, the number of simple
substances will be raised to _sixty-two_.]

2. Attempts have been made to indicate the classification of
chemical substances by some peculiarity in the Name; and the Metals,
for example, have been designated generally by names in _um_, like
the Latin names of the ancient metals, _aurum_, _ferrum_. This
artifice is a convenient nomenclature for the purpose of marking a
recognized difference; and it would be worth the while of chemists
to agree to make it universal, by writing molybden_um_ and
platin_um_; which is sometimes done, but not always.

3. I am not now to attempt to determine how far this
class,--Metals,--extends; but where the analogies of the class cease
to hold there the nomenclature must also change. Thus, some
chemists, as Dr. Thomson, have conceived that the base of Silica is
more analogous to Carbon and Boron, which form acids with oxygen,
than it is to the metals: and he has accordingly associated this
base with these substances, and has given it the same termination,
_Silicon_. But on the validity of this analogy chemists appear not
to be generally agreed.

4. There is another class of bodies which have attracted much notice
among modern chemists, and which have also been assimilated to each
other in the form of their names; the English writers calling them
_Chlorine_, _Fluorine_, _Iodine_, _Bromine_, while the French use
the terms _Chlore_, _Phtore_, _Iode_, _Brome_. We have already
noticed the establishment of the doctrine--that muriatic acid is
formed of a base, chlorine, and of hydrogen,--as a great reform in
the oxygen theory; with regard to which rival claims were advanced
by Davy, and by MM. Gay-Lussac and Thenard in 1800. Iodine, a
remarkable body which, from a dark powder, is converted into a
violet-colored gas by the application of heat, was also, in 1813,
the subject of a similar rivalry between the same English and French
chemists. Bromine {309} was only discovered as late as 1826; and
Fluorine, or _Phtore_, as, from its destructive nature, it has been
proposed to term it, has not been obtained as a separate substance,
and is inferred to exist by analogy only. The analogies of these
bodies (Chlore, Phtore, &c.) are very peculiar; for instance, by
combination with metals they form salts; by combination with
hydrogen they form very strong acids; and all, at the common
temperature of the atmosphere, operate on other bodies in the most
energetic manner. Berzelius[102\14] proposes to call them
_halogenous_ bodies, or _halogenes_.

[Note 102\14: _Chem._ i. 262.]

5. The number of Elementary Substances which are at present
presented in our treatises of chemistry[103\14] is _fifty-three_, [or
rather, as we have said above, _sixty-two_.] It is naturally often
asked what evidence we have, that all these are _elementary_, and
what evidence that they are _all_ the elementary bodies;--how we
know that new elements may not hereafter be discovered, or these
supposed simple bodies resolved into simpler still? To these
questions we can only answer, by referring to the history of
chemistry;--by pointing out what chemists have understood by
analysis, according to the preceding narrative. They have
considered, as the analysis of a substance, that elementary
constitution of it which gives the only intelligible explanation of
the results of chemical manipulation, and which is proved to be
complete as to quantity, by the balance, since the whole can only be
equal to all its parts. It is impossible to maintain that new
substances may not hereafter be discovered; for they may lurk, even
in familiar substances, in doses so minute that they have not yet
been missed amid the inevitable slight inaccuracies of all analysis;
in the way in which iodine and bromine remained so long undetected
in sea-water; and new minerals, or old ones not yet sufficiently
examined, can hardly fail to add something to our list. As to the
possibility of a further analysis of our supposed simple bodies, we
may venture to say that, in regard to such supposed simple bodies as
compose a numerous and well-characterized class, no such step can be
made, except through some great change in chemical theory, which
gives us a new view of all the general relations which chemistry has
yet discovered. The proper evidence of the reality of any supposed
new analysis is, that it is more consistent with the known analogies
of chemistry, to suppose the process analytical than synthetical.
Thus, as has already been said, chemists admit the existence of
fluorine, from the analogy of chlorine; and Davy, when it was found
{310} that ammonia formed an amalgam with mercury, was tempted to
assign to it a metallic basis. But then he again hesitates,[104\14]
and doubts whether the analogies of our knowledge are not better
preserved by supposing that ammonia, as a compound of hydrogen and
another principle, is "a type of the composition of the metals."

[Note 103\14: Turner, p. 971.]

[Note 104\14: _Elem. Chem. Phil._ 1812, p. 481.]

Our history, which is the history of what we know, has little to do
with such conjectures. There are, however, some not unimportant
principles which bear upon them, and which, as they are usually
employed, belong to the science which next comes under our review,
Mineralogy.



{{311}}
BOOK XV.

_THE ANALYTICO-CLASSIFICATORY SCIENCE._

HISTORY OF MINERALOGY.


  Κρύσταλλον φαέθοντα διαυγέα λάζεο χερσὶ,
  Λᾶαν ἀπόῤῥοιαν περιφεγγέος ἀμβρότου αἴγλης,
  Αἰθέρι δ' ἀθανάτων μέγα τέρπεται ἄφθιτον ἦτορ.
  Τόν κ' εἴπερ μετὰ χειρὰς ἔχων, περὶ νηὸν ἵκηαι,
  Οὔτις τοι μακάρων ἀρνήσεται εὐχωλῆσι.
          ORPHEUS. _Lithica._

  Now, if the bold but pious thought be thine,
  To reach our spacious temple's inner shrine,
  Take in thy reverent hands the crystal stone,
  Where heavenly light in earthy shroud is shown:--
  Where, moulded into measured form, with rays
  Complex yet clear, the eternal Ether plays;
  This if thou firmly hold and rightly use,
  Not long the gods thy ardent wish refuse.



{{313}}
INTRODUCTION.


_Sect._ 1.--_Of the Classificatory Sciences._

THE horizon of the sciences spreads wider and wider before us, as we
advance in our task of taking a survey of the vast domain. We have
seen that the existence of Chemistry as a science which declares the
ingredients and essential constitution of all kinds of bodies,
implies the existence of another corresponding science, which shall
divide bodies into kinds, and point out steadily and precisely what
bodies they are which we have analysed. But a science thus dividing
and defining bodies, is but one member of an order of sciences,
different from those which we have hitherto described; namely, of
the _classificatory sciences_. Such sciences there must be, not only
having reference to the bodies with which chemistry deals, but also
to all things respecting which we aspire to obtain any general
knowledge, as, for instance, plants and animals. Indeed it will be
found, that it is with regard to these latter objects, to organized
beings, that the process of scientific classification has been most
successfully exercised; while with regard to inorganic substances,
the formation of a satisfactory system of arrangement has been found
extremely difficult; nor has the necessity of such a system been
recognised by chemists so distinctly and constantly as it ought to
be. The best exemplification of these branches of knowledge, of
which we now have to speak, will, therefore, be found in the organic
world, in Botany and Zoology; but we will, in the first place, take
a brief view of the science which classifies inorganic bodies, and
of which Mineralogy is hitherto the very imperfect representative.

The principles and rules of the Classificatory Sciences, as well as
of those of the other orders of sciences, must be fully explained
when we come to treat of the Philosophy of the Sciences; and cannot
be introduced here, where we have to do with history only. But I may
observe very briefly, that with the process of _classing_, is joined
the process of _naming_;--that names imply classification;--and that
even the rudest and earliest application of language presupposes a
distribution of objects according to their kinds;--but that such a
spontaneous {314} and unsystematic distribution cannot, in the cases
we now have to consider, answer the purposes of exact and general
knowledge. Our classification of objects must be made consistent and
systematic, in order to be scientific; we must discover marks and
characters, properties and conditions, which are constant in their
occurrence and relations; we must form our classes, we must impose
our names, according to such marks. We can thus, and thus alone,
arrive at that precise, certain, and systematic knowledge, which we
seek; that is, at science. The object, then, of the classificatory
sciences is to obtain FIXED CHARACTERS of the kinds of things; and
the criterion of the fitness of names is, that THEY MAKE GENERAL
PROPOSITIONS POSSIBLE.

I proceed to review the progress of certain sciences on these
principles, and first, though briefly, the science of Mineralogy.


_Sect._ 2.--_Mineralogy as the Analytico-classificatory Science._

MINERALOGY, as it has hitherto been cultivated, is, as I have
already said, an imperfect representative of the department of human
knowledge to which it belongs. The attempts at the science have
generally been made by collecting various kinds of information
respecting mineral bodies; but the science which we require is a
complete and consistent classified system of all inorganic bodies.
For chemistry proceeds upon the principle that the constitution of a
body invariably determines its properties; and, consequently, its
kind: but we cannot apply this principle, except we can speak with
precision of the _kind_ of a body, as well as of its composition. We
cannot attach any sense to the assertion, that "soda or baryta has a
metal for its base," except we know what _a metal_ is, or at least
what properties it implies. It may not be, indeed it is not,
possible, to define the kinds of bodies by words only; but the
classification must proceed by some constant and generally
applicable process; and the knowledge which has reference to the
classification will be precise as far as this process is precise,
and vague as far as this is vague.

There must be, then, as a necessary supplement to Chemistry, a
Science of those properties of bodies by which we divide them into
_kinds_. Mineralogy is the branch of knowledge which has discharged
the office of such a science, so far as it has been discharged; and,
indeed, Mineralogy has been gradually approaching to a clear
consciousness of her real place, and of her whole task; I shall give
the history of some of the advances which have thus been made. They
are, principally, {315} the establishment and use of External
Characters, especially of _Crystalline Form_, as a fixed character
of definite substances; and the attempts to bring into view the
connexion of Chemical Constitution and External Properties, made in
the shape of mineralogical _Systems_; both those in which _chemical
methods of arrangement_ are adopted, and those which profess to
classify by the _natural-history method_.



{{316}}
CRYSTALLOGRAPHY.




CHAPTER I.

PRELUDE TO THE EPOCH OF DE LISLE AND HAÜY.


OF all the physical properties of bodies, there is none so fixed,
and in every way so remarkable, as this;--that the same chemical
compound always assumes, with the utmost precision, the same
geometrical form. This identity, however, is not immediately
obvious; it is often obscured by various mixtures and imperfections
in the substance; and even when it is complete, it is not
immediately recognized by a common eye, since it consists, not in
the equality of the sides or faces of the figures, but in the
equality of their angles. Hence it is not surprising that the
constancy of form was not detected by the early observers. Pliny
says,[1\15] "Why crystal is generated in a hexagonal form, it is
difficult to assign a reason; and the more so, since, while its
faces are smoother than any art can make them, the pyramidal points
are _not all of the same kind_." The quartz crystals of the Alps, to
which he refers, are, in some specimens, very regular, while in
others, one side of the pyramid becomes much the largest; yet the
angles remain constantly the same. But when the whole shape varied
so much, the angles also seemed to vary. Thus Conrad Gessner, a very
learned naturalist, who, in 1564, published at Zurich his work, _De
rerum Fossilium, Lapidum et Gemmarum maxime, Figuris_, says,[2\15]
"One crystal differs from another in its angles, and consequently in
its figure." And Cæsalpinus, who, as we shall find, did so much in
establishing fixed characters in botany, was led by some of his
general views to disbelieve the fixity of the form of crystals. In
his work _De Metallicis_, published at Nuremberg in 1602, he
says,[3\15] "To ascribe to inanimate bodies a definite form, does
not appear consentaneous to reason; for it is the office of
organization to produce a definite form;" {317} an opinion very
natural in one who had been immersed in the study of the general
analogies of the forms of plants. But though this is excusable in
Cæsalpinus, the rejection of this definiteness of form a hundred
years later, when its existence had been proved, and its laws
developed by numerous observers, cannot be ascribed to anything but
strong prejudice; yet this was the course taken by no less a person
than Buffon. "The form of crystallization," says he,[4\15] "is _not
a constant character_, but is more equivocal and more variable than
any other of the characters by which minerals are to be
distinguished." And accordingly, he makes no use of this most
important feature in his history of minerals. This strange
perverseness may perhaps be ascribed to the dislike which Buffon is
said to have entertained for Linnæus, who had made crystalline form
a leading character of minerals.

[Note 1\15: _Nat. Hist._ xxvii. 2.]

[Note 2\15: p. 25.]

[Note 3\15: p. 97.]

[Note 4\15: _Hist. des Min._ p. 343.]

It is not necessary to mark all the minute steps by which
mineralogists were gradually led to see clearly the nature and laws
of the fixity of crystalline forms. These forms were at first
noticed in that substance which is peculiarly called rock-crystal or
quartz; and afterwards in various stones and gems, in salts obtained
from various solutions, and in snow. But those who observed the
remarkable regular figures which these substances assume, were at
first impelled onwards in their speculations by the natural tendency
of the human mind to generalize and guess, rather than to examine
and measure. They attempted to snatch at once the general laws of
geometrical regularity of these occurrences, or to connect them with
some doctrine concerning formative causes. Thus Kepler,[5\15] in his
_Harmonics of the World_, asserts a "_formatrix facultas_, which has
its seat in the entrails of the earth, and, after the manner of a
pregnant woman, expresses the five regular geometrical solids in the
forms of gems." But Philosophers, in the course of time, came to
build more upon observation, and less upon abstract reasonings.
Nicolas Steno, a Dane, published, in 1669, a dissertation _De Solido
intra Solidum Naturaliter contento_, in which he says,[6\15] that
though the sides of the hexagonal crystal may vary, _the angles are
not changed_. And Dominic Gulielmini, in a _Dissertation on Salts_,
published in 1707, says,[7\15] in a true inductive spirit, "Nature
does not employ all figures, but only certain ones of those which
are possible; and of these, the determination is not to be fetched
from the brain, or proved _à priori_, but obtained by experiments
and observations." And {318} he speaks[8\15] with entire decision on
this subject: "Nevertheless since there is here a principle of
crystallization, the inclination of the planes and of the angles is
always constant." He even anticipates, very nearly, the views of
later crystallographers as to the mode in which crystals are formed
from elementary molecules. From this time, many persons labored and
speculated on this subject; as Cappeller, whose _Prodromus
Crystallographiæ_ appeared at Lucern in 1723; Bourguet, who
published _Lettres Philosophiques sur la Formation de Sels et de
Cristaux_, at Amsterdam, in 1792; and Henckel, the "Physicus" of the
Elector of Saxony, whose _Pyritologia_ came forth in 1725. In this
last work we have an example of the description of the various forms
of special classes of minerals, (iron pyrites, copper pyrites, and
arsenic pyrites;) and an example of the enthusiasm which this
apparently dry and laborious study can excite: "Neither tongue nor
stone," he exclaims,[9\15] "can express the satisfaction which I
received on setting eyes upon this sinter covered with galena; and
thus it constantly happens, that one must have more pleasure in what
seems worthless rubbish, than in the purest and most precious ores,
if we know aught of minerals."

[Note 5\15: Linz. 1619, p. 161.]

[Note 6\15: p. 69.]

[Note 7\15: p. 19.]

[Note 8\15: p. 83.]

[Note 9\15: p. 343.]

Still, however, Henckel[10\15] disclaims the intention of arranging
minerals according to their mathematical forms; and this, which may
be considered as the first decided step in the formation of
crystallographic mineralogy, appears to have been first attempted by
Linnæus. In this attempt, however, he was by no means happy; nor
does he himself appear to have been satisfied. He begins his preface
by saying, "Lithology is not what I plume myself upon." (_Lithologia
mihi cristas non eriget_.) Though his sagacity, as a natural
historian, led him to see that crystalline form was one of the most
definite, and therefore most important, characters of minerals, he
failed in profiting by this thought, because, in applying it, he did
not employ the light of geometry, but was regulated by what appeared
to him resemblances, arbitrarily selected, and often
delusive.[11\15] Thus he derived the form of pyrites from that of
vitriol;[12\15] and brought together alum and diamond on account of
their common octohedral form. But he had the great merit of
animating to this study one to whom, more perhaps than to any other
person, it owes its subsequent progress; I mean Romé de Lisle.
"Instructed," this writer says, in his preface to his _Essais de
Crystallographie_, "by the works of the celebrated Von Linnée, how
{319} greatly the study of the angular form of crystals might become
interesting, and fitted to extend the sphere of our mineralogical
knowledge, I have followed them in all their metamorphoses with the
most scrupulous attention." The views of Linnæus, as to the
importance of this character, had indeed been adopted by several
others; as John Hill, the King's gardener at Kew, who, in 1777,
published his _Spathogenesia_; and Grignon, who, in 1775, says,
"These crystallizations may give the means of finding a new theory
of the generation of crystalline gems."

[Note 10\15: p. 167.]

[Note 11\15: Marx. _Gesch._ p. 97.]

[Note 12\15: _Syst. Nat._ vi. p. 220.]

The circumstance which threw so much difficulty in the way of those
who tried to follow out his thought was, that in consequence of the
apparent irregularity of crystals, arising from the extension or
contraction of particular sides of the figure, each kind of
substance may really appear under many different forms, connected
with each other by certain geometrical relations. These may be
conceived by considering a certain fundamental form to be cut into
new forms in particular ways. Thus if we take a cube, and cut off
all the eight corners, till the original faces disappear, we make it
an octohedron; and if we stop short of this, we have a figure of
fourteen faces, which has been called a _cubo-octohedron_. The first
person who appears distinctly to have conceived this _truncation_ of
angles and edges, and to have introduced the word, is
Démeste;[13\15] although Wallerius[14\15] had already said, in
speaking of the various crystalline forms of calcspar, "I conceive
it would be better not to attend to all differences, lest we be
overwhelmed by the number." And Werner, in his celebrated work _On
the External Characters of Minerals_,[15\15] had formally spoken of
_truncation_, _acuation_, and _acumination_, or replacement by a
plane, an edge, a point respectively, (_abstumpfung_, _zuschärfung_,
_zuspitzung_,) as ways in which the forms of crystals are modified
and often disguised. He applied this process in particular to show
the connexion of the various forms which are related to the cube.
But still the extension of the process to the whole range of minerals
and other crystalline bodies, was due to Romé de Lisle. {320}

[Note 13\15: _Lettres_, 1779, i. 48.]

[Note 14\15: _Systema Mineralogicum_, 1772-5, i. 143.]

[Note 15\15:  Leipzig, 1774.]




CHAPTER II.

EPOCH OF ROMÉ DE LISLE AND HAÜY.--ESTABLISHMENT OF THE FIXITY OF
CRYSTALLINE ANGLES, AND THE SIMPLICITY OF THE LAWS OF DERIVATION.


WE have already seen that, before 1780, several mineralogists had
recognized the constancy of the angles of crystals, and had seen (as
Démeste and Werner,) that the forms were subject to modifications of
a definite kind. But neither of these two thoughts was so
apprehended and so developed, as to supersede the occasion for a
discoverer who should put forward these principles as what they
really were, the materials of a new and complete science. The merit
of this step belongs jointly to Romé de Lisle and to Haüy. The
former of these two men had already, in 1772, published an _Essai de
Crystallographie_, in which he had described a number of crystals.
But in this work his views are still rude and vague; he does not
establish any connected sequence of transitions in each kind of
substance, and lays little or no stress on the angles. But in 1783,
his ideas[16\15] had reached a maturity which, by comparison,
excites our admiration. In this he asserts, in the most distinct
manner, the _invariability_ of the angles of crystals of each kind,
under all the changes of relative dimension which the faces may
undergo;[17\15] and he points out that this invariability applies
only to the _primitive forms_, from each of which many secondary
forms are derived by various changes.[18\15] Thus we cannot deny him
the merit of having taken steady hold on both the handles of this
discovery, though something still remained for another to do. Romé
pursues his general ideas into detail with great labor and skill. He
gives drawings of more than five hundred regular forms (in his first
work he had inserted only one hundred and ten; Linnæus only knew
forty); and assigns them to their proper substances; for instance,
thirty to calcspar, and sixteen to felspar. He also invented and
used a goniometer. We cannot doubt that he would have been {321}
looked upon as a great discoverer, if his fame had not been dimmed
by the more brilliant success of his contemporary Haüy.

[Note 16\15: _Cristallographie, ou Description de Formes propres à
tous les Corps du Règne Minéral._ 3 vols. and 1 vol. of plates.]

[Note 17\15: p. 68.]

[Note 18\15: p. 73.]

Réné-Just Haüy is rightly looked upon as the founder of the modern
school of crystallography; for all those who have, since him,
pursued the study with success, have taken his views for their
basis. Besides publishing a system of crystallography and of
mineralogy, far more complete than any which had yet appeared, the
peculiar steps in the advance which belong to him are, the discovery
of the importance of _cleavage_, and the consequent expression of
the laws of derivation of secondary from primary forms, by means of
the _decrements_ of the successive layers of _integrant molecules_.

The latter of these discoveries had already been, in some measure,
anticipated by Bergman, who had, in 1773, conceived a hexagonal
prism to be built up by the juxtaposition of solid rhombs on the
planes of a rhombic nucleus.[19\15] It is not clear[20\15] whether
Haüy was acquainted with Bergman's Memoir, at the time when the
cleavage of a hexagonal prism of calcspar, accidentally obtained,
led him to the same conception of its structure. But however this
might be, he had the indisputable credit of following out this
conception with all the vigor of originality, and with the most
laborious and persevering earnestness; indeed he made it the
business of his life. The hypothesis of a solid, built up of small
solids, had this peculiar advantage in reference to crystallography;
it rendered a reason of this curious fact;--that a certain series of
forms occur in crystals of the same kind, while other forms,
apparently intermediate between those which actually occur, are
rigorously excluded. The doctrine of decrements explained this; for
by placing a number of regularly-decreasing rows of equal solids,
as, for instance, of bricks, upon one another, we might form a
regular equal-sided triangle, as the gable of a house; and if the
breadth of the gable were one hundred bricks, the height of the
triangle might be one hundred, or fifty, or twenty-five; but it
would be found that if the height were an intermediate number, as
fifty-seven, or forty-three, the edge of the wall would become
irregular; and such irregularity is assumed to be inadmissible in
the regular structure of crystals. Thus this mode of conceiving
crystals allows of certain definite secondary forms, and no others.

[Note 19\15: _De Formis Crystallorum._ Nov. Act. Reg. Soc. Sc. Ups.
1773.]

[Note 20\15: _Traité de Minér._ 1822, i. 15.]

The mathematical deduction of the dimensions and proportions {322}
of these secondary forms;--the invention of a notation to express
them;--the examination of the whole mineral kingdom in accordance
with these views;--the production of a work[21\15] in which they are
explained with singular clearness and vivacity;--are services by
which Haüy richly earned the admiration which has been bestowed upon
him. The wonderful copiousness and variety of the forms and laws to
which he was led, thoroughly exercised and nourished the spirit of
deduction and calculation which his discoveries excited in him. The
reader may form some conception of the extent of his labors, by
being told--that the mere geometrical propositions which he found it
necessary to premise to his special descriptions, occupy a volume
and a half of his work;--that his diagrams are nearly a thousand in
number;--that in one single substance (calcspar) he has described
forty-seven varieties of form;--and that he has described one kind
of crystal (called by him _fer sulfuré parallélique_) which has one
hundred and thirty-four faces.

[Note 21\15: _Traité de Minéralogie_, 1801, 5 vols.]

In the course of a long life, he examined, with considerable care,
all the forms he could procure of all kinds of mineral; and the
interpretation which he gave of the laws of those forms was, in many
cases, fixed, by means of a name applied to the mineral in which the
form occurred; thus, he introduced such names as _équiaxe_,
_métastatique_, _unibinaire_, _perihexahèdre_, _bisalterne_, and
others. It is not now desirable to apply separate names to the
different forms of the same mineral species, but these terms
answered the purpose, at the time, of making the subjects of study
more definite. A symbolical notation is the more convenient mode of
designating such forms, and such a notation Haüy invented; but the
symbols devised by him had many inconveniences, and have since been
superseded by the systems of other crystallographers.

Another of Haüy's leading merits was, as we have already intimated,
to have shown, more clearly than his predecessors had done, that the
crystalline angles of substances are a criterion of the substances;
and that this is peculiarly true of the _angles of cleavage_;--that
is, the angles of those edges which are obtained by cleaving a
crystal in two different directions;--a mode of division which the
structure of many kinds of crystals allowed him to execute in the
most complete manner. As an instance of the employment of this
criterion, I may mention his separation of the sulphates of baryta
and strontia, which had {323} previously been confounded. Among
crystals which in the collections were ranked together as "heavy
spar," and which were so perfect as to admit of accurate
measurement, he found that those which were brought from Sicily, and
those of Derbyshire, differed in their cleavage angle by three
degrees and a half. "I could not suppose," he says,[22\15] "that
this difference was the effect of any law of decrement; for it would
have been necessary to suppose so rapid and complex a law, that such
an hypothesis might have been justly regarded as an abuse of the
theory." He was, therefore, in great perplexity. But a little while
previous to this, Klaproth had discovered that there is an earth
which, though in many respects it resembles baryta, is different
from it in other respects; and this earth, from the place where it
was found (in Scotland), had been named _Strontia_. The French
chemists had ascertained that the two earths had, in some cases,
been mixed or confounded; and Vauquelin, on examining the Sicilian
crystals, found that their base was strontia, and not, as in the
Derbyshire ones, baryta. The riddle was now read; all the crystals
with the larger angle belong to the one, all those with the smaller,
to the other, of these two sulphates; and crystallometry was clearly
recognized as an authorized test of the difference of substances
which nearly resemble each other.

[Note 22\15: _Traité_, ii. 320.]

Enough has been said, probably, to enable the reader to judge how
much each of the two persons, now under review, contributed to
crystallography. It would be unwise to compare such contributions to
science with the great discoveries of astronomy and chemistry; and
we have seen how nearly the predecessors of Romé and Haüy had
reached the point of knowledge on which these two crystallographers
took their stand. But yet it is impossible not to allow, that in
these discoveries, which thus gave form and substance to the science
of crystallography, we have a manifestation of no common sagacity
and skill. Here, as in other discoveries, were required ideas and
facts;--clearness of geometrical conception which could deal with
most complex relations of form; a minute and extensive acquaintance
with actual crystals; and the talent and habit of referring these
facts to the general ideas. Haüy, in particular, was happily endowed
for his task. Without being a great mathematician, he was
sufficiently a geometer to solve all the problems which his
undertaking demanded; and though the mathematical reasoning might
have been made more compendious {324} by one who was more at home in
mathematical generalization, probably this could hardly have been
done without making the subject less accessible and less attractive
to persons moderately disciplined in mathematics. In all his
reasonings upon particular cases, Haüy is acute and clear; while his
general views appear to be suggested rather by a lively fancy than
by a sage inductive spirit: and though he thus misses the character
of a great philosopher, the vivacity of style, and felicity and
happiness of illustration, which grace his book, and which agree
well with the character of an Abbé of the old French monarchy, had a
great and useful influence on the progress of the subject.

Unfortunately Romé de Lisle and Haüy were not only rivals, but in
some measure enemies. The former might naturally feel some vexation
at finding himself, in his later years (he died in 1790), thrown
into shade by his more brilliant successor. In reference to Haüy's
use of cleavage, he speaks[23\15] of "innovators in crystallography,
who may properly be called _crystalloclasts_." Yet he adopted, in
great measure, the same views of the formation of crystals by
laminæ,[24\15] which Haüy illustrated by the destructive process at
which he thus sneers. His sensitiveness was kept alive by the
conduct of the Academy of Sciences, which took no notice of him and
his labors;[25\15] probably because it was led by Buffon, who
disliked Linnæus, and might dislike Romé as his follower; and who,
as we have seen, despised crystallography. Haüy revenged himself by
rarely mentioning Romé in his works, though it was manifest that his
obligations to him were immense; and by recording his errors while
he corrected them. More fortunate than his rival, Haüy was, from the
first, received with favor and applause. His lectures at Paris were
eagerly listened to by persons from all quarters of the world. His
views were, in this manner, speedily diffused; and the subject was
soon pursued, in various ways, by mathematicians and mineralogists
in every country of Europe.

[Note 23\15: Pref. p. xxvii.]

[Note 24\15: T. ii. p. 21.]

[Note 25\15: Marx. _Gesch. d. Cryst._ 130.]




CHAPTER III.

RECEPTION AND CORRECTIONS OF THE HAUÏAN CRYSTALLOGRAPHY.


I HAVE not hitherto noticed the imperfections of the
crystallographic views and methods of Haüy, because my business in
the last section {325} was to mark the permanent additions he made
to the science. His system did, however, require completion and
rectification in various points; and in speaking of the
crystallographers of the subsequent time, who may all be considered
as the cultivators of the Hauïan doctrines, we must also consider
what they did in correcting them.

The three main points in which this improvement was needed were;--a
better determination of the crystalline forms of the special
substances;--a more general and less arbitrary method of considering
crystalline forms according to their symmetry; and a detection of
more general conditions by which the crystalline angle is regulated.
The first of these processes may be considered as the natural sequel
of the Hauïan epoch: the other two must be treated as separate steps
of discovery.

When it appeared that the angle of natural or of cleavage faces
could be used to determine the differences of minerals, it became
important to measure this angle with accuracy. Haüy's measurements
were found very inaccurate by many succeeding crystallographers:
Mohs says[26\15] that they are so generally inaccurate, that no
confidence can be placed in them. This was said, of course,
according to the more rigorous notions of accuracy to which the
establishment of Haüy's system led. Among the persons who
principally labored in ascertaining, with precision, the crystalline
angles of minerals, were several Englishmen, especially Wollaston,
Phillips, and Brooke. Wollaston, by the invention of his Reflecting
Goniometer, placed an entirely new degree of accuracy within the
reach of the crystallographer; the angle of two faces being, in this
instrument, measured by means of the reflected images of bright
objects seen in them, so that the measure is the more accurate the
more minute the faces are. In the use of this instrument, no one was
more laborious and successful than William Phillips, whose power of
apprehending the most complex forms with steadiness and clearness,
led Wollaston to say that he had "a geometrical sense." Phillips
published a Treatise on Mineralogy, containing a great collection of
such determinations; and Mr. Brooke, a crystallographer of the same
exact and careful school, has also published several works of the
same kind. The precise measurement of crystalline angles must be the
familiar employment of all who study crystallography; and,
therefore, any further enumeration of those {326} who have added in
this way to the stock of knowledge, would be superfluous.

[Note 26\15: Marx. p. 153.]

Nor need I dwell long on those who added to the knowledge which Haüy
left, of derived forms. The most remarkable work of this kind was
that of Count Bournon, who published a work on a single mineral
(calcspar) in three quarto volumes.[27\15] He has here given
representations of seven hundred forms of crystals, of which,
however, only fifty-six are essentially different. From this example
the reader may judge what a length of time, and what a number of
observers and calculators, were requisite to exhaust the subject.

[Note 27\15: _Traité complet de la Chaux Carbonatée et d'Aragonite_,
par M. le Comte de Bournon. London, 1808.]

If the calculations, thus occasioned, had been conducted upon the
basis of Haüy's system, without any further generalization, they
would have belonged to that process, the natural sequel of inductive
discoveries, which we call _deduction_; and would have needed only a
very brief notice here. But some additional steps were made in the
upward road to scientific truth, and of these we must now give an
account.




CHAPTER IV.

ESTABLISHMENT OF THE DISTINCTION OF SYSTEMS OF
CRYSTALLIZATION.--WEISS AND MOHS.


IN Haüy's views, as generally happens in new systems, however true,
there was involved something that was arbitrary, something that was
false or doubtful, something that was unnecessarily limited. The
principal points of this kind were;--his having made the laws of
crystalline derivation depend so much upon cleavage;--his having
assumed an atomic constitution of bodies as an essential part of his
system; and his having taken a set of primary forms, which, being
selected by no general view, were partly superfluous, and partly
defective.

How far evidence, such as has been referred to by various
philosophers, has proved, or can prove, that bodies are constituted
of indivisible atoms, will be more fully examined in the work which
treats of the Philosophy of this subject. There can be little doubt
that the {327} portion of Haüy's doctrine which most riveted popular
attention and applause, was his dissection of crystals, in a manner
which was supposed to lead actually to their ultimate material
elements. Yet it is clear, that since the solids given by cleavage
are, in many cases, such as cannot make up a solid space, the
primary conception of a necessary geometrical identity between the
results of division and the elements of composition, which is the
sole foundation of the supposition that crystallography points out
the actual elements, disappears on being scrutinized: and when Haüy,
pressed by this difficulty, as in the case of fluor-spar, put his
integrant octohedral molecules together, touching by the edges only,
his method became an empty geometrical diagram, with no physical
meaning.

The real fact, divested of the hypothesis which was contained in the
fiction of decrements, was, that when the relation of the derivative
to the primary faces is expressed by means of numerical indices,
these numbers are integers, and generally very small ones; and this
was the form which the law gradually assumed, as the method of
derivation was made more general and simple by Weiss and others.

"When, in 1809, I published my Dissertation," says Weiss,[28\15] "I
shared the common opinion as to the necessity of the assumption and
the reality of the existence of a primitive form, at least in a
sense not very different from the usual sense of the expression.
While I sought," he adds, referring to certain doctrines of general
philosophy which he and others entertained, "a _dynamical_ ground
for this, instead of the untenable atomistic view, I found that, out
of my primitive forms, there was gradually unfolded to my hands,
that which really governs them, and is not affected by their casual
fluctuations, the fundamental relations of those Dimensions
according to which a multiplicity of internal oppositions,
necessarily and mutually interdependent, are developed in the mass,
each having its own polarity; so that the crystalline character is
co-extensive with these polarities."

[Note 28\15: _Mem. Acad. Berl._ 1816, p. 307.]

The "Dimensions" of which Weiss here speaks, are the _Axes of
Symmetry_ of the crystal; that is, those lines in reference to
which, every face is accompanied by other faces, having like
positions and properties. Thus a rhomb, or more properly a
_rhombohedron_,[29\15] of {328} calcspar may be placed with one of
its obtuse corners uppermost, so that all the three faces which meet
there are equally inclined to the vertical line. In this position,
every derivative face, which is obtained by any modification of the
faces or edges of the rhombohedron, implies either three or six such
derivative faces; for no one of the three upper faces of the
rhombohedron has any character or property different from the other
two; and, therefore, there is no reason for the existence of a
derivative from one of these primitive faces, which does not equally
hold for the other primitive faces. Hence the derivative forms will,
in all cases, contain none but faces connected by this kind of
correspondence. The axis thus made vertical will be an Axis of
Symmetry, and the crystal will consist of three divisions, ranged
round this axis, and exactly resembling each other. According to
Weiss's nomenclature, such a crystal is "three-and-three-membered."

[Note 29\15: I use this name for the solid figure, since _rhomb_ has
always been used for a plane figure.]

But this is only one of the kinds of symmetry which crystalline
forms may exhibit. They may have _three axes_ of complete and
_equal_ symmetry at right angles to each other, as the cube and the
regular octohedron;--or, _two axes_ of equal symmetry, perpendicular
to each other and to a _third axis_, which is not affected with the
same symmetry with which they are; such a figure is a square
pyramid;--or they may have _three_ rectangular _axes_, all of
_unequal_ symmetry, the modifications referring to each axis
separately from the other two.

These are essential and necessary distinctions of crystalline form;
and the introduction of a classification of forms founded on such
relations, or, as they were called, _Systems of Crystallization_,
was a great improvement upon the divisions of the earlier
crystallographers, for those divisions were separated according to
certain arbitrarily-assumed primary forms. Thus Romé de Lisle's
fundamental forms were, the tetrahedron, the cube, the octohedron,
the rhombic prism, the rhombic octohedron, the dodecahedron with
triangular faces: Haüy's primary forms are the cube, the
rhombohedron, the oblique rhombic prism, the right rhombic prism,
the rhombic dodecahedron, the regular octohedron, tetrahedron, and
six-sided prism, and the bipyramidal dodecahedron. This division, as
I have already said, errs both by excess and defect, for some of
these primary forms might be made derivatives from others; and no
solid reason could be assigned why they were not. Thus the cube may
be derived from the tetrahedron, by truncating the edges; and the
rhombic dodecahedron again from the cube, by truncating its edges;
while the square pyramid could not be legitimately identified with
the derivative of any of these forms; for if we were to {329} derive
it from the rhombic prism, why should the acute angles always suffer
decrements corresponding in a certain way to those of the obtuse
angles, as they must do in order to give rise to a square pyramid?

The introduction of the method of reference to Systems of
Crystallization has been a subject of controversy, some ascribing
this valuable step to Weiss, and some to Mohs.[30\15] It appears, I
think, on the whole, that Weiss first published works in which the
method is employed; but that Mohs, by applying it to all the known
species of minerals, has had the merit of making it the basis of
real crystallography. Weiss, in 1809, published a Dissertation _On
the mode of investigating the principal geometrical character of
crystalline forms_, in which he says,[31\15] "No part, line, or
quantity, is so important as the axis; no consideration is more
essential or of a higher order than the relation of a crystalline
plane to the axis;" and again, "An axis is any line governing the
figure, about which all parts are similarly disposed, and with
reference to which they correspond mutually." This he soon followed
out by examination of some difficult cases, as Felspar and Epidote.
In the Memoirs of the Berlin Academy,[32\15] for 1814-15, he
published _An Exhibition of the natural Divisions of Systems of
Crystallization_. In this Memoir, his divisions are as follows:--The
_regular_ system, the _four-membered_, the _two-and-two-membered_,
the _three-and-three-membered_, and some others of inferior degrees
of symmetry. These divisions are by Mohs (_Outlines of Mineralogy_,
1822), termed the _tessular_, _pyramidal_, _prismatic_, and
_rhombohedral_ systems respectively. Hausmann, in his
_Investigations concerning the Forms of Inanimate Nature_,[33\15]
makes a nearly corresponding arrangement;--the _isometric_,
_monodimetric_, _trimetric_, and _monotrimetic_; and one or other of
these sets of terms have been adopted by most succeeding writers.

[Note 30\15: _Edin. Phil. Trans._ 1823, vols. xv. and xvi.]

[Note 31\15: pp. 16, 42.]

[Note 32\15: Ibid.]

[Note 33\15: Göttingen, 1821.]

In order to make the distinctions more apparent, I have purposely
omitted to speak of the systems which arise when the _prismatic_
system loses some part of its symmetry;--when it has only half or a
quarter its complete number of faces;--or, according to Mohs's
phraseology, when it is _hemihedral_ or _tetartohedral_. Such
systems are represented by the singly-oblique or doubly-oblique
prism; they are termed by Weiss _two-and-one-membered_, and
_one-and-one-membered_; by other writers, _Monoklinometric_, and
_Triklinometric_ Systems. There are also other {330} peculiarities
of Symmetry, such, for instance, as that of the _plagihedral_ faces
of quartz, and other minerals.

The introduction of an arrangement of crystalline forms into
systems, according to their degree of symmetry, was a step which was
rather founded on a distinct and comprehensive perception of
mathematical relations, than on an acquaintance with experimental
facts, beyond what earlier mineralogists had possessed. This
arrangement was, however, remarkably confirmed by some of the
properties of minerals which attracted notice about the time now
spoken of, as we shall see in the next chapter.




CHAPTER V.

RECEPTION AND CONFIRMATION OF THE DISTINCTION OF SYSTEMS OF
CRYSTALLIZATION.


DIFFUSION OF THE DISTINCTION OF SYSTEMS.--The distinction of systems
of crystallization was so far founded on obviously true views, that
it was speedily adopted by most mineralogists. I need not dwell on
the steps by which this took place. Mr. Haidinger's translation of
Mohs was a principal occasion of its introduction in England. As an
indication of dates, bearing on this subject, perhaps I may be
allowed to notice, that there appeared in the _Philosophical
Transactions for_ 1825, _A General Method of Calculating the
**Angles of Crystals_, which I had written, and in which I referred
only to Haüy's views; but that in 1826,[34\15] I published a Memoir
_On the Classification of Crystalline Combinations_, founded on the
methods of Weiss and Mohs, especially the latter; with which I had
in the mean time become acquainted, and which appeared to me to
contain their own evidence and recommendation. General methods, such
as was attempted in the Memoir just quoted, are part of that process
in the history of sciences, by which, when the principles are once
established, the mathematical operation of deducing their
consequences is made more and more general and symmetrical: which we
have seen already exemplified in the history of celestial mechanics
after the time of Newton. It does not enter into our plan, to dwell
upon the various steps in this way {331} made by Levy, Naumann,
Grassmann, Kupffer, Hessel, and by Professor Miller among ourselves.
I may notice that one great improvement was, the method introduced
by Monteiro and Levy, of determining the laws of derivation of
forces by means of the _parallelisms of edges_; which was afterwards
extended so that faces were considered as belonging to _zones_. Nor
need I attempt to enumerate (what indeed it would be difficult to
describe in words) the various methods of _notation_ by which it has
been proposed to represent the faces of crystals, and to facilitate
the calculations which have reference to them.

[Note 34\15: _Camb. Trans._ vol. ii. p. 391.]

[2nd Ed.] [My Memoir of 1825 depended on the views of Haüy in so far
as that I started from his "primitive forms;" but being a general
method of expressing all forms by co-ordinates, it was very little
governed by these views. The mode of representing crystalline forms
which I proposed seemed to contain its own evidence of being more
true to nature than Haüy's theory of decrements, inasmuch as my
method expressed the faces at much lower numbers. I determine a face
by means of the dimensions of the primary form _divided_ by certain
numbers; Haüy had expressed the face virtually by the same
dimensions _multiplied_ by numbers. In cases where my notation gives
such numbers as (3, 4, 1), (1, 3, 7), (5, 1, 19), his method
involves the higher numbers (4, 3, 12), (21, 7, 3), (19, 95, 5). My
method however has, I believe, little value as a method of
"_calculating_ the angles of crystals."

M. Neumann, of Königsberg, introduced a very convenient and elegant
mode of representing the position of faces of crystals by
corresponding points on the surface of a circumscribing sphere. He
gave (in 1823) the laws of the derivation of crystalline faces,
expressed geometrically by the intersection of zones, (_Beiträge zur
Krystallonomie_.) The same method of indicating the position of
faces of crystals was afterwards, together with the notation,
re-invented by M. Grassmann, (_Zur Krystallonomie und Geometrischen
Combinationslehre_, 1829.) Aiding himself by the suggestions of
these writers, and partly adopting my method, Prof. Miller has
produced a work on Crystallography remarkable for mathematical
elegance and symmetry; and has given expressions really useful for
calculating the angles of crystalline faces, (_A Treatise on
Crystallography_. Cambridge, 1839.)]

_Confirmation of the Distinction of Systems by the Optical
Properties of Minerals.--Brewster._--I must not omit to notice the
striking confirmation which the distinction of systems of
crystallization received from optical discoveries, especially those
of Sir D. Brewster. Of the {332} history of this very rich and
beautiful department of science, we have already given some account,
in speaking of Optics. The first facts which were noticed, those
relating to double refraction, belonged exclusively to crystals of
the rhombohedral system. The splendid phenomena of the rings and
lemniscates produced by dipolarizing crystals, were afterwards
discovered; and these were, in 1817, classified by Sir David
Brewster, according to the crystalline forms to which they belong.
This classification, on comparison with the distinction of Systems
of Crystallization, resolved itself into a necessary relation of
mathematical symmetry: all crystals of the pyramidal and
rhombohedral systems, which from their geometrical character have a
single axis of symmetry, are also optically uniaxal, and produce by
dipolarization circular rings; while the prismatic system, which has
no such single axis, but three unequal axes of symmetry, is optically
biaxal, gives lemniscates by dipolarized light, and according to
Fresnel's theory, has three rectangular axes of unequal elasticity.

[2nd Ed.] [I have placed Sir David Brewster's arrangement of
crystalline forms in this chapter, as an event belonging to the
_confirmation_ of the distinctions of forms introduced by Weiss and
Mohs; because that arrangement was established, not on
crystallographical, but on optical grounds. But Sir David Brewster's
optical discovery was a much greater step in science than the
systems of the two German crystallographers; and even in respect to
the crystallographical principle, Sir D. Brewster had an independent
share in the discovery. He divided crystalline forms into three
classes, enumerating the Hauïan "primitive forms" which belonged to
each; and as he found some exceptions to this classification, (such
as idocrase, &c.,) he ventured to pronounce that in those substances
the received primitive forms were probably erroneous; a judgment
which was soon confirmed by a closer crystallographical scrutiny. He
also showed his perception of the mineralogical importance of his
discovery by publishing it, not only in the _Phil. Trans._ (1818),
but also in the _Transactions of the Wernerian Society of Natural
History_. In a second paper inserted in this later series, read in
1820, he further notices Mohs's System of Crystallography, which had
then recently appeared, and points out its agreement with his own.

Another reason why I do not make his great optical discovery a
cardinal point in the history of crystallography is, that as a
crystallographical system it is incomplete. Although we are thus led
to distinguish the _tessular_ and the _prismatic_ systems (using
Mohs's terms) {333} from the _rhombohedral_ and the _square
prismatic_, we are not led to distinguish the latter two from each
other; inasmuch as they have no optical difference of character. But
this distinction is quite essential in crystallography; for these
two systems have faces formed by laws as different as those of the
other two systems.

Moreover, Weiss and Mohs not only divided crystalline forms into
certain classes, but showed that by doing this, the derivation of
all the existing forms from the fundamental ones assumed a new
aspect of simplicity and generality; and this was the essential part
of what they did.

On the other hand, I do not think it is too much to say as I have
elsewhere said[35\15] that "Sir D. Brewster's optical experiments
must have led to a classification of crystals into the above
systems, or something nearly equivalent, even if crystals had not
been so arranged by attention to their forms."]

[Note 35\15: _Philosophy of the Inductive Sciences_, B. viii. C.
iii. Art. 3.]

Many other most curious trains of research have confirmed the
general truth, that the degree and kind of geometrical symmetry
corresponds exactly with the symmetry of the optical properties. As
an instance of this, eminently striking for its singularity, we may
notice the discovery of Sir John Herschel, that the _plagihedral_
crystallization of quartz, by which it exhibits faces _twisted_ to
the right or the left, is accompanied by right-handed or left-handed
circular polarization respectively. No one acquainted with the
subject can now doubt, that the correspondence of geometrical and
optical symmetry is of the most complete and fundamental kind.

[2nd Ed.] [Our knowledge with respect to the positions of the
optical axes of the oblique prismatic crystals is still imperfect.
It appears to be ascertained that, in singly oblique crystals, one
of the axes of optical elasticity coincides with the rectangular
crystallographic axis. In doubly oblique crystals, one of the axes
of optical elasticity is, in many cases, coincident with the axis of
a principal zone. I believe no more determinate laws have been
discovered.]

Thus the highest generalization at which mathematical
crystallographers have yet arrived, may be considered as fully
established; and the science of Crystallography, in the condition in
which these place it, is fit to be employed as one of the members of
Mineralogy, and thus to fill its appropriate place and office. {334}




CHAPTER VI.

CORRECTION OF THE LAW OF THE SAME ANGLE FOR THE SAME SUBSTANCE.


DISCOVERY OF ISOMORPHISM. MITSCHERLICH.--The discovery of which we
now have to speak may appear at first sight too large to be included
in the history of crystallography, and may seem to belong rather to
chemistry. But it is to be recollected that crystallography, from
the time of its first assuming importance in the hands of Haüy,
founded its claim to notice entirely upon its connexion with
chemistry; crystalline forms were properties of _something_; but
_what_ that something was, and how it might be modified without
becoming something else, no crystallographer could venture to
decide, without the aid of chemical analysis. Haüy had assumed, as
the general result of his researches, that the same chemical
elements, combined in the same proportions, would always exhibit the
same crystalline form; and reciprocally, that the same form and
angles (except in the obvious case of the tessular system, in which
the angles are determined by its _being_ the tessular system,)
implied the same chemical constitution. But this dogma could only be
considered as an approximate conjecture; for there were many glaring
and unexplained exceptions to it. The explanation of several of
these was beautifully described by the discovery that there are
various elements which are _isomorphous_ to each other; that is,
such that one may take the place of another without altering the
crystalline form; and thus the chemical composition may be much
changed, while the crystallographic character is undisturbed.

This truth had been caught sight of, probably as a guess only, by
Fuchs as early as 1815. In speaking of a mineral which had been
called Gehlenite, he says, "I hold the oxide of iron, not for an
essential component part of this genus, but only as a _vicarious_
element, replacing so much lime. We shall find it necessary to
consider the results of several analyses of mineral bodies in this
point of view, if we wish, on the one hand, to bring them into
agreement with the doctrine of chemical proportions, and on the
other, to avoid unnecessarily splitting up genera." In a lecture _On
the Mutual Influence of_ {335} _Chemistry and Mineralogy_,[36\15] he
again draws attention to his term _vicarious_ (_vicarirende_), which
undoubtedly expresses the nature of the general law afterwards
established by Mitscherlich in 1822.

[Note 36\15: Munich, 1820.]

But Fuchs's conjectural expression was only a prelude to
Mitscherlich's experimental discovery of isomorphism. Till many
careful analyses had given substance and signification to this
conception of vicarious elements, it was of small value. Perhaps no
one was more capable than Berzelius of turning to the best advantage
any ideas which were current in the chemical world; yet we find
him,[37\15] in 1820, dwelling upon a certain vague view of these
cases,--that "oxides which contain equal doses of oxygen must have
their general properties common;" without tracing it to any definite
conclusions. But his scholar, Mitscherlich, gave this proposition a
real crystallographical import. Thus he found that the carbonates of
lime (calcspar,) of magnesia, of protoxide of iron, and of protoxide
of manganese, agree in many respects of form, while the homologous
angles vary through one or two degrees only; so again the carbonates
of baryta, strontia, lead, and lime (arragonite), agree nearly; the
different kinds of felspar vary only by the substitution of one
alkali for another; the phosphates are almost identical with the
arseniates of several bases. These, and similar results, were
expressed by saying that, in such cases, the bases, lime, protoxide
of iron, and the rest, are _isomorphous_; or in the latter instance,
that the arsenic and phosphoric acids are isomorphous.

[Note 37\15: _Essay on the Theory of Chemical Proportions_, p. 122.]

Since, in some of these cases, the substitution of one element of
the isomorphous group for another does alter the angle, though
slightly, it has since been proposed to call such groups
_plesiomorphous_.

This discovery of isomorphism was of great importance, and excited
much attention among the chemists of Europe. The history of its
reception, however, belongs, in part, to the classification of
minerals; for its effect was immediately to metamorphose the
existing chemical systems of arrangement. But even those
crystallographers and chemists who cared little for general systems
of classification, received a powerful impulse by the expectation,
which was now excited, of discovering definite laws connecting
chemical constitution with crystalline form. Such investigations
were soon carried on with great activity. Thus, at a recent period,
Abich analysed a number of tessular minerals, spinelle, pleonaste,
gahnite, franklinite, and chromic iron oxide; and {336} seems to
have had some success in **giving a common type to their chemical
formulæ, as there is a common type in their crystallization.

[2nd Ed.] [It will be seen by the above account that Prof.
Mitscherlich's merit in the great discovery of Isomorphism is not at
all narrowed by the previous conjectures of M. Fuchs. I am informed,
moreover, that M. Fuchs afterwards (in Schweigger's _Journal_)
retracted the opinions he had put forward on this subject.]

_Dimorphism._--My business is, to point out the connected truths
which have been obtained by philosophers, rather than insulated
difficulties which still stand out to perplex them. I need not,
therefore, dwell on the curious cases of _dimorphism_; cases in
which the same definite chemical compound of the same elements
appears to have two different forms; thus the carbonate of lime has
two forms, _calcspar_ and _arragonite_, which belong to different
systems of crystallization. Such facts may puzzle us; but they
hardly interfere with any received general truths, because we have
as yet no truths of very high order respecting the connexion of
chemical constitution and crystalline form. Dimorphism does not
interfere with isomorphism; the two classes of facts stand at the
same stage of inductive generalization, and we wait for some higher
truth which shall include both, and rise above them.

[2nd Ed.] [For additions to our knowledge of the Dimorphism of
Bodies, see Professor Johnstone's valuable _Report_ on that subject
in the _Reports of the British Association_ for 1837. Substances
have also been found which are _trimorphous_. We owe to Professor
Mitscherlich the discovery of dimorphism, as well as of isomorphism:
and to him also we owe the greater part of the knowledge to which
these discoveries have led.]




CHAPTER VII.

ATTEMPTS TO ESTABLISH THE FIXITY OF OTHER PHYSICAL
PROPERTIES.--WERNER.


THE reflections from which it appeared, (at the end of the last
Book,) that in order to obtain general knowledge respecting bodies,
we must give scientific fixity to our appreciation of their
properties, applies to their other properties as well as to their
crystalline {337} form. And though none of the other properties have
yet been referred to standards so definite as that which geometry
supplies for crystals, a system has been introduced which makes
their measures far more constant and precise than they are to a
common undisciplined sense.

The author of this system was Abraham Gottlob Werner, who had been
educated in the institutions which the Elector of Saxony had
established at the mines of Freiberg. Of an exact and methodical
intellect, and of great acuteness of the senses, Werner was well
fitted for the task of giving fixity to the appreciation of outward
impressions; and this he attempted in his _Dissertation on the
external Characters of Fossils_, which was published at Leipzig in
1774. Of the precision of his estimation of such characters, we may
judge from the following story, told by his biographer
Frisch.[38\15] One of his companions had received a quantity of
pieces of amber, and was relating to Werner, then very young, that
he had found in the lot one piece from which he could extract no
signs of electricity. Werner requested to be allowed to put his hand
in the bag which contained these pieces, and immediately drew out
the unelectrical piece. It was yellow chalcedony, which is
distinguishable from amber by its weight and coldness.

[Note 38\15: _Werner's Leben_, p. 26.]

The principal external characters which were subjected by Werner to
a systematic examination were color, lustre, hardness, and specific
gravity. His subdivisions of the first character (_Color_), were
very numerous; yet it cannot be doubted that if we recollect them by
the eye, and not by their names, they are definite and valuable
characters, and especially the metallic colors. Breithaupt, merely
by the aid of this character, distinguished two new compounds among
the small grains found along with the grains of platinum, and
usually confounded with them. The kinds of _Lustre_, namely,
_glassy_, _fatty_, _adamantine_, _metallic_, are, when used in the
same manner, equally valuable. _Specific Gravity_ obviously admits
of a numerical measure; and the _Hardness_ of a mineral was pretty
exactly defined by the substances which it would scratch, and by
which it was capable of being scratched.

Werner soon acquired a reputation as a mineralogist, which drew
persons from every part of Europe to Freiberg in order to hear his
lectures; and thus diffused very widely his mode of employing
external characters. It was, indeed, impossible to attend so closely
to {338} these characters as the Wernerian method required, without
finding that they were more distinctive than might at first sight be
imagined; and the analogy which this mode of studying Mineralogy
established between that and other branches of Natural History,
recommended the method to those in whom a general inclination to
such studies was excited. Thus Professor Jameson of Edinburgh, who
had been one of the pupils of Werner at Freiberg, not only published
works in which he promulgated the mineralogical doctrines of his
master, but established in Edinburgh a "Wernerian Society," having
for its object the general cultivation of Natural History.

Werner's standards and nomenclature of external characters were
somewhat modified by Mohs, who, with the same kinds of talents and
views, succeeded him at Freiberg. Mohs reduced hardness to numerical
measure by selecting ten known minerals, each harder than the other
in order, from _talc_ to _corundum_ and _diamond_, and by making the
place which these minerals occupy in the list, the numerical measure
of the hardness of those which are compared with them. The result of
the application of this fixed measurement and nomenclature of
external characters will appear in the History of Classification, to
which we now proceed.



{{339}}
SYSTEMATIC MINERALOGY.




CHAPTER VIII.

ATTEMPTS AT THE CLASSIFICATION OF MINERALS.


_Sect._ 1.--_Proper object of Classification._

THE fixity of the crystalline and other physical properties of
minerals is turned to account by being made the means of classifying
such objects. To use the language of Aristotle,[39\15]
Classification is the _architectonic_ science, to which
Crystallography and the Doctrine of External Characters are
subordinate and ministerial, as the art of the bricklayer and
carpenter are to that of the architect. But classification itself is
useful only as subservient to an ulterior science, which shall
furnish us with knowledge concerning things so classified. To
classify is to divide and to name; and the value of the Divisions
which we thus make, and of the names which we give them, is
this;--that they render exact knowledge and general propositions
possible. Now the knowledge which we principally seek concerning
minerals is a knowledge of their chemical composition; the general
propositions to which we hope to be led are such as assert relations
between their intimate constitution and their external attributes.
Thus our Mineralogical Classification must always have an eye turned
towards Chemistry. We cannot get rid of the fundamental conviction,
that the elementary composition of bodies, since it fixes their
essence, must determine their properties. Hence all mineralogical
arrangements, whether they profess it or not, must be, in effect,
chemical; they must have it for their object to bring into view a
set of relations, which, whatever else they may be, are at least
chemical relations. We may begin with the outside, but it is only in
order to reach the inner {340} structure. We may classify without
reference to chemistry; but if we do so, it is only that we may
assert chemical propositions with reference to our classification.

[Note 39\15: _Eth. Nicom._ i. 2.]

But, as we have already attempted to show, we not only may, but we
_must_ classify, by other than chemical characters, in order to be
able to make our classification the basis of chemical knowledge. In
order to assert chemical truths concerning bodies, we must have the
bodies known by some tests not chemical. The chemist cannot assert
that Arragonite does or does not contain Strontia, except the
mineralogist can tell him whether any given specimen is or is not
_Arragonite_. If chemistry be called upon to supply the
_definitions_ as well as the _doctrines_ of mineralogy, the science
can only consist of identical propositions.

Yet chemistry has been much employed in mineralogical
classifications, and, it is generally believed, with advantage to
the science: How is this consistent with what has been said?

To this the answer is, that when this _has_ been done with
advantage, the authority of external characters, as well as of
chemical constitution, has really been brought into play. We have
two sets of properties to compare, chemical and physical; to exhibit
the connexion of these is the object of scientific mineralogy. And
though this connexion would be most distinctly asserted, if we could
keep the two sets of properties distinct, yet it may be brought into
view in a great degree, by classifications in which both are
referred to as guides. Since the governing principle of the attempts
at classification is the conviction that the chemical constitution
and the physical properties have a definite relation to each other,
we appear entitled to use both kinds of evidence, in proportion as
we can best obtain each; and then the general consistency and
convenience of our system will be the security for its containing
substantial knowledge, though this be not presented in a rigorously
logical or systematic form.

Such _mixed systems_ of classification, resting partly on chemical
and partly on physical characters, naturally appeared as the
earliest attempts in this way, before the two members of the subject
had been clearly separated in men's minds; and these systems,
therefore, we must first give an account of.


_Sect._ 2.--_Mixed Systems of Classification._

_Early Systems._--The first attempts at classifying minerals went
upon the ground of those differences of general aspect which had
been {341} recognized in the formation of common language; as
_earths_, _stones_, _metals_. But such arrangements were manifestly
vague and confused; and when chemistry had advanced to power and
honor, her aid was naturally called in to introduce a better order.
"Hiarne and Bromell were, as far as I know," says[40\15] Cronstedt,
"the first who founded any mineral system upon chemical principles;
to them we owe the three known divisions of the most simple mineral
bodies; viz., the _calcarei_, _vitrescentes_, and _apyri_." But
Cronstedt's own _Essay towards a System of Mineralogy_, published in
Swedish in 1758, had perhaps more influence than any other, upon
succeeding systems. In this, the distinction of earths and stones,
and also of vitrescent and non-vitrescent earths (_apyri_), is
rejected. The earths are classed as _calcareous_, _siliceous_,
_argillaceous_, and the like. Again, calcareous earth is pure (_calc
spar_), or united with acid of vitriol (_gypsum_), or united with
the muriatic add (_sal ammoniac_), and the like. It is easy to see
that this is the method, which, in its general principle, has been
continued to our own time. In such methods, it is supposed that we
can recognize the substance by its general appearance, and on this
assumption, its place in the system conveys to us chemical knowledge
concerning it.

[Note 40\15: _Mineralogy_, Pref. p. viii.]

But as the other branches of Natural History, and especially Botany,
assumed a systematic form, many mineralogists became dissatisfied
with this casual and superficial mode of taking account of external
characters; they became convinced, that in Mineralogy as in other
sciences, classification must have its system and its rules. The
views which Werner ascribes to his teacher, Pabst van Ohain,[41\15]
show the rise of those opinions which led through Werner to Mohs:
"He was of opinion that a natural mineral system must be constructed
by chemical determinations, and external characters at the same time
(_methodus mixta_); but that along with this, mineralogists ought
also to construct and employ what he called an _artificial system_,
which might serve us as a guide (_loco indicis_) how to introduce
newly-discovered fossils into the system, and how to find easily and
quickly those already known and introduced." Such an artificial
system, containing not the grounds of classification, but marks for
recognition, was afterwards attempted by Mohs, and termed by him the
_Characteristic_ of his system.

[Note 41\15: Frisch. _Werner's Leben_, p. 15.]

_Werner's System._--But, in the mean time, Werner's classification
had an extensive reign, and this was still a mixed system. Werner
himself, indeed, never published a system of mineralogy. "We might
{342} almost imagine," Cuvier says,[42\15] "that when he had
produced his nomenclature of external characters, he was affrighted
with his own creation; and that the reason of his writing so little
after his first essay, was to avoid the shackles which he had
imposed upon others." His system was, indeed, made known both in and
out of Germany, by his pupils; but in consequence of Werner's
unwillingness to give it on his own authority, it assumed, in its
published forms, the appearance of an extorted secret imperfectly
told. A _Notice of the Mineralogical Cabinet of Mine-Director Pabst
von Ohain_, was, in 1792, published by Karsten and Hoffman, under
Werner's direction; and conveyed by example, his views of
mineralogical arrangement; and[43\15] in 1816 his _Doctrine of
Classification_ was surreptitiously copied from his manuscript, and
published in a German Journal, termed _The Hesperus_. But it was
only in 1817, after his death, that there appeared _Werner's Last
Mineral System_, edited from his papers by Breithaupt and Köhler:
and by this time, as we shall soon see, other systems were coming
forwards on the stage.

[Note 42\15: Cuv. _El._ ii. 314.]

[Note 43\15: Frisch. p. 52.]

A very slight notice of Werner's arrangement will suffice to show
that it was, as we have termed it, a Mixed System. He makes four
great Classes of fossils, _Earthy_, _Saline_, _Combustible_,
_Metallic_: the earthy fossils are in eight Genera--Diamond, Zircon,
Silica, Alumina, Talc, Lime, Baryta, Hallites. It is clear that
these genera are in the main chemical, for chemistry alone can
definitely distinguish the different Earths which characterize them.
Yet the Wernerian arrangement supposed the distinctions to be
practically made by reference to those external characters which the
teacher himself could employ with such surpassing skill. And though
it cannot be doubted, that the chemical views which prevailed around
him had a latent influence on his classification in some cases, he
resolutely refused to bend his system to the authority of chemistry.
Thus,[44\15] when he was blamed for having, in opposition to the
chemists, placed diamond among the earthy fossils, he persisted in
declaring that, mineralogically considered, it was a stone, and
could not be treated as anything else.

[Note 44\15: Frisch. p. 62.]

This was an indication to that tendency, which, under his successor,
led to a complete separation of the two grounds of classification.
But before we proceed to this, we must notice what was doing at this
period in other parts of Europe.

_Haüy's System._--Though Werner, on his own principles, ought to
{343} have been the first person to see the immense value of the
most marked of external characters, crystalline form, he did not, in
fact, attach much importance to it. Perhaps he was in some measure
fascinated by a fondness for those characters which he had himself
systematized, and the study of which did not direct him to look for
geometrical relations. However this may be, the glory of giving to
Crystallography its just importance in Mineralogy is due to France:
and the Treatise of Haüy, published in 1801, is the basis of the
best succeeding works of mineralogy. In this work, the arrangement
is professedly chemical; and the classification thus established is
employed as the means of enunciating crystallographic and other
properties. "The principal object of this Treatise," says the
author,[45\15] "is the exposition and development of a method
founded on certain principles, which may serve as a frame-work for
all the knowledge which Mineralogy can supply, aided by the
different sciences which can join hands with her and march on the
same line.**" It is worthy of notice, as characteristic of this
period of Mixed Systems, that the classification of Haüy, though
founded on principles so different from the Wernerian ones, deviates
little from it in the general character of the divisions. Thus, the
first Order of the first Class of Haüy is _Acidiferous Earthy
Substances_; the first genus is _Lime_; the species are, _Carbonate
of Lime_, _Phosphate of Lime_, _Fluate of Lime_, _Sulphate of Lime_,
and so on.

[Note 45\15: Disc. Prél. p. xvii.]

_Other Systems._--Such mixed methods were introduced also into this
country, and have prevailed, we may say, up to the present time. The
_Mineralogy_ of William Phillips, which was published in 1824, and
which was an extraordinary treasure of crystallographic facts, was
arranged by such a mixed system; that is, by a system professedly
chemical; but, inasmuch as a rigid chemical system is impossible,
and the assumption of such a one leads into glaring absurdities, the
system was, in this and other attempts of the same kind, corrected
by the most arbitrary and lax application of other considerations.

It is a curious example of the difference of national intellectual
character, that the manifest inconsistencies of the prevalent
systems, which led in Germany, as we shall see, to bold and sweeping
attempts at reform, produced in England a sort of contemptuous
despair with regard to systems in general;--a belief that no system
could be consistent or useful;--and a persuasion that the only
valuable knowledge is the accumulation of particular facts. This is
not the place to {344} explain how erroneous and unphilosophical
such an opinion is. But we may notice that while such a temper
prevails among us, our place in this science can never be found in
advance of that position which we are now considering as exemplified
in the period of Werner and Haüy. So long as we entertain such views
respecting the objects of Mineralogy, we can have no share in the
fortunes of the succeeding period of its history, to which I now
proceed.




CHAPTER IX.

ATTEMPTS AT THE REFORM OF MINERALOGICAL SYSTEMS.--SEPARATION OF THE
CHEMICAL AND NATURAL HISTORY METHODS.


_Sect._ 1.--_Natural History System of Mohs._

THE chemical principle of classification, if pursued at random, as
in the cases just spoken of leads to results at which a
philosophical spirit revolts; it separates widely substances which
are not distinguishable; joins together bodies the most dissimilar;
and in hardly any instance does it bring any truth into view. The
vices of classifications like that of Haüy could not long be
concealed; but even before time had exposed the weakness of his
system, Haüy himself had pointed out, clearly and without
reserve,[46\15] that a chemical system is only one side of the
subject, and supposes, as its counterpart, a science of external
characters. In the mean time, the Wernerians were becoming more and
more in love with the form which they had given to such a science.
Indeed, the expertness which Werner and his scholars acquired in the
use of external characters, justified some partiality for them. It
is related of him,[47\15] that, by looking at a piece of iron-ore,
and poising it in his hand, he was able to tell, almost precisely,
the proportion of pure metal which it contained. And in the last
year of his life,[48\15] he had marked out, as the employment of the
ensuing winter, the study of the system of Berzelius, with a view to
find out the laws of combination as disclosed by external
characters. In the same spirit, his pupil {345} Breithaupt[49\15]
attempted to discover the ingredients of minerals by their
peculiarities of crystallization. The persuasion that there must be
_some_ connexion between composition and properties, transformed
itself, in their minds, into a belief that they could seize the
nature of the connexion by a sort of instinct.

[Note 46\15: See his Disc. Prél.]

[Note 47\15: Frisch. _Werner's Leben_, p. 78.]

[Note 48\15: Frisch. 3.]

[Note 49\15: _Dresdn. Auswahl_, vol. ii. p. 97.]

This opinion of the independency of the science of external
characters, and of its sufficiency for its own object, at last
assumed its complete form in the bold attempt to construct a system
which should borrow nothing from chemistry. This attempt was made by
Frederick Mohs, who had been the pupil of Werner, and was afterwards
his successor in the school of Freiberg; and who, by the acute and
methodical character of his intellect, and by his intimate knowledge
of minerals, was worthy of his predecessor. Rejecting altogether all
divisions of which the import was chemical, Mohs turned for
guidance, or at least for the light of analogy, to botany. His
object was to construct a _Natural System_ of mineralogy. What the
conditions and advantages of a natural system of any province of
nature are, we must delay to explain till we have before us, in
botany, a more luminous example of such a scheme. But further; in
mineralogy, as in botany, besides the Natural System, by which we
_form_ our classes, it is necessary to have an _Artificial System_
by which we _recognize_ them;--a principle which, we have seen, had
already taken root in the school of Freiberg. Such an artificial
system Mohs produced in his _Characteristic of the Mineral Kingdom_,
which was published at Dresden in 1820; and which, though extending
only to a few pages, excited a strong interest in Germany, where
men's minds were prepared to interpret the full import of such a
work. Some of the traits of such a "Characteristic" had, indeed,
been previously drawn by others; as for example, by Haüy, who
notices that each of his Classes has peculiar characters. For
instance, his First Class (acidiferous substances,) alone possesses
these combinations of properties; "division into a regular
octohedron, without being able to scratch glass; specific gravity
above 3·5, without being able to scratch glass." The extension of
such characters into a scheme which should exhaust the whole mineral
kingdom, was the undertaking of Mohs.

Such a collection of marks of classes, implied a classification
previously established, and accordingly, Mohs had created his own
mineral system. His aim was to construct it, as we shall hereafter
see that other natural systems are constructed, by taking into
account _all_ the {346} resemblances and differences of the objects
classified. It is obvious that to execute such a work, implied a
most intimate and universal acquaintance with minerals;--a power of
combining in one vivid survey the whole mineral kingdom. To
illustrate the spirit in which Professor Mohs performed his task, I
hope I may be allowed to refer to my own intercourse with him. At an
early period of my mineralogical studies, when the very conception
of a Natural System was new to me, he, with great kindliness of
temper, allowed me habitually to propose to him the scruples which
arose in my mind, before I could admit principles which appeared to
me then so vague and indefinite; and answered my objections with
great patience and most instructive clearness. Among other
difficulties, I one day propounded to him this;--"You have published
a Treatise on Mineralogy, in which you have described _all_ the
important properties of all known minerals. On your principles,
then, it ought to be possible, merely by knowing the descriptions in
your book, and without seeing any minerals, to construct a natural
system; and this natural system ought to turn out identical with
that which you have produced, by so careful an examination of the
minerals themselves." He pondered a moment, and then he answered,
"It is true; but what an enormous _imagination_ (_einbildungskraft_,
_power of inward imagining_), a man must have for such a work!"
Vividness of conception of sensible properties, and the steady
intuition (_anschauung_) of objects, were deemed by him, and by the
Wernerian school in general, to be the most essential conditions of
complete knowledge.

It is not necessary to describe Mohs's system in detail; it may
sufficiently indicate its form to state that the following
substances, such as I before gave as examples of other arrangements,
calcspar, gypsum, fluor spar, apatite, heavy spar, are by Mohs
termed respectively, _Rhombohedral Lime Haloide_, _Gyps Haloide_,
_Octohedral Fluor Haloide_, _Rhombohedral Fluor Haloide_, _Prismatic
Hal Baryte_. These substances are thus referred to the _Orders_
Haloide, and Baryte; to _Genera_ Lime Haloide, Fluor Haloide, Hal
Baryte; and the _Species_ is an additional particularization.

Mohs not only aimed at framing such a system, but was also ambitious
of giving to all minerals _Names_ which should accord with the
system. This design was too bold to succeed. It is true, that a new
nomenclature was much needed in mineralogy: it is true, too, that it
was reasonable to expect, from an improved classification, an
improved nomenclature, such as had been so happily obtained in
botany by the {347} reform of Linnæus. But besides the defects of
Mohs's system, he had not prepared his verbal novelties with the
temperance and skill of the great botanical reformer. He called upon
mineralogists to change the name of almost every mineral with which
they were acquainted; and the proposed appellations were mostly of a
cumbrous form, as the above example may serve to show. Such names
could have obtained general currency, only after a general and
complete acceptance of the system; and the system did not possess,
in a sufficient degree, that evidence which alone could gain it a
home in the belief of philosophers,--the coincidence of its results
with those of Chemistry. But before I speak finally of the fortunes
of the Natural-history System, I will say something of the other
attempt which was made about the same time to introduce a Reform
into Mineralogy from the opposite extremity of the science.


_Sect._ 2.--_Chemical System of Berzelius and others._

IF the students of external characters were satisfied of the
independence of their method, the chemical analysts were naturally
no less confident of the legitimate supremacy of their principles:
and when the beginning of the present century had been distinguished
by the establishment of the theory of definite proportions, and by
discoveries which pointed to the electro-chemical theory, it could
not appear presumption to suppose, that the classification of
bodies, so far as it depended on chemistry, might be presented in a
form more complete and scientific than at any previous time.

The attempt to do this was made by the great Swedish chemist Jacob
Berzelius. In 1816, he published his _Essay to establish a purely
Scientific System of Mineralogy, by means of the Application of the
Electro-chemical Theory and the Chemical Doctrine of Definite
Proportions_. It is manifest that, for minerals which are
constituted by the law of Definite Proportions, this constitution
must be a most essential part of their character. The
electro-chemical theory was called in aid, in addition to the
composition, because, distinguishing the elements of all compounds
as electro-positive and electro-negative, and giving to every
element a place in a series, and a place defined by the degree of
these relations, it seemed to afford a rigorous and complete
principle of arrangement. Accordingly, Berzelius, in his First
System, arranged minerals according to their electro-positive
element, and the elements according to their electro-positive rank;
{348} and supposed that he had thus removed all that was arbitrary
and vague in the previous chemical systems of mineralogy.

Though the attempt appeared so well justified by the state of
chemical science, and was so plausible in its principle, it was not
long before events showed that there was some fallacy in these
specious appearances. In 1820, Mitscherlich discovered Isomorphism:
by that discovery it appeared that bodies containing very different
electro-positive elements could not be distinguished from each
other; it was impossible, therefore, to put them in distant portions
of the classification;--and thus the first system of Berzelius
crumbled to pieces.

But Berzelius did not so easily resign his project. With the most
unhesitating confession of his first failure, but with undaunted
courage, he again girded himself to the task of rebuilding his
edifice. Defeated at the electro-positive position, he now resolved
to make a stand at the electro-negative element. In 1824, he
published in the Transactions of the Swedish Academy, a Memoir _On
the Alterations in the Chemical Mineral System, which necessarily
follow from the Property exhibited by Isomorphous Bodies, of
replacing each other in given Proportions_. The alteration was, in
fact, an inversion of the system, with an attempt still to preserve
the electro-chemical principle of arrangement. Thus, instead of
arranging metallic minerals according to the _metal_, under iron,
copper, &c., all the _sulphurets_ were classed together, all the
_oxides_ together, all the _sulphates_ together, and so in other
respects. That such an order was a great improvement on the
preceding one, cannot be doubted; but we shall see, I think, that as
a strict scientific system it was not successful. The discovery of
isomorphism, however, naturally led to such attempts. Thus Gmelin
also, in 1825, published a mineral system,[50\15] which, like that
of Berzelius, founded its leading distinctions on the
electro-negative, or, as it was sometimes termed, the _formative_
element of bodies; and, besides this, took account of the _numbers_
of atoms or proportions which appear in the composition of the body;
distinguishing, for instance, Silicates, as simple silicates, double
silicates, and so on, to _quintuple_ silicate (_Pechstein_) and
_sextuple_ silicate (_Perlstein_). In like manner, Nordenskiöld
devised a system resting on the same bases, taking into account also
the crystalline form. In 1824, Beudant published his _Traité
Elémentaire de Minéralogie_, in which he professes to found his
arrangement on the electro-negative element, and on Ampère's
circular {349} arrangement of elementary substances. Such schemes
exhibit rather a play of the mere logical faculty, exercising itself
on assumed principles, than any attempt at the real interpretation
of nature. Other such pure chemical systems may have been published,
but it is not necessary to accumulate instances. I proceed to
consider their result.

[Note 50\15: _Zeitsch. der Min._ 1825, p. 435.]


_Sect._ 3.--_Failure of the Attempts at Systematic Reform._

IT may appear presumptuous to speak of the failure of those whom,
like Berzelius and Mohs, we acknowledge as our masters, at a period
when, probably, they and some of their admirers still hold them to
have succeeded in their attempt to construct a consistent system.
But I conceive that my office as an historian requires me to exhibit
the fortunes of this science in the most distinct form of which they
admit, and that I cannot evade the duty of attempting to seize the
true aspect of recent occurrences in the world of science. Hence I
venture to speak of the failure of both the attempts at framing a
pure scientific system of mineralogy,--that founded on the chemical,
and that founded on the natural-history principle; because it is
clear that they have not obtained that which alone we could,
according to the views here presented, consider as success,--a
coincidence of each with the other. A Chemical System of
arrangement, which should bring together, in all cases, the
substances which come nearest each other in external properties;--a
Natural-history System, which should be found to arrange bodies in
complete accordance with their chemical constitution:--if such
systems existed, they might, with justice, claim to have succeeded.
Their agreement would be their verification. The interior and
exterior system are the type and the antitype, and their entire
correspondence would establish the mode of interpretation beyond
doubt. But nothing less than this will satisfy the requisitions of
science. And when, therefore, the chemical and the natural-history
system, though evidently, as I conceive, tending towards each other,
are still far from coming together, it is impossible to allow that
either method has been successful in regard to its proper object.

But we may, I think, point out the fallacy of the principles, as well
as the imperfection of the results, of both of those methods. With
regard to that of Berzelius, indeed, the history of the subject
obviously betrays its unsoundness. The electro-positive principle was,
in a very short time after its adoption, proved and acknowledged to be
utterly untenable: what security have we that the electro-negative
element is {350} more trustworthy? Was not the necessity of an entire
change of system, a proof that the ground, whatever that was, on which
the electro-chemical principle was adopted, was an unfounded
assumption? And, in fact, do we not find that the same argument which
was allowed to be fatal to the First System of Berzelius, applies in
exactly the same manner against the Second? If the electro-positive
elements be often isomorphous, are not the electro-negative elements
sometimes isomorphous also? for instance, the arsenic and phosphoric
acids. But to go further, what _is_ the ground on which the
electro-chemical arrangement is adopted? Granted that the electrical
relations of bodies are important; but how do we come to know that
these relations have anything to do with mineralogy? How does it
appear that on them, principally, depend those external properties
which mineralogy must study? How does it appear that because sulphur
is the electro-negative part of one body, and an acid the
electro-negative part of another, these two elements similarly affect
the compounds? How does it appear that there is any analogy whatever
in their functions? We allow that the composition must, in _some way_,
determine the classified place of the mineral,--but why in _this_ way?

I do not dwell on the remark which Berzelius himself[51\15] makes on
Nordenskiöld's system;--that it assumes a perfect knowledge of the
composition in every case; although, considering the usual
discrepancies of analyses of minerals, this objection must make all
pure chemical systems useless. But I may observe, that mineralogists
have not yet determined what characters are sufficiently affixed to
determine a species of minerals. We have seen that the ancient
notion of the composition of a species, has been unsettled by the
discovery of isomorphism. The tenet of the constancy of the angle is
rendered doubtful by cases of plesiomorphism. The optical
properties, which are so closely connected with the crystalline, are
still so imperfectly known, that they are subject to changes which
appear capricious and arbitrary. Both the chemical and the optical
mineralogists have constantly, of late, found occasion to separate
species which had been united, and to bring together those which had
been divided. Everything shows that, in this science, we have our
classification still to begin. The detection of that fixity of
characters, on which a right establishment of species must rest, is
not yet complete, great as the progress is which we have made, by
acquiring a knowledge of the laws of crystallization and of {351}
definite chemical constitution. Our ignorance may surprise us; but
it may diminish our surprise to recollect, that the knowledge which
we seek is that of the laws of the physical constitution of all
bodies whatever; for to us, as mineralogists, all chemical compounds
are minerals.

[Note 51\15: _Jahres Bericht._ viii. 188.]

The defect of the principle of the natural-history classifiers may be
thus stated:--in studying the external characters of bodies, they take
for granted that they can, without any other light, discover the
relative value and importance of those characters. The grouping of
Species into a Genus, of Genera into an Order, according to the method
of this school, proceeds by no definite rules, but by a latent talent
of appreciation,--a sort of classifying instinct. But this course
cannot reasonably be expected to lead to scientific truth; for it can
hardly be hoped, by any one who looks at the general course of
science, that we shall discover the relation between external
characters and chemical composition, otherwise than by tracing their
association in cases where both are known. It is urged that in other
classificatory sciences, in botany, for example, we obtain a natural
classification from external characters without having recourse to any
other source of knowledge. But this is not true in the sense here
meant. In framing a natural system of botany, we have constantly
before our eyes the principles of physiology; and we estimate the
value of the characters of a plant by their bearing on its
functions,--by their place in its organization. In an unorganic body,
the chemical constitution is the law of its being; and we shall never
succeed in framing a science of such bodies but by studiously
directing our efforts to the interpretation of that law.

On these grounds, then, I conceive, that the bold attempts of Mohs
and of Berzelius to give new forms to mineralogy, cannot be deemed
successful in the manner in which their authors aspired to succeed.
Neither of them can be marked as a permanent reformation of the
science. I shall not inquire how far they have been accepted by men
of science, for I conceive that their greatest effect has been to
point out improvements which might be made in mineralogy without
going the whole length either of the _pure_ chemical, or of the
_pure_ natural-history system.


_Sect._ 4.--_Return to Mixed Systems with Improvements._

IN spite of the efforts of the purists, mineralogists returned to
mixed systems of classification; but these systems are much better
than they were before such efforts were made. {352}

The Second System of Berzelius, though not tenable in its rigorous
form, approaches far nearer than any previous system to a complete
character, bringing together like substances in a large portion of
its extent. The System of Mohs also, whether or not unconsciously
swayed by chemical doctrines, forms orders which have a community of
chemical character; thus, the minerals of the order _Haloide_ are
salts of oxides, and those of the order _Pyrites_ are sulphurets of
metals. Thus the two methods appear to be converging to a common
centre; and though we are unable to follow either of them to this
point of union, we may learn from both in what direction we are to
look for it. If we regard the best of the pure systems hitherto
devised as indications of the nature of that system, perfect both as
a chemical and as a natural-history system, to which a more complete
condition of mineralogical knowledge may lead us, we may obtain,
even at present, a tolerably good approximation to a complete
classification; and such a one, if we recollect that it must be
imperfect, and is to be held as provisional only, may be of no small
value and use to us.

The best of the mixed systems produced by this compromise again
comes from Freiberg, and was published by Professor Naumann in 1828.
Most of his orders have both a chemical character and great external
resemblances. Thus his _Haloides_, divided into _Unmetallic_ and
_Metallic_, and these again into _Hydrous_ and _Anhydrous_, give
good natural groups. The most difficult minerals to arrange in all
systems are the siliceous ones. These M. Naumann calls _Silicides_,
and subdivides them into _Metallic_, _Unmetallic_, and _Amphoteric_
or mixed; and again, into _Hydrous_ and _Anhydrous_. Such a system
is at least a good basis for future researches; and this is, as we
have said, all that we can at present hope for. And when we
recollect that the natural-history principle of classification has
begun, as we have already seen, to make its appearance in our
treatises of chemistry, we cannot doubt that some progress is making
towards the object which I have pointed out. But we know not yet how
far we are from the end. The combination of chemical,
crystallographical, physical and optical properties into some lofty
generalization, is probably a triumph reserved for future and
distant years.

_Conclusion._--The history of Mineralogy, both in its successes and
by its failures, teaches us this lesson;--that in the sciences of
classification, the establishment of the fixity of characters, and
the discovery of such characters as are fixed, are steps of the
first importance in the progress of these sciences. The recollection
of this maxim may aid us in {353} shaping our course through the
history of other sciences of this kind; in which, from the extent of
the subject, and the mass of literature belonging to it, we might at
first almost despair of casting the history into distinct epochs and
periods. To the most prominent of such sciences, Botany, I now
proceed.



{{355}}
BOOK XVI.


_CLASSIFICATORY SCIENCES._


HISTORY
OF
SYSTEMATIC BOTANY AND ZOOLOGY.


  . . . . . Vatem aspicies quæ rupe sub altâ
  Fata canit, foliisque notas et nomina mandat.
  Quæcunque in foliis descripsit carmina virgo
  Digerit in numerum atque antro seclusa relinquit
  Illa manent immorta locis neque ab ordine cedunt.
          VIRGIL. _Æn._ iii. 443.

  Behold the Sibyl!--Her who weaves a long,
  A tangled, full, yet sweetly flowing song.
  Wondrous her skill; for leaf on leaf she frames
  Unerring symbols and enduring names;
  And as her nicely measured line she binds,
  For leaf on leaf a fitting place she finds;
  Their place once found, no more the leaves depart,
  But fixed rest:--such is her magic art.



{{357}}
INTRODUCTION.


WE now arrive at that study which offers the most copious and
complete example of the sciences of classification, I mean Botany.
And in this case, we have before us a branch of knowledge of which
we may say, more properly than of any of the sciences which we have
reviewed since Astronomy, that it has been constantly advancing,
more or less rapidly, from the infancy of the human race to the
present day. One of the reasons of this resemblance in the fortunes
of two studies so widely dissimilar, is to be found in a simplicity
of principle which they have in common; the ideas of Likeness and
Difference, on which the knowledge of plants depends, are, like the
ideas of Space and Time, which are the foundation of astronomy,
readily apprehended with clearness and precision, even without any
peculiar culture of the intellect. But another reason why, in the
history of Botany, as in that of Astronomy, the progress of
knowledge forms an unbroken line from the earliest times, is
precisely the great difference of the kind of knowledge which has
been attained in the two cases. In Astronomy, the discovery of
general truths began at an early period of civilization; in Botany,
it has hardly yet begun; and thus, in each of these departments of
study, the lore of the ancient is homogeneous with that of the
modern times, though in the one case it is science, in the other,
the absence of science, which pervades all ages. The resemblance of
the form of their history arises from the diversity of their
materials.

I shall not here dwell further upon this subject, but proceed to
trace rapidly the progress of _Systematic Botany_, as the
classificatory science is usually denominated, when it is requisite
to distinguish between that and Physiological Botany. My own
imperfect acquaintance with this study admonishes me not to venture
into its details, further than my purpose absolutely requires. I
trust that, by taking my views principally from writers who are
generally allowed to possess the best insight into the science, I
may be able to draw the larger features of its history with
tolerable correctness; and if I succeed in this, I shall attain an
object of great importance in my general scheme. {358}



CHAPTER I.

IMAGINARY KNOWLEDGE OF PLANTS.


THE apprehension of such differences and resemblances as those by
which we group together and discriminate the various kinds of plants
and animals, and the appropriation of words to mark and convey the
resulting notions, must be presupposed, as essential to the very
beginning of human knowledge. In whatever manner we imagine man to
be placed on the earth by his Creator, these processes must be
conceived to be, as our Scriptures represent them, contemporaneous
with the first exertion of reason, and the first use of speech. If
we were to indulge ourselves in framing a hypothetical account of
the origin of language, we should probably assume as the
first-formed words, those which depend on the visible likeness or
unlikeness of objects; and should arrange as of subsequent
formation, those terms which imply, in the mind, acts of wider
combination and higher abstraction. At any rate, it is certain that
the names of the kinds of vegetables and animals are very abundant
even in the most uncivilized stages of man's career. Thus we are
informed[1\16] that the inhabitants of New Zealand have a distinct
name of every tree and plant in their island, of which there are six
or seven hundred or more different kinds. In the accounts of the
rudest tribes, in the earliest legends, poetry, and literature of
nations, pines and oaks, roses and violets, the olive and the vine,
and the thousand other productions of the earth, have a place, and
are spoken of in a manner which assumes, that in such kinds of
natural objects, permanent and infallible distinctions had been
observed and universally recognized.

[Note 1\16: Yate's _New Zealand_, p. 238.]

For a long period, it was not suspected that any ambiguity or
confusion could arise from the use of such terms; and when such
inconveniences did occur, (as even in early times they did,) men
were far from divining that the proper remedy was the construction
of a science of classification. The loose and insecure terms of the
language of common life retained their place in botany, long after
their {359} defects were severely felt: for instance, the vague and
unscientific distinction of vegetables into _trees_, _shrubs_, and
_herbs_, kept its ground till the time of Linnæus.

While it was thus imagined that the identification of a plant, by
means of its name, might properly be trusted to the common
uncultured faculties of the mind, and to what we may call the
instinct of language, all the attention and study which were
bestowed on such objects, were naturally employed in learning and
thinking upon such circumstances respecting them as were supplied by
any of the common channels through which knowledge and opinion flow
into men's minds.

The reader need hardly be reminded that in the earlier periods of
man's mental culture, he acquires those opinions on which he loves
to dwell, not by the exercise of observation subordinate to reason;
but, far more, by his fancy and his emotions, his love of the
marvellous, his hopes and fears. It cannot surprise us, therefore,
that the earliest lore concerning plants which we discover in the
records of the past, consists of mythological legends, marvellous
relations, and extraordinary medicinal qualities. To the lively
fancy of the Greeks, the Narcissus, which bends its head over the
stream, was originally a youth who in such an attitude became
enamored of his own beauty: the hyacinth,[2\16] on whose petals the
notes of grief were traced (A I, A I), recorded the sorrow of Apollo
for the death of his favorite Hyacinthus: the beautiful lotus of
India,[3\16] which floats with its splendid flower on the surface of
the water, is the chosen seat of the goddess Lackshmi, the daughter
of Ocean.[4\16] In Egypt, too,[5\16] Osiris swam on a lotus-leaf and
Harpocrates was cradled in one. The lotus-eaters of Homer lost
immediately their love of home. Every one knows how easy it would be
to accumulate such tales of wonder or religion.

[Note 2\16: Lilium martagon.
  Ipse suos gemitus foliis inscribit et A I, A I,
  Flos habet inscriptum funestaque litera ducta est.--OVID.]

[Note 3\16: Nelumbium speciosum.]

[Note 4\16: Sprengel, _Geschichte der Botanik_, i. 27.]

[Note 5\16: Ib. i. 28.]

Those who attended to the effects of plants, might discover in them
some medicinal properties, and might easily imagine more; and when
the love of the marvellous was added to the hope of health, it is
easy to believe that men would be very credulous. We need not dwell
upon the examples of this. In Pliny's Introduction to that book of
his {360} Natural History which treats of the medicinal virtues of
plants, he says,[6\16] "Antiquity was so much struck with the
properties of herbs, that it affirmed things incredible. Xanthus,
the historian, says, that a man killed by a dragon, will be restored
to life by an herb which he calls _balin_; and that Thylo, when
killed by a dragon, was recovered by the same plant. Democritus
asserted, and Theophrastus believed, that there was an herb, at the
touch of which, the wedge which the woodman had driven into a tree
would leap out again. Though we cannot credit these stories, most
persons believe that almost anything might be effected by means of
herbs, if their virtues were fully known." How far from a reasonable
estimate of the reality of such virtues were the persons who
entertained this belief we may judge from the many superstitious
observances which they associated with the gathering and using of
medicinal plants. Theophrastus speaks of these;[7\16] "The
drug-sellers and the rhizotomists (root-cutters) tell us," he says,
"some things which may be true, but other things which are merely
solemn quackery;[8\16] thus they direct us to gather some plants,
standing from the wind, and with our bodies anointed; some by night,
some by day, some before the sun falls on them. So far there may be
something in their rules. But others are too fantastical and far
fetched. It is, perhaps, not absurd to use a prayer in plucking a
plant; but they go further than this. We are to draw a sword three
times round the mandragora, and to cut it looking to the west:
again, to dance round it, and to use obscene language, as they say
those who sow cumin should utter blasphemies. Again, we are to draw
a line round the black hellebore, standing to the east and praying;
and to avoid an eagle either on the right or on the left; for, say
they, 'if an eagle be near, the cutter will die in a year.'"

[Note 6\16: Lib. xxv. 5.]

[Note 7\16: _De Plantis_, ix. 9.]

[Note 8\16: Ἐπιτραγῳδοῦντες.]

This extract may serve to show the extent to which these
imaginations were prevalent, and the manner in which they were
looked upon by Theophrastus, our first great botanical author. And
we may now consider that we have given sufficient attention to these
fables and superstitions, which have no place in the history of the
progress of real knowledge, except to show the strange chaos of wild
fancies and legends out of which it had to emerge. We proceed to
trace the history of the knowledge of plants. {361}




CHAPTER II.

UNSYSTEMATIC KNOWLEDGE OF PLANTS.


A STEP was made towards the formation of the Science of Plants,
although undoubtedly a slight one, as soon as men began to collect
information concerning them and their properties, from a love and
reverence for knowledge, independent of the passion for the
marvellous and the impulse of practical utility. This step was very
early made. The "wisdom" of Solomon, and the admiration which was
bestowed upon it, prove, even at that period, such a working of the
speculative faculty: and we are told, that among other evidences of
his being "wiser than all men," "he spake of trees, from the
cedar-tree that is in Lebanon even unto the hyssop that springeth
out of the wall."[9\16] The father of history, Herodotus, shows us
that a taste for natural history had, in his time, found a place in
the minds of the Greeks. In speaking of the luxuriant vegetation of
the Babylonian plain,[10\16] he is so far from desiring to astonish
merely, that he says, "the blades of wheat and barley are full four
fingers wide; but as to the size of the trees which grow from millet
and sesame, though I could mention it, I will not; knowing well that
those who have not been in that country will hardly believe what I
have said already." He then proceeds to describe some remarkable
circumstances respecting the fertilization of the date-palms in
Assyria.

[Note 9\16: 1 Kings iv. 33.]

[Note 10\16: Herod. i. 193.]

This curious and active spirit of the Greeks led rapidly, as we have
seen in other instances, to attempts at collecting and systematizing
knowledge on almost every subject: and in this, as in almost every
other department, Aristotle may be fixed upon, as the representative
of the highest stage of knowledge and system which they ever
attained. The vegetable kingdom, like every other province of
nature, was one of the fields of the labors of this universal
philosopher. But though his other works on natural history have come
down to us, and are a most valuable monument of the state of such
knowledge in his time, his Treatise on Plants is lost. The book _De
Plantis_ {362} which appears with his name, is an imposture of the
middle ages, full of errors and absurdities.[11\16]

[Note 11\16: Mirbel, _Botanique_, ii. 505.]

His disciple, friend, and successor, Theophrastus of Eresos, is, as
we have said already, the first great writer on botany whose works
we possess; and, as may be said in most cases of the first great
writer, he offers to us a richer store of genuine knowledge and good
sense than all his successors. But we find in him that the Greeks of
his time, who aspired, as we have said, to collect and _systematize_
a body of information on every subject, failed in one half of their
object, as far as related to the vegetable world. Their attempts at
a systematic distribution of plants were altogether futile. Although
Aristotle's divisions of the animal kingdom are, even at this day,
looked upon with admiration by the best naturalists, the
arrangements and comparisons of plants which were contrived by
Theophrastus and his successors, have not left the slightest trace
in the modern form of the science; and, therefore, according to our
plan, are of no importance in our history. And thus we can treat all
the miscellaneous information concerning vegetables which was
accumulated by the whole of this school of writers, in no other way
than as something antecedent to the first progress towards
systematic knowledge.

The information thus collected by the unsystematic writers is of
various kinds; and relates to the economical and medicinal uses of
plants, their habits, mode of cultivation, and many other
circumstances: it frequently includes some description; but this is
always extremely imperfect, because the essential conditions of
description had not been discovered. Of works composed of materials
so heterogeneous, it can be of little use to produce specimens; but
I may quote a few words from Theophrastus, which may serve to
connect him with the future history of the science, as bearing upon
one of the many problems respecting the identification of ancient
and modern plants. It has been made a question whether the following
description does not refer to the potato.[12\16] He is speaking of
the differences of roots: "Some roots," he says, "are still
different from those which have been described; as that of the
_arachidna_[13\16] plant: for this bears fruit underground as well
as above: the fleshy part sends one thick root deep into the ground,
but the others, which bear the fruit, are more slender {363} and
higher up, and ramified. It loves a sandy soil, and has no leaf
whatever."

[Note 12\16: Theoph. i. 11.]

[Note 13\16: Most probably the _Arachnis hypogæa_, or ground-nut.]

The books of Aristotle and Theophrastus soon took the place of the
Book of Nature in the attention of the degenerate philosophers who
succeeded them. A story is told by Strabo[14\16] concerning the fate
of the works of these great naturalists. In the case of the wars and
changes which occurred among the successors of Alexander, the heirs
of Theophrastus tried to secure to themselves his books, and those
of his master, by burying them in the ground. There the manuscripts
suffered much from damp and worms; till Apollonicon, a
book-collector of those days, purchased them, and attempted, in his
own way, to supply what time had obliterated. When Sylla marched the
Roman troops into Athens, he took possession of the library of
Apollonicon; and the works which it contained were soon circulated
among the learned of Rome and Alexandria, who were thus enabled to
_Aristotelize_[15\16] on botany as on other subjects.

[Note 14\16: Strabo, lib. xiii. c. i. § 54.]

[Note 15\16: Ἀριστοτλίζειν.]

The library collected by the Attalic kings of Pergamus, and the
Alexandrian Museum, founded and supported by the Ptolemies of Egypt,
rather fostered the commentatorial spirit than promoted the increase
of any real knowledge of nature. The Romans, in this as in other
subjects, were practical, not speculative. They had, in the times of
their national vigor, several writers on agriculture, who were
highly esteemed; but no author, till we come to Pliny, who dwells on
the mere knowledge of plants. And even in Pliny, it is easy to
perceive that we have before us a writer who extracted his
information principally from books. This remarkable man,[16\16] in
the middle of a public and active life, of campaigns and voyages,
contrived to accumulate, by reading and study, an extraordinary
store of knowledge of all kinds. So unwilling was he to have his
reading and note-making interrupted, that, even before day-break in
winter, and from his litter as he travelled, he was wont to dictate
to his amanuensis, who was obliged to preserve his hand from the
numbness which the cold occasioned, by the use of gloves.[17\16]

[Note 16\16: Sprengel, i. 163.]

[Note 17\16: Plin. Jun. Epist. 3, 5.]

It has been ingeniously observed, that we may find traces in the
botanical part of his Natural History, of the errors which this
hurried and broken habit of study produced; and that he appears
frequently to have had books read to him and to have heard them
amiss.[18\16] Thus, {364} among several other instances,
Theophrastus having said that the plane-tree is in Italy
rare,[19\16] Pliny, misled by the similarity of the Greek word
(_spanian_, rare), says that the tree occurs in Italy and
Spain.[20\16] His work has, with great propriety, been called the
Encyclopædia of Antiquity; and, in truth, there are few portions of
the learning of the times to which it does not refer. Of the
thirty-seven Books of which it consists, no less than sixteen (from
the twelfth to the twenty-seventh) relate to plants. The information
which is collected in these books, is of the most miscellaneous
kind; and the author admits, with little distinction, truth and
error, useful knowledge and absurd fables. The declamatory style,
and the comprehensive and lofty tone of thought which we have
already spoken of as characteristic of the Roman writers, are
peculiarly observable in him. The manner of his death is well known:
it was occasioned by the eruption of Vesuvius, A.D. 79, to which, in
his curiosity, he ventured so near as to be suffocated.

[Note 18\16: Sprengel, i. 163.]

[Note 19\16: Theoph. iv. 7. Ἔν μὲν γὰρ τῷ Ἀδρίᾳ πλάτανον οὐ φασὶν
εἶναι πλῆν περὶ το Διομήδους ἱερόν, _σπανίαν_ δὲ καὶ ἐν Ἰταλίᾳ πάσῃ]

[Note 20\16: Plin. Nat. Hist. xii. 3. Et alias (platanos) fuisse in
Italia, ac nominatim _Hispania_, apud auctores invenitur.]

Pliny's work acquired an almost unlimited authority, as one of the
standards of botanical knowledge, in the middle ages; but even more
than his, that of his contemporary, Pedanius Dioscorides, of
Anazarbus in Cilicia. This work, written in Greek, is held by the
best judges[21\16] to offer no evidence that the author observed for
himself. Yet he says expressly in his Preface, that his love of
natural history, and his military life, have led him into many
countries, in which he has had opportunity to become acquainted with
the nature of herbs and trees.[22\16] He speaks of six hundred
plants, but often indicates only their names and properties, giving
no description by which they can be identified. The main cause of
his great reputation in subsequent times was, that he says much of
the medicinal virtues of vegetables.

[Note 21\16: Mirbel, 510.]

[Note 22\16: Sprengel, i. 136.]

We come now to the ages of darkness and lethargy, when the habit of
original thought seems to die away, as the talent of original
observation had done before. Commentators and mystics succeed to the
philosophical naturalists of better times. And though a new race,
altogether distinct in blood and character from the Greek,
appropriates to itself the stores of Grecian learning, this movement
does not, as might be expected, break the chains of literary
slavery. The Arabs {365} bring, to the cultivation of the science of
the Greeks, their own oriental habit of submission, their oriental
love of wonder; and thus, while they swell the herd of commentators
and mystics, they produce no philosopher.

Yet the Arabs discharged an important function in the history of
human knowledge,[23\16] by preserving, and transmitting to more
enlightened times, the intellectual treasures of antiquity. The
unhappy dissensions which took place in the Christian church had
scattered these treasures over the East, at a period much antecedent
to the rise of the Saracen power. In the fifth century, the
adherents of Nestorius, bishop of Constantinople, were declared
heretical by the Council of Ephesus (A.D. 431), and driven into
exile. In this manner, many of the most learned and ingenious men of
the Christian world were removed to the Euphrates, where they formed
the _Chaldean_ church, erected the celebrated Nestorian school of
Edessa, and gave rise to many offsets from this in various regions.
Already, in the fifth century, Hibas, Cumas, and Probus, translated
the writings of Aristotle into Syriac. But the learned Nestorians
paid an especial attention to the art of medicine, and were the most
zealous students of the works of the Greek physicians. At
Djondisabor, in Khusistan, they became an ostensible medical school,
who distributed academical honors as the result of public
disputations. The califs of Bagdad heard of the fame and the wisdom
of the doctors of Djondisabor, summoned some of them to Bagdad, and
took measures for the foundation of a school of learning in that
city. The value of the skill, the learning, and the virtues of the
Nestorians, was so strongly felt, that they were allowed by the
Mohammedans the free exercise of the Christian religion, and
intrusted with the conduct of the studies of those of the Moslemin,
whose education was most cared for. The affinity of the Syriac and
Arabic languages made the task of instruction more easy. The
Nestorians translated the works of the ancients out of the former
into the latter language: hence there are still found Arabic
manuscripts of Dioscorides, with Syriac words in the margin. Pliny
and Aristotle likewise assumed an Arabic dress; and were, as well as
Dioscorides, the foundation of instruction in all the Arabian
academies; of which a great number were established throughout the
Saracen empire, from Bokhara in the remotest east, to Marocco and
Cordova in the west. After some time, the Mohammedans themselves
began to translate and {366} extract from their Syriac sources; and
at length to write works of their own. And thus arose vast
libraries, such as that of Cordova, which contained 250,000 volumes.

[Note 23\16: Sprengel, i. 203.]

The Nestorians are stated[24\16] to have first established among the
Arabs those collections of medicinal substances (_Apothecæ_), from
which our term _Apothecary_ is taken; and to have written books
(_Dispensatoria_) containing systematic instructions for the
employment of these medicaments; a word which long continued to be
implied in the same sense, and which we also retain, though in a
modified application (_Dispensary_).

[Note 24\16: Sprengel, i. 205.]

The directors of these collections were supposed to be intimately
acquainted with plants; and yet, in truth, the knowledge of plants
owed but little to them; for the Arabic Dioscorides was the source
and standard of their knowledge. The flourishing commerce of the
Arabians, their numerous and distant journeys, made them, no doubt,
practically acquainted with the productions of lands unknown to the
Greeks and Romans. Their Nestorian teachers had established
Christianity even as far as China and Malabar; and their travellers
mention[25\16] the camphor of Sumatra, the aloe-wood of Socotra near
Java, the tea of China. But they never learned the art of converting
their practical into speculative knowledge. They treat of plants
only in so far as their use in medicine is concerned,[26\16] and
followed Dioscorides in the description, and even in the order of
the plants, except when they arrange them according to the Arabic
alphabet. With little clearness of view, they often mistake what
they read:[27\16] thus when Dioscorides says that _ligusticon_ grows
on the _Apennine_, a mountain not far from the _Alps_; Avicenna,
misled by a resemblance of the Arabic letters, quotes him as saying
that the plant grows on _Akabis_, a mountain near _Egypt_.

[Note 25\16: Sprengel, i. 206.]

[Note 26\16: Ib. i. 207.]

[Note 27\16: Ib. i. 211.]

It is of little use to enumerate such writers. One of the most noted
of them was Mesuë, physician of the Calif of Kahirah. His work,
which was translated into Latin at a later period, was entitled, _On
Simple Medicines_; a title which was common to many medical
treatises, from the time of Galen in the second century. Indeed, of
this opposition of _simple_ and _compound_ medicines, we still have
traces in our language: {367}
    He would ope his leathern scrip,
  And show me _simples_ of a thousand names,
  Telling their strange and vigorous faculties.
          MILTON, _Comus_.

Where the subject of our history is so entirely at a stand, it is
unprofitable to dwell on a list of names. The Arabians, small as
their science was, were able to instruct the Christians. Their
writings were translated by learned Europeans, for instance Michael
Scot, and Constantine of Africa, a Carthaginian who had lived forty
years among the Saracens[28\16] and who died A.D. 1087. Among his
works, is a Treatise, _De Gradibus_, which contains the Arabian
medicinal lore. In the thirteenth century occur Encyclopædias, as
that of Albertus Magnus, and of Vincent of Beauvais; but these
contain no natural history except traditions and fables. Even the
ancient writers were altogether perverted and disfigured. The
Dioscorides of the middle ages varied materially from ours.[29\16]
Monks, merchants, and adventurers travelled far, but knowledge was
little increased. Simon of Genoa,[30\16] a writer on plants in the
fourteenth century, boasts that he perambulated the East in order to
collect plants. "Yet in his _Clavis Sanationis_," says a modern
botanical writer,[31\16] "we discover no trace of an acquaintance
with nature. He merely compares the Greek, Arabic, and Latin names
of plants, and gives their medicinal effect after his
predecessors:"--so little true is it, that the use of the senses
alone necessarily leads to real knowledge.

[Note 28\16: Sprengel, i. 230.]

[Note 29\16: Ib. i. 239.]

[Note 30\16: Ib. i. 241.]

[Note 31\16: Ib. ib.]

Though the growing activity of thought in Europe, and the revived
acquaintance with the authors of Greece in their genuine form, were
gradually dispelling the intellectual clouds of the middle ages, yet
during the fifteenth century, botany makes no approach to a
scientific form. The greater part of the literature of this subject
consisted of Herbals, all of which were formed on the same plan, and
appeared under titles such as _Hortus_, or _Ortus Sanitatis_. There
are, for example, three[32\16] such German Herbals, with woodcuts,
which date about 1490. But an important peculiarity in these works
is that they contain some indigenous species placed side by side
with the old ones. In 1516, _The Grete Herbal_ was published in
England, also with woodcuts. It contains an account of more than
four hundred vegetables, and their {368} products; of which one
hundred and fifty are English, and are no way distinguished from the
exotics by the mode in which they are inserted in the work.

[Note 32\16: Augsburg, 1488. Mainz, 1491. Lubec, 1492.]

We shall see, in the next chapter, that when the intellect of Europe
began really to apply itself to the observation of nature, the
progress towards genuine science soon began to be visible, in this
as in other subjects; but before this tendency could operate freely,
the history of botany was destined to show, in another instance, how
much more grateful to man, even when roused to intelligence and
activity, is the study of tradition than the study of nature. When
the scholars of Europe had become acquainted with the genuine works
of the ancients in the original languages, the pleasure and
admiration which they felt, led them to the most zealous endeavors
to illustrate and apply what they read. They fell into the error of
supposing that the plants described by Theophrastus, Dioscorides,
Pliny, must be those which grew in their own fields. And thus
Ruellius,[33\16] a French physician, who only travelled in the
environs of Paris and Picardy, imagined that he found there the
plants of Italy and Greece. The originators of genuine botany in
Germany, Brunfels and Tragus (Bock), committed the same mistake; and
hence arose the misapplication of classical names to many genera.
The labors of many other learned men took the same direction, of
treating the ancient writers as if they alone were the sources of
knowledge and truth.

[Note 33\16: _De Natura Stirpium_, 1536.]

But the philosophical spirit of Europe was already too vigorous to
allow this superstitious erudition to exercise a lasting sway.
Leonicenus, who taught at Ferrara till he was almost a hundred years
old, and died in 1524,[34\16] disputed, with great freedom, the
authority of the Arabian writers, and even of Pliny. He saw, and
showed by many examples, how little Pliny himself knew of nature,
and how many errors he had made or transmitted. The same
independence of thought with regard to other ancient writers, was
manifested by other scholars. Yet the power of ancient authority
melted away but gradually. Thus Antonius Brassavola, who established
on the banks of the Po the first botanical garden of modern times,
published in 1536, his _Examen omnium Simplicium Medicamentorum_;
and, as Cuvier says,[35\16] though he studied plants in nature, his
book (written in the {369} Platonic form of dialogue), has still the
character of a commentary on the ancients.

[Note 34\16: Sprengel, i. 252.]

[Note 35\16: _Hist. des Sc. Nat._ partie ii. 169.]

The Germans appear to have been the first to liberate themselves
from this thraldom, and to publish works founded mainly on actual
observation. The first of the botanists who had this great merit is
Otho Brunfels of Mentz, whose work, _Herbarum Vivæ Icones_, appeared
in 1530. It consists of two volumes in folio, with wood-cuts; and in
1532, a German edition was published. The plants which it contains
are given without any arrangement, and thus he belongs to the period
of unsystematic knowledge. Yet the progress towards the formation of
a system manifested itself so immediately in the series of German
botanists to which he belongs, that we might with almost equal
propriety transfer him to the history of that progress; to which we
now proceed.




CHAPTER III.

FORMATION OF A SYSTEM OF ARRANGEMENT OF PLANTS.


_Sect._ 1.--_Prelude to the Epoch of Cæsalpinus._

THE arrangement of plants in the earliest works was either
arbitrary, or according to their use, or some other extraneous
circumstance, as in Pliny. This and the division of vegetables by
Dioscorides into _aromatic_, _alimentary_, _medicinal_, _vinous_,
is, as will be easily seen, a merely casual distribution. The
Arabian writers, and those of the middle ages, showed still more
clearly their insensibility to the nature of system, by adopting an
alphabetical arrangement; which was employed also in the Herbals of
the sixteenth century. Brunfels, as we have said, adopted no
principle of order; nor did his successor, Fuchs. Yet the latter
writer urged his countrymen to put aside their Arabian and barbarous
Latin doctors, and to observe the vegetable kingdom for themselves;
and he himself set the example of doing this, examined plants with
zeal and accuracy, and made above fifteen hundred drawings of
them.[36\16] {370}

[Note 36\16: His _Historia Stirpium_ was published at Basil in 1542.]

The difficulty of representing plants in any useful way by means of
drawings, is greater, perhaps, than it at first appears. So long as
no distinction was made of the importance of different organs of the
plant, a picture representing merely the obvious general appearance
and larger parts, was of comparatively small value. Hence we are not
to wonder at the slighting manner in which Pliny speaks of such
records. "Those who gave such pictures of plants," he says,
"Crateuas, Dionysius, Metrodorus, have shown nothing clearly, except
the difficulty of their undertaking. A picture may be mistaken, and
is changed and disfigured by copyists; and, without these
imperfections, it is not enough to represent the plant in one state,
since it has four different aspects in the four seasons of the year."

The diffusion of the habit of exact drawing, especially among the
countrymen of Albert Durer and Lucas Cranach, and the invention of
wood-cuts and copper-plates, remedied some of these defects.
Moreover, the conviction gradually arose in men's minds that the
structure of the flower and the fruit are the most important
circumstances in fixing the identity of the plant. Theophrastus
speaks with precision of the organs which he describes, but these
are principally the leaves, roots, and stems. Fuchs uses the term
_apices_ for the anthers, and _gluma_ for the blossom of grasses,
thus showing that he had noticed these parts as generally present.

In the next writer whom we have to mention, we find some traces of a
perception of the real resemblances of plants beginning to appear.
It is impossible to explain the progress of such views without
assuming in the reader some acquaintance with plants; but a very few
words may suffice to convey the requisite notions. Even in plants
which most commonly come in our way, we may perceive instances of
the resemblances of which we speak. Thus, Mint, Marjoram, Basil,
Sage, Lavender, Thyme, Dead-nettle, and many other plants, have a
tubular flower, of which the mouth is divided into two lips; hence
they are formed into a family, and termed _Labiatæ_. Again, the
Stock, the Wall-flower, the Mustard, the Cress, the Lady-smock, the
Shepherd's purse, have, among other similarities, their blossoms
with four petals arranged crosswise; these are all of the order
_Cruciferæ_. Other flowers, apparently more complex, still resemble
each other, as Daisy. Marigold, Aster, and Chamomile; these belong
to the order _Compositæ_. And though the members of each such family
may differ widely in their larger parts, their stems and leaves, the
close study of nature leads the botanist irresistibly to consider
their resemblances as {371} occupying a far more important place
than their differences. It is the general establishment of this
conviction and its consequences which we have now to follow.

The first writer in whom we find the traces of an arrangement
depending upon these natural resemblances, is Hieronymus Tragus,
(Jerom Bock,) a laborious German botanist, who, in 1551, published a
herbal. In this work, several of the species included in those
natural families to which we have alluded,[37\16] as for instance
the Labiatæ, the Cruciferæ, the Compositæ, are for the most part
brought together; and thus, although with many mistakes as to such
connexions, a new principle of order is introduced into the subject.

[Note 37\16: Sprengel, i. 270.]

In pursuing the development of such principles of natural order, it
is necessary to recollect that the principles lead to an assemblage
of divisions and groups, successively subordinate, the lower to the
higher, like the brigades, regiments, and companies of an army, or
the provinces, towns, and parishes of a kingdom. Species are
included in Genera, Genera in Families or Orders, and orders in
Classes. The perception that there is some connexion among the
species of plants, was the first essential step; the detection of
different marks and characters which should give, on the one hand,
limited groups, on the other, comprehensive divisions, were other
highly important parts of this advance. To point out every
successive movement in this progress would be a task of extreme
difficulty, but we may note, as the most prominent portions of it,
the establishment of the groups which immediately include Species,
that is, _the formation of Genera_; and the invention of a method
which should distribute into consistent and distinct divisions the
whole vegetable kingdom, that is, _the construction of a System_.

To the second of these two steps we have no difficulty in assigning
its proper author. It belongs to Cæsalpinus, and marks the first
great epoch of this science. It is less easy to state to what
botanist is due the establishment of Genera; yet we may justly
assign the greater part of the merit of this invention, as is
usually done, to Conrad Gessner of Zurich. This eminent naturalist,
after publishing his great work on animals, died[38\16] of the
plague in 1565, at the age of forty-nine, while he was preparing to
publish a History of Plants, a sequel to his History of Animals. The
fate of the work thus left {372} unfinished was remarkable. It fell
into the hands of his pupil, Gaspard Wolf, who was to have published
it, but wanting leisure for the office, sold it to Joachim
Camerarius, a physician and botanist of Nuremberg, who made use of
the engravings prepared by Gessner, in an Epitome which he published
in 1586. The text of Gessner's work, after passing through various
hands, was published in 1754 under the title of _Gessneri Opera
Botanica per duo Sæcula desiderata, &c._, but is very incomplete.

[Note 38\16: Cuvier, _Leçons sur l'Hist. des Sciences Naturelles_,
partie ii. p. 193.]

The imperfect state in which Gessner left his botanical labors,
makes it necessary to seek the evidence of his peculiar views in
scattered passages of his correspondence and other works. One of his
great merits was, that he saw the peculiar importance of the flower
and fruit as affording the characters by which the affinities of
plants were to be detected; and that he urged this view upon his
contemporaries. His plates present to us, by the side of each plant,
its flower and its fruit, carefully engraved. And in his
communications with his botanical correspondents, he repeatedly
insists on these parts. Thus[39\16] in 1565 he writes to Zuinger
concerning some foreign plants which the latter possessed: "Tell me
if your plants have fruit and flower, as well as stalk and leaves,
for those are of much the greater consequence. By these three
marks,--flower, fruit, and seed,--I find that Saxifraga and
Consolida Regalis are related to Aconite." These characters, derived
from the _fructification_ (as the assemblage of flower and fruit is
called), are the means by which genera are established, and hence,
by the best botanists, Gessner is declared to be the inventor of
genera.[40\16] {373}

[Note 39\16: _Epistolæ_, fol. 113 a; see also fol. 65 b.]

[Note 40\16: Haller, _Biblio Botanica_, i. 284. Methodi Botanicæ
rationem primus pervidit;--dari nempe et genera quæ plures species
comprehenderent et classes quæ multa genera. Varias etiam classes
naturales expressit. Characterem in flore inque semine posuit,
&c.--_Rauwolfio Socio Epist._ Wolf, p. 39.

Linnæus, _Genera Plantarum_, Pref. xiii. "A fructificatione plantas
distinguere in genera, infinitæ sapientiæ placuisse, detexit
posterior ætas, et quidem primus, sæculi sui ornamentum, Conradus
Gessnerus, uti patet ex Epistolis ejus postremis, et Tabulis per
Carmerarium editis."

Cuvier says (_Hist. des Sc. Nat._ 2^e p^e, p. 193), after speaking to
the same effect, "Il fit voir encore que toutes les plantes qui ont
des fleurs et des fruits semblables se ressemblent par leurs
propriétés, et que quand on rapproche ces plantes on obtient ainsi une
classification naturelle." I do not know if he here refers to any
particular passages of Gessner's work.]

The labors of Gessner in botany, both on account of the unfinished
state in which he left the application of his principles, and on
account of the absence of any principles manifestly applicable to
the whole extent of the vegetable kingdom, can only be considered as
a prelude to the epoch in which those defects were supplied. To that
epoch we now proceed.


_Sect._ 2.--_Epoch of Cæsalpinus.--Formation of a System of
Arrangement._

IF any one were disposed to question whether Natural History truly
belongs to the domain of Inductive Science;--whether it is to be
prosecuted by the same methods, and requires the same endowments of
mind as those which lead to the successful cultivation of the
Physical Sciences,--the circumstances under which Botany has made
its advance appear fitted to remove such doubts. The first decided
step in this study was merely the construction of a classification
of its subjects. We shall, I trust, be able to show that such a
classification includes, in reality, the establishment of one
general principle, and leads to more. But without here dwelling on
this point, it is worth notice that the person to whom we owe this
classification, Andreas Cæsalpinus of Arezzo, was one of the most
philosophical men of his time, profoundly skilled in the
Aristotelian lore which was then esteemed, yet gifted with courage
and sagacity which enabled him to weigh the value of the Peripatetic
doctrines, to reject what seemed error, and to look onwards to a
better philosophy. "How are we to understand," he inquires, "that we
must proceed from universals to particulars (as Aristotle directs),
when particulars are better known?"[41\16] Yet he treats the Master
with deference, and, as has been observed,[42\16] we see in his
great botanical work deep traces of the best features of the
Aristotelian school, logic and method; and, indeed, in this work he
frequently refers to his _Quæstiones Peripateticæ_. His book,
entitled _De Plantis libri_ xvi. appeared at Florence in 1583. The
aspect under which his task presented itself to his mind appears to
me to possess so much interest, that I will transcribe a few of his
reflections. After speaking of the splendid multiplicity of the
productions of nature, and the confusion which has hitherto
prevailed among writers on plants, {374} the growing treasures of
the botanical world; he adds,[43\16] "In this immense multitude of
plants, I see that want which is most felt in any other unordered
crowd: if such an assemblage be not arranged into brigades like an
army, all must be tumult and fluctuation. And this accordingly
happens in the treatment of plants: for the mind is overwhelmed by
the confused accumulation of things, and thus arise endless mistake
and angry altercation." He then states his general view, which, as
we shall see, was adopted by his successors. "_Since all science
consists in the collection of similar, and the distinction of
dissimilar things_, and since the consequence of this is a
distribution into genera and species, which are to be natural
classes governed by real differences, I have attempted to execute
this task in the whole range of plants;--ut si quid pro ingenii mei
tenuitate in hujusmodi studio profecerim, ad communem utilitatem
proferam." We see here how clearly he claims for himself the credit
of being the first to execute this task of arrangement.

[Note 41\16: _Quæstiones Peripateticæ_, (1569,) lib. i. quæst. i.]

[Note 42\16: Cuvier, p. 198.]

[Note 43\16: Dedicatio, a 2.]

After certain preparatory speculations, he says,[44\16] "Let us now
endeavor to mark the kinds of plants by essential circumstances in
the fructification." He then observes, "In the constitution of
organs three things are mainly important--the number, the position,
the figure." And he then proceeds to exemplify this: "Some have
under one flower, ONE _seed_, as _Amygdala_, or ONE
seed-_receptacle_, as _Rosa_; or TWO _seeds_, as _Ferularia_, or TWO
seed-_receptacles_, as _Nasturtium_; or three, as the _Tithymalum_
kind have THREE _seeds_, the _Bulbaceæ_ THREE _receptacles_; or
four, as _Marrubium_, FOUR _seeds_, _Siler_ FOUR _receptacles_; or
more, as _Cicoraceæ_, and _Acanaceæ_ have MORE _seeds_, _Pinus_,
MORE _receptacles_."

[Note 44\16: Lib. i. c. 13, 14.]

It will be observed that we have here ten classes made out by means
of number alone, added to the consideration of whether the seed is
alone in its covering, as in a cherry, or contained in a receptacle
with several others, as in a berry, pod, or capsule. Several of
these divisions are, however, further subdivided according to other
circumstances, and especially according as the vital part of the
seed, which he called the heart (_cor_[45\16]), is situated in the
upper or lower part of the seed. As our object here is only to
indicate the principle of the method of Cæsalpinus, I need not
further dwell on the details, and still less on the defects by which
it is disfigured, as, for instance, the retention of the old
distinction of Trees, Shrubs, and Herbs. {375}

[Note 45\16: _Corculum_, of Linnæus.]

To some persons it may appear that this arbitrary distribution of
the vegetable kingdom, according to the number of parts of a
particular kind, cannot deserve to be spoken of as a great
discovery. And if, indeed, the distribution had been arbitrary, this
would have been true; the real merit of this and of every other
system is, that while it is artificial in its form, it is natural in
its results. The plants which are associated by the arrangement of
Cæsalpinus, are those which have the closest resemblances in the
most essential points. Thus, as Linnæus says, though the first in
attempting to form natural orders, he observed as many as the most
successful of later writers. Thus his _Legumina_[46\16] correspond
to the natural order _Leguminosæ_; his _genus Ferulaceum_[47\16] to
the _Umbellatæ_; his _Bulbaceæ_[48\16] to _Liliaceæ_; his
_Anthemides_[49\16] to the _Compositæ_; in like manner, the
_Boragineæ_ are brought together,[50\16] and the _Labiatæ_. That
such assemblages are produced by the application of his principles,
is a sufficient evidence that they have their foundation in the
general laws of the vegetable world. If this had not been the case,
the mere application of number or figure alone as a standard of
arrangement, would have produced only intolerable anomalies. If, for
instance, Cæsalpinus had arranged plants by the number of flowers on
the same stalk, he would have separated individuals of the same
species; if he had distributed them according to the number of
leaflets which compose the leaves, he would have had to place far
asunder different species of the same genus. Or, as he himself
says,[51\16] "If we make one genus of those which have a round root,
as Rapum, Aristolochia, Cyclaminus, Aton, we shall separate from
this genus those which most agree with it, as Napum and Raphanum,
which resemble Rapum, and the long Aristolochia, which resembles the
round; while we shall join the most remote kinds, for the nature of
Cyclaminus and Rapum is altogether diverse in all other respects. Or
if we attend to the differences of stalk, so as to make one genus of
those which have a naked stalk, as the Junci, Cæpe, Aphacæ, along
with Cicoraceæ, Violæ, we shall still connect the most unlike
things, and disjoin the closest affinities. And if we note the
differences of leaves, or even flowers, we fall into the same
difficulty; for many plants very different in kind have leaves very
similar, as Polygonum and Hypericum, Ernea and Sesamois, Apium and
Ranunculus; and plants of the same genus have sometimes very
different {376} leaves, as the several species of Ranunculus and of
Lactuca. Nor will color or shape of the flowers help us better; for
what has Vitis in common with Œnanthe, except the resemblance of the
flower?" He then goes on to say, that if we seek a too close
coincidence of all the characters we shall have no Species; and thus
shows us that he had clearly before his view the difficulty, which
he had to attack, and which it is his glory to have overcome, that
of constructing Natural Orders.

[Note 46\16: Lib. vi.]

[Note 47\16: Lib. vii.]

[Note 48\16: Lib. x.]

[Note 49\16: Lib. xii.]

[Note 50\16: Lib. xi.]

[Note 51\16: Lib. i. cap. xii. p. 25.]

But as the principles of Cæsalpinus are justified, on the one hand,
by their leading to _Natural Orders_, they are recommended on the
other by their producing a _System_ which applies through the whole
extent of the vegetable kingdom. The parts from which he takes his
characters must occur in all flowering-plants, for all such plants
have seeds. And these seeds, if not very numerous for each flower,
will be of a certain definite number and orderly distribution. And
thus every plant will fall into one part or other of the same system.

It is not difficult to point out, in this induction of Cæsalpinus,
the two elements which we have so often declared must occur in all
inductive processes; the exact acquaintance with _facts_, and the
general and applicable _ideas_ by which these facts are brought
together. Cæsalpinus was no mere dealer in intellectual relations or
learned traditions, but a laborious and persevering collector of
plants and of botanical knowledge. "For many years," he says in his
Dedication, "I have been pursuing my researches in various regions,
habitually visiting the places in which grew the various kinds of
herbs, shrubs, and trees; I have been assisted by the labors of many
friends, and by gardens established for the public benefit, and
containing foreign plants collected from the most remote regions."
He here refers to the first garden directed to the public study of
Botany, which was that of Pisa,[52\16] instituted in 1543, by order
of the Grand Duke Cosmo the First. The management of it was confided
first to Lucas Ghini, and afterwards to Cæsalpinus. He had collected
also a herbarium of dried plants, which he calls the rudiment of his
work. "Tibi enim," he says, in his dedication to Francis Medici,
Grand Duke of Etruria, "apud quem extat ejus rudimentum ex plantis
libro agglutinatis a me compositum." And, throughout, he speaks with
the most familiar and vivid acquaintance of the various vegetables
which he describes.

[Note 52\16: Cuv. 187.]

But Cæsalpinus also possessed fixed and general views concerning the
relation and functions of the parts of plants, and ideas of symmetry
{377} and system; without which, as we see in other botanists of his
and succeeding times, the mere accumulation of a knowledge of
details does not lead to any advance in science. We have already
mentioned his reference to general philosophical principles, both of
the Peripatetics and of his own. The first twelve chapters of his
work are employed in explaining the general structure of plants, and
especially that point to which he justly attaches so much
importance, the results of the different situation of the _cor_ or
_corculum_ of the seed. He shows[53\16] that if we take the root, or
stem, or leaves, or blossom, as our guide in classification, we
shall separate plants obviously alike, and approximate those which
have merely superficial resemblances. And thus we see that he had in
his mind ideas of fixed resemblance and symmetrical distribution,
which he sedulously endeavored to apply to plants; while his
acquaintance with the vegetable kingdom enabled him to see in what
manner these ideas were not, and in what manner they were, really
applicable.

[Note 53\16: Lib. i. cap. xii.]

The great merit and originality of Cæsalpinus have been generally
allowed, by the best of the more modern writers on Botany. Linnæus
calls him one of the founders of the science; "Primus verus
systematicus;"[54\16] and, as if not satisfied with the expression
of his admiration in prose, hangs a poetical garland on the tomb of
his hero. The following distich concludes his remarks on this
writer:
  Quisquis hic extiterit primos concedet honores
  Cæsalpine tibi; primaque serta dabit:
and similar language of praise has been applied to him by the best
botanists up to Cuvier,[55\16] who justly terms his book "a work of
genius."

[Note 54\16: _Philosoph. Bot._ p. 19.]

[Note 55\16: Cuv. _Hist._ 193.]

Perhaps the great advance made in this science by Cæsalpinus, is
most strongly shown by this; that no one appeared, to follow the
path which he had opened to system and symmetry, for nearly a
century. Moreover, when the progress of this branch of knowledge was
resumed, his next successor, Morison, did not choose to acknowledge
that he had borrowed so much from so old a writer; and thus, hardly
mentions his name, although he takes advantage of his labors, and
even transcribes his words without acknowledgement, as I shall show.
The pause between the great invention of Cæsalpinus, and its natural
sequel, the developement and improvement of his method, is so
marked, that I {378} will, in order to avoid too great an
interruption of chronological order, record some of its
circumstances in a separate section.


_Sect._ 3.--_Stationary Interval._

THE method of Cæsalpinus was not, at first, generally adopted. It
had, indeed, some disadvantages. Employed in drawing the
boundary-lines of the larger divisions of the vegetable kingdom, he
had omitted those smaller groups, Genera, which were both most
obvious to common botanists, and most convenient in the description
and comparison of plants. He had also neglected to give the Synonyms
of other authors for the plants spoken of by him; an appendage to
botanical descriptions, which the increase of botanical information
and botanical books had now rendered indispensable. And thus it
happened, that a work, which must always be considered as forming a
great epoch in the science to which it refers, was probably little
read, and in a short time could be treated as if it were quite
forgotten.

In the mean time, the science was gradually improved in its details.
Clusius, or Charles de l'Ecluse, first taught botanists to describe
well. "Before him," says Mirbel,[56\16] "the descriptions were
diffuse, obscure, indistinct; or else concise, incomplete, vague.
Clusius introduced exactitude, precision, neatness, elegance,
method: he says nothing superfluous; he omits nothing necessary." He
travelled over great part of Europe, and published various works on
the more rare of the plants which he had seen. Among such plants, we
may note now one well known, the potato; which he describes as being
commonly used in Italy in 1586;[57\16] thus throwing doubt, at
least, on the opinion which ascribes the first introduction of it
into Europe to Sir Walter Raleigh, on his return from Virginia,
about the same period. As serving to illustrate, both this point,
and the descriptive style of Clusius, I quote, in a note, his
description of the flower of this plant.[58\16] {379}

[Note 56\16: _Physiol. Veg._ p. 525.]

[Note 57\16: Clusius. _Exotic_. iv. c. 52, p. lxxix.]

[Note 58\16: "Papas Peruanorum. Arachidna, Theoph. forte. Flores
elegantes, uncialis amplitudinis aut majores, angulosi, singulari
folio constantes, sed ita complicato ut quinque folia discreta
videantur, coloris exterius ex purpura candicantis, interius
purpurascentis, radiis quinque herbaceis ex umbilico stellæ instar
prodeuntibus, et totidem staminibus flavis in umbonem coeuntibus."

He says that the Italians do not know whence they had the plant, and
that they call it _Taratouffli_. The name _Potato_ was, in England,
previously applied to the Sweet Potato (_Convolvulus batatas_),
which was the _common_ Potato, in distinction to the _Virginian
_Potato, at the time of Gerard's Herbal. (1597?) Gerard's figures of
both plants are copied from those of Clusius.

It may be seen by the description of Arachidna, already quoted from
Theophrastus, (above,) that there is little plausibility in
Clusius's conjecture of the plant being known to the ancients. I
need not inform the botanist that this opinion is untenable.]

The addition of exotic species to the number of known plants was
indeed going on rapidly during the interval which we are now
considering. Francis Hernandez, a Spaniard, who visited America
towards the end of the sixteenth century, collected and described
many plants of that country, some of which were afterwards published
by Recchi.[59\16] Barnabas Cobo, who went as a missionary to America
in 1596, also described plants.[60\16] The Dutch, among other
exertions which they made in their struggle with the tyranny of
Spain, sent out an expedition which, for a time, conquered the
Brazils; and among other fruits of this conquest, they published an
account of the natural history of the country.[61\16] To avoid
interrupting the connexion of such labors, I will here carry them on
a little further in the order of time. Paul Herman, of Halle, in
Saxony, went to the Cape of Good Hope and to Ceylon; and on his
return, astonished the botanists of Europe by the vast quantity of
remarkable plants which he introduced to their knowledge.[62\16]
Rheede, the Dutch governor of Malabar, ordered descriptions and
drawings to be made of many curious species, which were published in
a large work in twelve folio volumes.[63\16] Rumphe, another Dutch
consul at Amboyna,[64\16] labored with zeal and success upon the
plants of the Moluccas. Some species which occur in Madagascar
figured in a description of that island composed by the French
Commandant Flacourt.[65\16] Shortly afterwards, Engelbert
Kæmpfer,[66\16] a Westphalian of great acquirements and undaunted
courage, visited Persia, Arabia Felix, the Mogul Empire, Ceylon,
Bengal, Sumatra, Java, Siam, Japan; Wheler travelled in Greece and
Asia Minor; and Sherard, the English consul, published an account of
the plants of the neighborhood of Smyrna. {380}

[Note 59\16: _Nova Plantarum Regni Mexicana Historia_, Rom. 1651,
fol.]

[Note 60\16: Sprengel, _Gesch. der Botanik_, ii. 62.]

[Note 61\16: _Historia Naturalis Brasiliæ_, L. B. 1648, fol. (Piso
and Maregraf).]

[Note 62\16: _Museum Zeylanicum_, L. B. 1726.]

[Note 63\16: _Hortus Malabaricus_, 1670-1703.]

[Note 64\16: _Herbarium Amboinense_, Amsterdam, 1741-51, fol.]

[Note 65\16: _Histoire de la grande Isle Madagascar_, Paris, 1661.]

[Note 66\16: _Amœnitates Exoticæ_, Lemgov. 1712. 4to.]

At the same time, the New World excited also the curiosity of
botanists. Hans Sloane collected the plants of Jamaica; John
Banister those of Virginia; William Vernon, also an Englishman, and
David Kriege, a Saxon, those of Maryland; two Frenchmen, Surian and
Father Plumier, those of Saint Domingo.

We may add that public botanical gardens were about this time
established all over Europe. We have already noticed the institution
of that of Pisa in 1543; the second was that of Padua in 1545; the
next, that of Florence in 1556; the fourth, that of Bologna, 1568;
that of Rome, in the Vatican, dates also from 1568.

The first transalpine garden of this kind arose at Leyden in 1577;
that of Leipzig in 1580. Henry the Fourth of France established one
at Montpellier in 1597. Several others were instituted in Germany;
but that of Paris did not begin to exist till 1626; that of Upsal,
afterwards so celebrated, took its rise in 1657, that of Amsterdam
in 1684. Morison, whom we shall soon have to mention, calls himself,
in 1680, the first Director of the Botanical Garden at Oxford.

[2nd Ed.] [To what is above said of Botanical Gardens and Botanical
Writers, between the times of Cæsalpinus and Morison, I may add a
few circumstances. The first academical garden in France was that at
Montpellier, which was established by Peter Richier de Belleval, at
the end of the sixteenth century. About the same period, rare
flowers were cultivated at Paris, and pictures of them made, in
order to supply the embroiderers of the court-robes with new
patterns. Thus figures of the most beautiful flowers in the garden
of Peter Robins were published by the court-embroiderer Peter
Vallet, in 1608, under the title of _Le Jardin du Roi Henry IV_. But
Robins' works were of great service to botany; and his garden
assisted the studies of Renealmus (Paul Reneaulme), whose _Specimen
Historiæ Plantarum_ (Paris, 1611), is highly spoken of by the best
botanists. Recently, Mr. Robert Brown has named after him a new
genus of _Irideæ_ (RENEALMIA); adding, "Dixi in memoriam PAULI
RENEALMI, botanici sui ævi accuratissimi, atque staminum primi
scrutatoris; qui non modo eorum numerum et situm, sed etiam
filamentorum proportionem passim descripsit, et characterem
tetradynamicum siliquosarum perspexit." (_Prodromus Floræ Novæ
Hollandiæ_, p. 448.)

The oldest Botanical Garden in England is that at Hampton Court,
founded by Queen Elizabeth, and much enriched by Charles II. and
William III. (Sprengel, _Gesch. d. Bot._ vol. ii. p. 96.)]

In the mean time, although there appeared no new system which {381}
commanded the attention of the botanical world, the feeling of the
importance of the affinities of plants became continually more
strong and distinct.

Lobel, who was botanist to James the First, and who published his
_Stirpium Adversaria Nova_ in 1571, brings together the natural
families of plants more distinctly than his predecessors, and even
distinguishes (as Cuvier states,[67\16]) monocotyledonous from
dicotyledonous plants; one of the most comprehensive division-lines
of botany, of which succeeding times discovered the value more
completely. Fabius Columna,[68\16] in 1616, gave figures of the
fructification of plants on copper, as Gessner had before done on
wood. But the elder Bauhin (John), notwithstanding all that
Cæsalpinus had done, retrograded, in a work published in 1619, into
the less precise and scientific distinctions of--trees with nuts;
with berries; with acorns; with pods; creeping plants, gourds, &c.:
and no clear progress towards a system was anywhere visible among
the authors of this period.

[Note 67\16: Cuv. _Leçons, &c._ 198.]

[Note 68\16: Ib. 206.]

While this continued to be the case, and while the materials, thus
destitute of order, went on accumulating, it was inevitable that the
evils which Cæsalpinus had endeavored to remedy, should become more
and more grievous. "The nomenclature of the subject[69\16] was in
such disorder, it was so impossible to determine with certainty the
plants spoken of by preceding writers, that thirty or forty
different botanists had given to the same plant almost as many
different names. Bauhin called by one appellation, a species which
Lobel or Matheoli designated by another. There was an actual chaos,
a universal confusion, in which it was impossible for men to find
their way." We can the better understand such a state of things,
from having, in our own time, seen another classificatory science,
Mineralogy, in the very condition thus described. For such a state
of confusion there is no remedy but the establishment of a true
system of classification; which by its real foundation renders a
reason for the place of each species; and which, by the fixity of
its classes, affords a basis for a standard nomenclature, as finally
took place in Botany. But before such a remedy is obtained, men
naturally try to alleviate the evil by tabulating the synonyms of
different writers, as far as they are able to do so. The task of
constructing such a _Synonymy_ of botany at the period of which we
speak, was undertaken by Gaspard Bauhin, the brother of John, but
nineteen years younger. This work, the _Pinax Theatri Botanici_, was
printed {382} at Basil in 1623. It was a useful undertaking at the
time; but the want of any genuine order in the _Pinax_ itself,
rendered it impossible that it should be of great permanent utility.

[Note 69\16: Ib. 212.]

After this period, the progress of almost all the sciences became
languid for a while; and one reason of this interruption was, the
wars and troubles which prevailed over almost the whole of Europe.
The quarrels of Charles the First and his parliament, the civil wars
and the usurpation, in England; in France, the war of the League,
the stormy reign of Henry the Fourth, the civil wars of the minority
of Louis the Thirteenth, the war against the Protestants and the war
of the Fronde in the minority of Louis the Fourteenth; the bloody
and destructive Thirty Years' War in Germany; the war of Spain with
the United Provinces and with Portugal;--all these dire agitations
left men neither leisure nor disposition to direct their best
thoughts to the promotion of science. The baser spirits were
brutalized; the better were occupied by high practical aims and
struggles of their moral nature. Amid such storms, the intellectual
powers of man could not work with their due calmness, nor his
intellectual objects shine with their proper lustre.

At length a period of greater tranquillity gleamed forth, and the
sciences soon expanded in the sunshine. Botany was not inert amid
this activity, and rapidly advanced in a new direction, that of
physiology; but before we speak of this portion of our subject, we
must complete what we have to say of it as a classificatory science.


_Sect._ 4.--_Sequel to the Epoch of Cæsalpinus. Further Formation
and Adoption of Systematic Arrangement._

SOON after the period of which we now speak, that of the restoration
of the Stuarts to the throne of England, systematic arrangements of
plants appeared in great numbers; and in a manner such as to show
that the minds of botanists had gradually been ripening for this
improvement, through the influence of preceding writers, and the
growing acquaintance with plants. The person whose name is usually
placed first on this list, Robert Morison, appears to me to be much
less meritorious than many of those who published very shortly after
him; but I will give him the precedence in my narrative. He was a
Scotchman, who was wounded fighting on the royalist side in the
civil wars of England. On the triumph of the republicans, he
withdrew to France, when he became director of the garden of Gaston,
Duke of Orléans at Blois; and there he came under the notice of our
Charles {383} the Second; who, on his restoration, summoned Morison
to England, where he became Superintendent of the Royal Gardens, and
also of the Botanic Garden at Oxford. In 1669, he published _Remarks
on the Mistakes of the two Bauhins_, in which he proves that many
plants in the _Pinax_ are erroneously placed, and shows considerable
talent for appreciating natural families and genera. His great
systematic work appeared from the University press at Oxford in
1680. It contains a system, but a system, Cuvier says,[70\16] which
approaches rather to a natural method than to a rigorous
distribution, like that of his predecessor Cæsalpinus, or that of
his successor Ray. Thus the herbaceous plants are divided into
_climbers_, _leguminous_, _siliquose_, _unicapsalar_, _bicapsular_,
_tricapsular_, _quadricapsular_, _quinquecapsular_; this division
being combined with characters derived from the number of petals.
But along with these numerical elements, are introduced others of a
loose and heterogeneous kind, for instance, the classification of
herbs as _lactescent_ and _emollient_. It is not unreasonable to
say, that such a scheme shows no talent for constructing a complete
system; and that the most distinct part of it, that dependent on the
fruit, was probably borrowed from Cæsalpinus. That this is so, we
have, I think, strong proof; for though Morison nowhere, I believe,
mentions Cæsalpinus, except in one place in a loose enumeration of
botanical writers,[71\16] he must have made considerable use of his
work. For he has introduced into his own preface a passage copied
literally[72\16] from the dedication of Cæsalpinus; which passage we
have already quoted (p. 374,) beginning, "Since all science consists
in the collection of similar, and the distinction of dissimilar
things." And that the mention of the original is not omitted by
accident, appears from this; that Morison appropriates also the
conclusion of the passage, which has a personal reference, "_Conatus
sum id præstare in universa plantarum historia, ut si quid pro
ingenii mei tenuitate in hujusmodi studio profecerim, ad communem
utilitatem proferrem._" That Morison, thus, at so long an interval
after the publication of the work of Cæsalpinus, borrowed from him
without acknowledgement, and adopted his system so as to mutilate
it, proves that he had neither the temper nor the talent of a
discoverer; and justifies us withholding from him the credit which
belongs to those, who, in his time, resumed the great undertaking of
constructing a vegetable system.

[Note 70\16: Cuv. _Leçons_, &c. p. 486.]

[Note 71\16: Pref. p. i.]

[Note 72\16: Ib. p. ii.]

Among those whose efforts in this way had the greatest and earliest
{384} influence, was undoubtedly our countryman, John Ray, who was
Fellow of Trinity College, Cambridge, at the same time with Isaac
Newton. But though Cuvier states[73\16] that Ray was the model of
the systematists during the whole of the eighteenth century, the
Germans claim a part of his merit for one of their countrymen,
Joachim Jung, of Lubeck, professor at Hamburg.[74\16] Concerning the
principles of this botanist, little was known during his life. But a
manuscript of his book was communicated[75\16] to Ray in 1660, and
from this time forwards, says Sprengel, there might be noticed in
the writings of Englishmen, those better and clearer views to which
Jung's principles gave birth. Five years after the death of Jung,
his _Doxoscopia Physica_ was published, in 1662; and in 1678, his
_Isagoge Phytoscopica_. But neither of these works was ever much
read; and even Linnæus, whom few things escaped which concerned
botany, had, in 1771, seen none of Jung's works.

[Note 73\16: _Leçons Hist. Sc._ p. 487.]

[Note 74\16: Sprengel, ii. 27.]

[Note 75\16: Ray acknowledges this in his _Index Plant. Agri
Cantab._ p. 87, and quotes from it the definition of _caulis_.]

I here pass over Jung's improvements of botanical language, and
speak only of those which he is asserted to have suggested in the
arrangement of plants. He examines, says Sprengel,[76\16] the value
of characters of species, which, he holds, must not be taken from
the thorns, nor from color, taste, smell, medicinal effects, time
and place of blossoming. He shows, in numerous examples, what plants
must be separated, though called by a common name, and what most be
united, though their names are several.

[Note 76\16: Sprengel, ii. 29.]

I do not see in this much that interferes with the originality of
Ray's method,[77\16] of which, in consequence of the importance
ascribed to it by Cuvier, as we have already seen, I shall give an
account, following that great naturalist.[78\16] I confine myself to
the ordinary plants, and omit the more obscure vegetables, as
mushrooms, mosses, ferns, and the like.

[Note 77\16: _Methodus Plantarum Nova_, 1682. _Historia Plantarum_,
1686.]

[Note 78\16: Cuv.  _Leçons Hist. Sc._ 488.]

Such plants are _composite_ or _simple_. The _composite_ flowers are
those which contain many florets in the same _calyx_.[79\16] These
are subdivided according as they are composed altogether of complete
florets, {385} or of half florets, or of a centre of complete
florets, surrounded by a circumference or ray of demi-florets. Such
are the divisions of the _corymbiferæ_, or _compositæ_.

[Note 79\16: _Involucrum_, in modern terminology.]

In the _simple_ flowers, the seeds are _naked_, or in a _pericarp_.
Those with _naked_ seeds are arranged according to the number of the
seeds, which may be one, two, three, four, or more. If there is only
one, no subdivision is requisite: if there are two, Ray makes a
subdivision, according as the flower has five petals, or a continuous
corolla. Here we come to several natural families. Thus, the flowers
with two seeds and five petals are the _Umbelliferous_ plants; the
monopetalous flowers with two seeds are the _Stellatæ_. He founds the
division of four-seeded flowers on the circumstance of the leaves
being opposite, or alternate; and thus again, we have the natural
families of _Asperifoliæ_, as _Echium_, &c., which have the leaves
alternate, and the _Verticillatæ_, as _Salvia_, in which the leaves
are opposite. When the flower has more than four seeds, he makes no
subdivision.

So much for simple flowers with naked seeds. In those where the
seeds are surrounded by a _pericarp_, or fruit, this fruit is large,
soft, and fleshy, and the plants are _pomiferous_; or it is small
and juicy, and the fruit is a berry, as a Gooseberry.

If the fruit is not juicy, but _dry_, it is multiple or simple. If
it be simple, we have the _leguminose_ plants. If it be multiple,
the form of the flower is to be attended to. The flower may be
_monopetalous_, or _tetrapetalous_, or _pentapetalous_, or with
still _more_ divisions. The monopetalous may be _regular_ or
_irregular_; so may the tetrapetalous. The regular tetrapetalous
flowers are, for example, the _Cruciferæ_, as Stock and Cauliflower;
the irregular, are the _papilionaceous_ plants, Peas, Beans, and
Vetches; and thus we again come to natural families. The remaining
plants are divided in the same way, into those with _imperfect_, and
those with _perfect_, flowers. Those with _imperfect_ flowers are
the _Grasses_, the _Rushes_ (_Junci_), and the like; among those
with _perfect_ flowers, are the _Palmaceæ_, and the _Liliaceæ_.

We see that the division of plants is complete as a system; all
flowers must belong to one or other of the divisions. Fully to
explain the characters and further subdivisions of these families,
would be to write a treatise on botany; but it is easily seen that
they exhaust the subject as far as they go.

Thus Ray constructed his system partly on the fruit and partly on
the flower; or more properly, according to the expression of
Linnæus, {386} comparing his earlier with his later system, he began
by being a _fructicist_, and ended by being a _corollist_.[80\16]

[Note 80\16: Ray was a most industrious herbalizer, and I cannot
understand on what ground Mirbel asserts (_Physiol. Veg._, tom. ii.
p. 531,) that he was better acquainted with books than with plants.]

As we have said, a number of systems of arrangement of plants were
published about this time, some founded on the fruit, some on the
corolla, some on the calyx, and these employed in various ways.
Rivinus[81\16] (whose real name was Bachman,) classified by the
flower alone; instead of combining it with the fruit, as Ray had
done.[82\16] He had the further merit of being the first who
rejected the old division, of _woody_ and _herbaceous_ plants; a
division which, though at variance with any system founded upon the
structure of the plants was employed even by Tournefort, and only
finally expelled by Linnæus.

[Note 81\16: Cuv. _Leçons_, 491.]

[Note 82\16: _Historia Generalis ad rem Herbariam_, 1690.]

It would throw little light upon the history of botany, especially
for our purpose, to dwell on the peculiarities of these transitory
systems. Linnæus,[83\16] after his manner, has given a
classification of them. Rivinus, as we have just seen, was a
_corollist_, according to the regularity and number of the petals;
Hermann was a _fructicist_. Christopher Knaut[84\16] adopted the
system of Ray, but inverted the order of its parts; Christian Knaut
did nearly the same with regard to that of Rivinus, taking number
before regularity in the flower.[85\16]

[Note 83\16: _Philos. Bot._ p. 21.]

[Note 84\16: _Enumeratio Plantarum_, &c., 1687.]

[Note 85\16: Linn.]

Of the systems which prevailed previous to that of Linnæus,
Tournefort's was by far the most generally accepted. Joseph Pitton
de Tournefort was of a noble family in Provence, and was appointed
professor at the Jardin du Roi in 1683. His well-known travels in
the Levant are interesting on other subjects, as well as botany. His
_Institutio Rei Herbariæ_, published in 1700, contains his method,
which is that of a _corollist_. He is guided by the regularity or
irregularity of the flowers, by their form, and by the situation of
the receptacle of the seeds below the calyx, or within it. Thus his
classes are--those in which the flowers are _campaniform_, or
bell-shaped; those in which they are _infundibuliform_, or
funnel-shaped, as Tobacco; then the irregular flowers, as the
_Personatæ_, which resemble an ancient mask; the _Labiatæ_, with
their two lips; the _Cruciform_; the _Rosaceæ_, with flowers like a
rose; the _Umbelliferæ_; the _Caryophylleæ_, as the {387} Pink; the
_Liliaceæ_, with six petals, as the Tulip, Narcissus, Hyacinth,
Lily; the _Papilionaceæ_, which are leguminous plants, the flower of
which resembles a butterfly, as Peas and Beans; and finally, the
_Anomalous_, as Violet, Nasturtium, and others.

Though this system was found to be attractive, as depending, in an
evident way, on the most conspicuous part of the plant, the flower,
it is easy to see that it was much less definite than systems like
that of Rivinus, Hermann, and Ray, which were governed by number.
But Tournefort succeeded in giving to the characters of genera a
degree of rigor never before attained, and abstracted them in a
separate form. We have already seen that the reception of botanical
Systems has depended much on their arrangement into Genera.

Tournefort's success was also much promoted by the author inserting
in his work a figure of a flower and fruit belonging to each genus;
and the figures, drawn by Aubriet, were of great merit. The study of
botany was thus rendered easy, for it could be learned by turning
over the leaves of a book. In spite of various defects, these
advantages gave this writer an ascendancy which lasted, from 1700,
when his book appeared, for more than half a century. For though
Linnæus began to publish in 1735, his method and his nomenclature
were not generally adopted till 1760.




CHAPTER IV.

THE REFORM OF LINNÆUS.


_Sect._ 1.--_Introduction of the Reform._

ALTHOUGH, perhaps, no man of science ever exercised a greater sway
than Linnæus, or had more enthusiastic admirers, the most
intelligent botanists always speak of him, not as a great
discoverer, but as a judicious and strenuous _Reformer_. Indeed, in
his own lists of botanical writers, he places himself among the
"Reformatores;" and it is apparent that this is the nature of his
real claim to admiration; for the doctrine of the sexes of plants,
even if he had been the first to establish it, was a point of
botanical physiology, a province of the {388} science which no one
would select as the peculiar field of Linnæus's glory; and the
formation of a system of arrangement on the basis of this doctrine,
though attended with many advantages, was not an improvement of any
higher order than those introduced by Ray and Tournefort. But as a
Reformer of the state of Natural History in his time, Linnæus was
admirable for his skill, and unparalleled in his success. And we
have already seen, in the instance of the reform of mineralogy, as
attempted by Mohs and Berzelius, that men of great talents and
knowledge may fail in such an undertaking.

It is, however, only by means of the knowledge which he displays,
and of the beauty and convenience of the improvements which he
proposes, that any one can acquire such an influence as to procure
his suggestions to be adopted. And even if original circumstances of
birth or position could invest any one with peculiar prerogatives
and powers in the republic of science, Karl Linné began his career
with no such advantages. His father was a poor curate in Smaland, a
province of Sweden; his boyhood was spent in poverty and privation;
it was with great difficulty that, at the age of twenty-one, he
contrived to subsist at the University of Upsal, whither a strong
passion for natural history had urged him. Here, however, he was so
far fortunate, that Olaus Rudbeck, the professor of botany,
committed to him the care of the Botanic Garden.[86\16] The perusal
of the works of Vaillant and Patrick Blair suggested to him the idea
of an arrangement of plants, formed upon the sexual organs, the
stamens and pistils; and of such an arrangement he published a
sketch in 1731, at the age of twenty-four.

[Note 86\16: Sprengel, ii. 232.]

But we must go forwards a few years in his life, to come to the
period to which his most important works belong. University and
family quarrels induced him to travel; and, after various changes of
scene, he was settled in Holland, as the curator of the splendid
botanical garden of George Clifford, an opulent banker. Here it
was[87\16] that he laid the foundation of his future greatness. In
the two years of his residence at Harlecamp, he published nine
works. The first, the _Systema Naturæ_, which contained a
comprehensive sketch of the whole domain of Natural History, excited
general astonishment, by the acuteness of the observations, the
happy talent of combination, and the clearness of the systematic
views. Such a work could not fail to procure considerable respect
for its author. His _Hortus Cliffortiana_ {389} and _Musa
Cliffortiana_ added to this impression. The weight which he had thus
acquired, he proceeded to use for the improvement of botany. His
_Fundamenta Botanica_ and _Bibliotheca Botanica_ appeared in 1736;
his _Critica Botanica_ and _Genera Plantarum_ in 1737; his _Classes
Plantarum_ in 1738; his _Species Plantarum_ was not published till
1753; and all these works appeared in many successive editions,
materially modified.

[Note 87\16: Ibid. 234.]

This circulation of his works showed that his labors were producing
their effect. His reputation grew; and he was soon enabled to exert
a personal, as well as a literary, influence, on students of natural
history. He became Botanist Royal, President of the Academy of
Sciences at Stockholm, and Professor in the University of Upsal; and
this office he held for thirty-six years with unrivalled credit;
exercising, by means of his lectures, his constant publications, and
his conversation, an extraordinary power over a multitude of zealous
naturalists, belonging to every part of the world.

In order to understand more clearly the nature and effect of the
reforms introduced by Linnæus into botany, I shall consider them
under the four following heads;--_Terminology_, _Nomenclature_,
_Artificial System_, and _Natural System_.


_Sect._ 2.--_Linnæan Reform of Botanical Terminology._

IT must be recollected that I designate as _Terminology_, the system
of _terms_ employed in the _description_ of objects of natural
history; while by _Nomenclature_, I mean the collection of the
_names_ of _species_. The reform of the descriptive part of botany
was one of the tasks first attempted by Linnæus; and his terminology
was the instrument by which his other improvements were effected.

Though most readers, probably, entertain, at first, a persuasion
that a writer ought to content himself with the use of common words
in their common sense, and feel a repugnance to technical terms and
arbitrary rules of phraseology, as pedantic and troublesome; it is
soon found, by the student of any branch of science that, without
technical terms and fixed rules, there can be no certain or
progressive knowledge. The loose and infantine grasp of common
language cannot hold objects steadily enough for scientific
examination, or lift them from one stage of generalization to
another. They must be secured by the rigid mechanism of a scientific
phraseology. This necessity had been felt in all the sciences, from
the earliest periods of their progress. But the {390} conviction had
never been acted upon so as to produce a distinct and adequate
descriptive botanical language. Jung, indeed,[88\16] had already
attempted to give rules and precepts which should answer this
purpose; but it was not till the _Fundamenta Botanica_ appeared,
that the science could be said to possess a fixed and complete
terminology.

[Note 88\16: _Isagoge Phytoscopica_, 1679.]

To give an account of such a terminology, is, in fact, to give a
description of a dictionary and grammar, and is therefore what
cannot here be done in detail. Linnæus's work contains about a
thousand terms of which the meaning and application are distinctly
explained; and rules are given, by which, in the use of such terms,
the botanist may avoid all obscurity, ambiguity, unnecessary
prolixity and complexity, and even inelegance and barbarism. Of
course the greater part of the words which Linnæus thus recognized
had previously existed in botanical writers; and many of them had
been defined with technical precision. Thus Jung[89\16] had already
explained what was a _composite_, what a _pinnate_ leaf; what kind
of a bunch of flowers is a _spike_, a _panicle_, an _umbel_, a
_corymb_, respectively. Linnæus extended such distinctions,
retaining complete clearness in their separation. Thus, with him,
composite leaves are further distinguished as _digitate_, _pinnate_,
_bipinnate_, _pedate_, and so on; pinnate leaves are _abruptly_ so,
or _with an odd_ one, or _with a tendril_; they are pinnate
_oppositely_, _alternately_, _interruptedly_, _articulately_,
_decursively_. Again, the _inflorescence_, as the mode of assemblage
of the flowers is called, may be a _tuft_ (fasciculus), a _head_
(capitulum), a _cluster_ (racemus), a _bunch_ (thyrsus), a
_panicle_, a _spike_, a _catkin_ (amentum), a _corymb_, an _umbel_,
a _cyme_, a _whorl_ (verticillus). And the rules which he gives,
though often apparently arbitrary and needless, are found, in
practice, to be of great service by their fixity and connexion. By
the good fortune of having had a teacher with so much delicacy of
taste as Linnæus, in a situation of so much influence, Botany
possesses a descriptive language which will long stand as a model
for all other subjects.

[Note 89\16: Sprengel, ii. 28.]

It may, perhaps, appear to some persons, that such a terminology as
we have here described must be enormously cumbrous; and that, since
the terms are arbitrarily invested with their meaning, the invention
of them requires no knowledge of nature. With respect to the former
doubt, we may observe, that technical description is, in reality,
the only description which is clearly intelligible; but that
technical language cannot be understood without being learnt as any
other {391} language is learnt; that is, the reader must connect the
terms immediately with his own sensations and notions, and not
mediately, through a verbal explanation; he must not have to guess
their meaning, or to discover it by a separate act of interpretation
into more familiar language as often as they occur. The language of
botany must be the botanist's most familiar tongue. When the student
has thus learnt to _think_ in botanical language, it is no idle
distinction to tell him that a _bunch_ of grapes is not a _cluster_;
that is, a _thyrsus_ not a _raceme_. And the terminology of botany
is then felt to be a useful implement, not an oppressive burden. It
is only the schoolboy that complains of the irksomeness of his
grammar and vocabulary. The accomplished student possesses them
without effort or inconvenience.

As to the other question, whether the construction of such a botanical
grammar and vocabulary implies an extensive and accurate acquaintance
with the facts of nature, no one can doubt who is familiar with any
descriptive science. It is true, that a person might construct an
arbitrary scheme of distinctions and appellations, with no attention
to natural objects; and this is what shallow and self-confident
persons often set about doing, in some branch of knowledge with which
they are imperfectly acquainted. But the slightest attempt to use such
a phraseology leads to confusion; and any continued use of it leads to
its demolition. Like a garment which does not fit us, if we attempt to
work in it we tear it in pieces.

The formation of a good descriptive language is, in fact, an
inductive process of the same kind as those which we have already
noticed in the progress of natural history. It requires the
_discovery of fixed characters_, which discovery is to be marked and
fixed, like other inductive steps, by appropriate _technical terms_.
The characters must be so far fixed, that the things which they
connect must have a more permanent and real association than the
things which they leave unconnected. If one bunch of grapes were
really a racemus, and another a thyrsus, according to the definition
of these terms, this part of the Linnæan language would lose its
value; because it would no longer enable us to assert a general
proposition with respect to one kind of plants.


_Sect._ 3.--_Linnæan Reform of Botanical Nomenclature._

IN the ancient writers each recognized kind of plants had a distinct
name. The establishment of Genera led to the practice of designating
{392} Species by the name of the genus, with the addition of a
"phrase" to distinguish the species. These phrases, (expressed in
Latin in the ablative case,) were such as not only to mark, but to
describe the species, and were intended to contain such features of
the plant as were sufficient to distinguish it from others of the
same genus. But in this way the designation of a plant often became
a long and inconvenient assemblage of words. Thus different kinds of
Rose were described as,
  Rosa campestris, spinis carens, biflora (_Rosa alpina_.)
  Rosa aculeata, foliis odoratis subtus rubiginosis (_R. eglanteria_.)
  Rosa carolina fragrans, foliis medio tenus serratis (_R. carolina_.)
  Rosa sylvestris vulgaris, flore odorato incarnato (_R. canina_.)
And several others. The prolixity of these appellations, their
variety in every different author, the insufficiency and confusion
of the distinctions which they contained, were felt as extreme
inconveniences. The attempt of Bauhin to remedy this evil by a
Synonymy, had, as we have seen, failed at the time, for want of any
directing principle; and was become still more defective by the
lapse of years and the accumulation of fresh knowledge and new
books. Haller had proposed to distinguish the species of each genus
by the numbers 1, 2, 3, and so on; but botanists found that their
memory could not deal with such arbitrary abstractions. The need of
some better nomenclature was severely felt.

The remedy which Linnæus finally introduced was the use of _trivial_
names; that is, the designation of each species by the name of the
genus along with a _single_ conventional word, imposed without any
general rule. Such names are added above in parentheses, to the
specimens of the names previously in use. But though this remedy was
found to be complete and satisfactory, and is now universally
adopted in every branch of natural history, it was not one of the
reforms which Linnæus at first proposed. Perhaps he did not at first
see its full value; or, if he did, we may suppose that it required
more self-confidence than he possessed, to set himself to introduce
and establish ten thousand new names in the botanical world.
Accordingly, the first attempts of Linnæus at the improvement of the
nomenclature of botany were, the proposal of fixed and careful rules
for the generic name, and for the descriptive phrase. Thus, in his
_Critica Botanica_, he gives many precepts concerning the selection
of the names of {393} genera, intended to secure convenience or
elegance. For instance, that they are to be single words;[90\16] he
substitutes _atropa_ for _bella donna_, and _leontodon_ for _dens
leonis_; that they are not to depend upon the name of another
genus,[91\16] as _acriviola_, _agrimonoides_; that they are
not[92\16] to be "sesquipedalia;" and, says he, any word is
sesquipedalian to me, which has more than twelve letters, as
_kalophyllodendron_, for which he substitutes _calophyllon_. Though
some of these rules may seem pedantic, there is no doubt that, taken
altogether, they tend exceedingly, like the labors of purists in
other languages, to exclude extravagance, caprice, and barbarism in
botanical speech.

[Note 90\16: _Phil. Bot._ 224.]

[Note 91\16: Ib. 228, 229.]

[Note 92\16: Ib. 252.]

The precepts which he gives for the matter of the "descriptive
phrase," or, as it is termed in the language of the Aristotelian
logicians, the "differentia," are, for the most part, results of the
general rule, that the most fixed characters which can be found are
to be used; this rule being interpreted according to all the
knowledge of plants which had then been acquired. The language of
the rules was, of course, to be regulated by the terminology, of
which we have already spoken.

Thus, in the _Critica Botanica_, the name of a plant is considered
as consisting of a generic word and a specific phrase; and these
are, he says,[93\16] the right and left hands of the plant. But he
then speaks of another kind of name; the _trivial_ name, which is
opposed to the scientific. Such names were, he says,[94\16] those of
his predecessors, and especially of the most ancient of them.
Hitherto[95\16] no rules had been given for their use. He
manifestly, at this period, has small regard for them. "Yet," he
says, "trivial names may, perhaps, be used on this account,--that
the _differentia_ often turns out too long to be convenient in
common use, and may require change as new species are discovered.
However," he continues, "in this work we set such names aside
altogether, and attend only to the _differentiæ_."

[Note 93\16: Ib. 266.]

[Note 94\16: Ib. 261.]

[Note 95\16: Ib. 260.]

Even in the _Species Plantarum_, the work which gave general
currency to these trivial names, he does not seem to have yet dared
to propose so great a novelty. They only stand in the margin of the
work. "I have placed them there," he says in his Preface, "that,
without circumlocution, we may call every herb by a single name; I
have done this without selection, which would require more time. And
I beseech all sane botanists to avoid most religiously ever {394}
proposing a trivial name without a sufficient specific distinction,
lest the science should fall into its former barbarism."

It cannot be doubted, that the general reception of these trivial
names of Linnæus, as the current language among botanists, was due, in
a very great degree, to the knowledge, care, and skill with which his
characters, both of genera and of species, were constructed. The
rigorous rules of selection and expression which are proposed in the
_Fundamenta Botanica_ and _Critica Botanica_, he himself conformed to;
and this scrupulosity was employed upon the results of immense labor.
"In order that I might make myself acquainted with the species of
plants," he says, in the preface to his work upon them, "I have
explored the Alps of Lapland, the whole of Sweden, a part of Norway,
Denmark, Germany, Belgium, England, France: I have examined the
Botanical Gardens of Paris, Oxford, Chelsea, Harlecamp, Leyden,
Utrecht, Amsterdam, Upsal, and others: I have turned over the Herbals
of Burser, Hermann, Clifford, Burmann, Oldenland, Gronovius, Royer,
Sloane, Sherard, Bobart, Miller, Tournefort, Vaillant, Jussieu,
**Surian, Beck, Brown, &c.: my dear disciples have gone to distant
lands, and sent me plants from thence; Kerlen to Canada, Hasselquist
to Egypt, Asbech to China, Toren to Surat, Solander to England,
Alstrœmer to Southern Europe, Martin to Spitzbergen, Pontin to
Malabar, Kœhler to Italy, Forskähl to the East, Lœfling to Spain,
Montin to Lapland: my botanical friends have sent me many seeds and
dried plants from various countries: Lagerström many from the East
Indies; Gronovius most of the Virginian; Gmelin all the Siberian;
Burmann those of the Cape." And in consistency with this habit of
immense collection of materials, is his maxim,[96\16] that "a person
is a better botanist in proportion as he knows more species." It will
easily be seen that this maxim, like Newton's declaration that
discovery requires patient thought alone, refers only to the exertions
of which the man of genius is conscious; and leaves out of sight his
peculiar endowments, which he does not see because they are part of
his power of vision. With the taste for symmetry which dictated the
_Critica Botanica_, and the talent for classification which appears in
the _Genera Plantarum_, and the _Systema Naturæ_, a person must
undoubtedly rise to higher steps of classificatory knowledge and
skill, as he became acquainted with a greater number of facts.

[Note 96\16: _Phil. Bot._ 259.]

The acknowledged superiority of Linnæus in the knowledge of the
{395} matter of his science, induced other persons to defer to him
in what concerned its form; especially when his precepts were, for
the most part, recommended strongly both by convenience and
elegance. The trivial names of the _Species Plantarum_ were
generally received; and though some of the details may have been
altered, the immense advantage of the scheme ensures its permanence.


_Sect._ 4.--_Linnæus's Artificial System._

WE have already seen, that, from the time of Cæsalpinus, botanists
had been endeavoring to frame a systematic arrangement of plants.
All such arrangements were necessarily both artificial and natural:
they were _artificial_, inasmuch as they depended upon assumed
principles, the number, form, and position of certain parts, by the
application of which the whole vegetable kingdom was imperatively
subdivided; they were _natural_, inasmuch as the justification of
this division was, that it brought together those plants which were
naturally related. No system of arrangement, for instance, would
have been tolerated which, in a great proportion of cases, separated
into distant parts of the plan the different species of the same
genus. As far as the main body of the genera, at least, all systems
are natural.

But beginning from this line, we may construct our systems with two
opposite purposes, according as we endeavor to carry our assumed
principle of division rigorously and consistently through the
system, or as we wish to associate natural families of a wider kind
than genera. The former propensity leads to an artificial, the
latter to a natural method. Each is a _System of Plants_; but in the
first, the emphasis is thrown on the former word of the title, in
the other, on the latter.

The strongest recommendation of an artificial system, (besides its
approaching to a natural method,) is, that it shall be capable of
easy use; for which purpose, the facts on which it depends must be
apparent in their relations, and universal in their occurrence. The
system of Linnæus, founded upon the number, position, and other
circumstances of the stamina and pistils, the reproductive organs of
the plants, possessed this merit in an eminent degree, as far as
these characters are concerned; that is, as far as the classes and
orders. In its further subdivision into genera, its superiority was
mainly due to the exact observation and description, which we have
already had to notice as talents which Linnæus peculiarly possessed.

The Linnæan system of plants was more definite than that of {396}
Tournefort, which was governed by the corolla; for number is more
definite than irregular form. It was more readily employed than any
of those which depend on the fruit, for the flower is a more obvious
object, and more easily examined. Still, it can hardly be doubted,
that the circumstance which gave the main currency to the system of
Linnæus was its physiological signification: it was the _Sexual
System_. The relation of the parts to which it directed the
attention, interested both the philosophical faculty and the
imagination. And when, soon after the system had become familiar in
our own country, the poet of _The Botanic Garden_ peopled the bell
of every flower with "Nymphs" and "Swains," his imagery was felt to
be by no means forced and far-fetched.

The history of the doctrine of the sexes of plants, as a point of
physiology, does not belong to this place; and the Linnæan system of
classification need not be longer dwelt upon for our present
purpose. I will only explain a little further what has been said,
that it is, up to a certain point, a natural system. Several of
Linnæus's classes are, in a great measure, natural associations,
kept together in violation of his own artificial rules. Thus the
class _Diadelphia_, in which, by the system, the filaments of the
stamina should be bound together in two parcels, does, in fact,
contain many genera which are_ monadelphous_, the filaments of the
stamina all cohering so as to form one bundle only; as in _Genista_,
_Spartium_, _Anthyllis_, _Lupinus_, &c. And why is this violation of
rule? Precisely because these genera all belong to the natural tribe
of Papilionaceous plants, which the author of the system could not
prevail upon himself to tear asunder. Yet in other cases Linnæus was
true to his system, to the injury of natural alliances, as he was,
for instance, in another portion of this very tribe of
_Papilionaceæ_; for there are plants which undoubtedly belong to the
tribe, but which have ten separate stamens; and these he placed in
the order _Decandria_. Upon the whole, however, he inclines rather
to admit transgression of art than of nature.

The reason of this inclination was, that he rightly considered an
artificial method as instrumental to the investigation of a natural
one; and to this part of his views we now proceed.


_Sect._ 5.--_Linnæus's Views on a Natural Method._

THE admirers of Linnæus, the English especially, were for some time
in the habit of putting his Sexual System in opposition to the
Natural Method, which about the same time was attempted in France.
And {397} as they often appear to have imagined that the ultimate
object of botanical methods was to know the name of plants, they
naturally preferred the Swedish method, which is excellent as a
_finder_. No person, however, who wishes to know botany as a
science, that is, as a body of general truths, can be content with
making names his ultimate object. Such a person will be constantly
and irresistibly led on to attempt to catch sight of the natural
arrangement of plants, even before he discovers, as he will discover
by pursuing such a course of study, that the knowledge of the
natural arrangement is the knowledge of the essential construction
and vital mechanism of plants. He will consider an artificial method
as a means of arriving at a natural method. Accordingly, however
much some of his followers may have overlooked this, it is what
Linnæus himself always held and taught. And though what he executed
with regard to this object was but little,[97\16] the distinct
manner in which he presented the relations of an artificial and
natural method, may justly be looked upon as one of the great
improvements which he introduced into the study of his science.

[Note 97\16: The natural orders which he proposed are a bare
enumeration of genera, and have not been generally followed.]

Thus in the _Classes Plantarum_ (1747), he speaks of the difficulty of
the task of discovering the natural orders, and of the attempts made
by others. "Yet," he adds, "I too have labored at this, have done
something, have much still to do, and shall labor at the object as
long as I live." He afterwards proposed sixty-seven orders, as the
fragments of a natural method, always professing their
imperfection.[98\16] And in others of his works[99\16] he lays down
some antitheses on the subject after his manner. "The natural orders
teach us the nature of plants; the artificial orders enable us to
recognize plants. The natural orders, without a key, do not constitute
a Method; the Method ought to be available without a master."

[Note 98\16: _Phil. Bot._ p. 80.]

[Note 99\16: _Genera Plantarum_, 1764. See _Prælect. in Ord. Nat._
p. xlviii.]

That extreme difficulty must attend the formation of a Natural Method,
may be seen from the very indefinite nature of the Aphorisms upon this
subject which Linnæus has delivered, and which the best botanists of
succeeding times have assented to. Such are these;--the Natural Orders
must be formed by attention, not to one or two, but to _all_ the parts
of plants;--the same organs are of great importance in regulating the
divisions of one part of the system, and {398} of small importance in
another part;[100\16]--the Character does not constitute the Genus,
but the Genus the Character;--the Character is necessary, not to make
the Genus, but to recognize it. The vagueness of these maxims is
easily seen; the rule of attending to all the parts, implies, that we
are to estimate their relative importance, either by physiological
considerations (and these again lead to arbitrary rules, as, for
instance, the superiority of the function of nutrition to that of
reproduction), or by a sort of latent naturalist instinct, which
Linnæus in some passages seems to recognize. "The Habit of a plant,"
he says,[101\16] "must be secretly consulted. A practised botanist
will distinguish, at the first glance, the plants of different
quarters of the globe, and yet will be at a loss to tell by what mark
he detects them. There is, I know not what look,--sinister, dry,
obscure in African plants; superb and elevated, in the Asiatic; smooth
and cheerful, in the American; stunted and indurated, in the Alpine."

[Note 100\16: _Phil. Bot._ p. 172.]

[Note 101\16: Ib. p. 171.]

Again, the rule that the same parts are of very different value in
different Orders, not only leaves us in want of rules or reasons
which may enable us to compare the marks of different Orders, but
destroys the systematic completeness of the natural arrangement. If
some of the Orders be regulated by the flower and others by the
fruit, we may have plants, of which the flower would place them in
one Order, and the fruit in another. The answer to this difficulty
is the maxim already stated;--that no Character _makes_ the Order;
and that if a Character do not enable us to recognize the Order, it
does not answer its purpose, and ought to be changed for another.

This doctrine, that the Character is to be employed as a servant and
not as a master, was a stumbling-block in the way of those disciples
who looked only for dogmatical and universal rules. One of Linnæus's
pupils, Paul Dietrich Giseke, has given us a very lively account of
his own perplexity on having this view propounded to him, and of the
way in which he struggled with it. He had complained of the want of
intelligible grounds, in the collection of natural orders given by
Linnæus. Linnæus[102\16] wrote in answer, "You ask me for the
characters of the Natural Orders: I confess I cannot give them."
Such a reply naturally increased Giseke's difficulties. But
afterwards, in 1771, he had the good fortune to spend some time at
Upsal; and he narrates a conversation which he held with the great
{399} teacher on this subject, and which I think may serve to show
the nature of the difficulty;--one by no means easily removed, and
by the general reader, not even readily comprehended with
distinctness. Giseke began by conceiving that an Order _must_ have
that attribute from which its name is derived;--that the _Umbellatæ_
must have their flower disposed in an umbel. The "mighty master"
smiled,[103\16] and told him not to look at names, but at nature.
"But" (said the pupil) "what is the use of the name, if it does not
mean what it professes to mean?" "It is of small import" (replied
Linnæus) "_what_ you _call_ the Order, if you take a proper series
of plants and give it some name, which is clearly understood to
apply to the plants which you have associated. In such cases as you
refer to, I followed the logical rule, of borrowing a name _a
potiori_, from the principal member. Can you" (he added) "give me
the character of any single Order?" _Giseke._ "Surely, the character
of the _Umbellatæ_ is, that they have an umbel?" _Linnæus._ "Good;
but there are plants which have an umbel, and are not of the
_Umbellatæ_." _G._ "I remember. We must therefore add, that they
have two naked seeds." _L._ "Then, _Echinophora_, which has only one
seed, and _Eryngium_, which has not an umbel, will not be
_Umbellatæ_; and yet they are of the Order." _G._ "I would place
_Eryngium_ among the _Aggregatæ_. _L._ "No; both are beyond dispute
_Umbellatæ_. _Eryngium_ has an involucrum, five stamina, two
pistils, &c. Try again for your Character." _G._ "I would transfer
such plants to the end of the Order, and make them form the
transition to the next Order. _Eryngium_ would connect the
_Umbellatæ_ with the _Aggregatæ_." _L._ "Ah! my good friend, the
_Transition_ from Order to Order is one thing; the _Character_ of an
Order is another. The Transitions I could indicate; but a Character
of a Natural Order is impossible. I will not give my reasons for the
distribution of Natural Orders which I have published. You or some
other person, after twenty or after fifty years, will discover them,
and see I was in the right."

[Note 102\16: _Linnæi Prælectiones_, Pref. p. xv.]

[Note 103\16: "Subrisit ὁ πανυ."]

I have given a portion of this curious conversation in order to show
that the attempt to establish Natural Orders leads to convictions
which are out of the domain of the systematic grounds on which they
profess to proceed. I believe the real state of the case to be that
the systematist, in such instances, is guided by an unformed and
undeveloped apprehension of physiological functions. The ideas of
the form, {400} number, and figure of parts are, in some measure,
overshadowed and superseded by the rising perception of organic and
vital relations; and the philosopher who aims at a Natural Method,
while he is endeavoring merely to explore the apartment in which he
had placed himself, that of Arrangement, is led beyond it, to a
point where another light begins, though dimly, to be seen; he is
brought within the influence of the ideas of Organization and Life.

The sciences which depend on these ideas will be the subject of our
consideration hereafter. But what has been said may perhaps serve to
explain the acknowledged and inevitable imperfection of the
unphysiological Linnæan attempts towards a natural method.
"Artificial Glasses are," Linnæus says, "a substitute for Natural,
till Natural are detected." But we have not yet a Natural Method.
"Nor," he says, in the conversation above cited, "can we have a
Natural Method; for a Natural Method implies Natural Classes and
Orders; and these Orders must have Characters." "And they," he adds
in another place,[104\16] "who, though they cannot obtain a complete
Natural Method, arrange plants according to the fragments of such a
method, to the rejection of the Artificial, seem to me like persons
who pull down a convenient vaulted room, and set about building
another, though they cannot turn the vault which is to cover it."

[Note 104\16: _Gen. Plant. in Prælect._ p. xii.]

How far these considerations deterred other persons from turning
their main attention to a natural method, we shall shortly see; but
in the mean time, we must complete the history of the Linnæan Reform.


_Sect._ 6.--_Reception and Diffusion of the Linnæan Reform._

WE have already seen that Linnæus received, from his own country,
honors and emoluments which mark his reputation as established, as
early as 1740; and by his publications, his lectures, and his
personal communications, he soon drew round him many disciples, whom
he impressed strongly with his own doctrines and methods. It would
seem that the sciences of classification tend, at least in modern
times more than other sciences, to collect about the chair of the
teacher a large body of zealous and obedient pupils; Linnæus and
Werner were by far the most powerful heads of schools of any men who
appeared in the course of the last century. Perhaps one reason of
this is, that in these sciences, consisting of such an enormous
multitude of species, of descriptive {401} particulars, and of
previous classifications, the learner is dependent upon the teacher
more completely, and for a longer time than in other subjects of
speculation: he cannot so soon or so easily cast off the aid and
influence of the master, to pursue reasonings and hypotheses of his
own. Whatever the cause may be, the fact is, that the reputation and
authority of Linnæus, in the latter part of his life, were immense.
He enjoyed also royal favor, for the King and Queen of Sweden were
both fond of natural history. In 1753, Linnæus received from the
hand of his sovereign the knighthood of the Polar Star, an honor
which had never before been conferred for literary merit; and in
1756, was raised to the rank of Swedish nobility by the title of Von
Linné; and this distinction was confirmed by the Diet in 1762. He
lived, honored and courted, to the age of seventy-one; and in 1778
was buried in the cathedral of Upsal, with many testimonials of
public respect and veneration.

De Candolle[105\16] assigns, as the causes of the successes of the
Linnæan system,--the specific names,--the characteristic
phrase,--the fixation of descriptive language,--the distinction of
varieties and species,--the extension of the method to all the
kingdoms of nature,--and the practice of introducing into it the
species most recently discovered. This last course Linnæus
constantly pursued; thus making his works the most valuable for
matter, as they were the most convenient in form. The general
diffusion of his methods over Europe may be dated, perhaps, a few
years after 1760, when the tenth and the succeeding editions of the
_Systema Naturæ_ were in circulation, professing to include every
species of organized beings. But his pupils and correspondents
effected no less than his books, in giving currency to his system.
In Germany,[106\16] it was defended by Ludwig, Gesner, Fabricius.
But Haller, whose reputation in physiology was as great as that of
Linnæus in methodology, rejected it as too merely artificial. In
France, it did not make any rapid or extensive progress: the best
French botanists were at this time occupied with the solution of the
great problem of the construction of a Natural Method. And though
the rhetorician Rousseau charmed, we may suppose, with the elegant
precision of the _Philosophia Botanica_, declared it to be the most
philosophical work he had ever read in his life, Buffon and
Andanson, describers and philosophers of a more ambitious school,
felt a repugnance to the rigorous rules, and limited, but finished,
undertakings of the Swedish naturalist. To resist his {402} criticism
and his influence, they armed themselves with dislike and contempt.

[Note 105\16: _Théor. Elém._ p. 40.]

[Note 106\16: Sprengel, ii. 244.]

In England the Linnæan system was very favorably received:--perhaps
the more favorably, for being a strictly artificial system. For the
indefinite and unfinished form which almost inevitably clings to a
natural method, appears to be peculiarly distasteful to our
countrymen. It might seem as if the suspense and craving which comes
with knowledge confessedly incomplete were so disagreeable to them,
that they were willing to avoid it, at any rate whatever; either by
rejecting system altogether, or by accepting a dogmatical system
without reserve. The former has been their course in recent times with
regard to Mineralogy; the latter was their proceeding with respect to
the Linnæan Botany. It is in this country alone, I believe, that
_Wernerian_ and _Linnæan_ Societies have been instituted. Such
appellations somewhat remind us of the Aristotelian and Platonic
schools of ancient Greece. In the same spirit it was, that the
Artificial System was at one time here considered, not as subsidiary
and preparatory to the Natural Orders, but as opposed to them. This
was much as if the disposition of an army in a review should be
considered as inconsistent with another arrangement of it in a battle.

When Linnæus visited England in 1736, Sloane, then the patron of
natural history in this country, is said to have given him a cool
reception, such as was perhaps most natural from an old man to a
young innovator; and Dillenius, the Professor at Oxford, did not
accept the sexual system. But as Pulteney, the historian of English
Botany, says, when his works became known, "the simplicity of the
classical characters, the uniformity of the generic notes, all
confined to the parts of the fructification, and the precision which
marked the specific distinctions, merits so new, soon commanded the
assent of the unprejudiced."

Perhaps the progress of the introduction of the Linnæan System into
England will be best understood from the statement of T. Martyn, who
was Professor of Botany in the University of Cambridge, from 1761 to
1825. "About the year 1750," he says,[107\16] "I was a pupil of the
school of our great countryman Ray; but the rich vein of knowledge,
the profoundness and precision, which I remarked everywhere in the
_Philosophia Botanica_, (published in 1751,) withdrew me from my
first master, and I became a decided convert to that system of
botany which has since been generally received. In 1753, the
_Species_ {403} _Plantarum_, which first introduced the specific
names, made me a Linnæan completely." In 1763, he introduced the
system in his lectures at Cambridge, and these were the first
Linnæan lectures in England. Stillingfleet had already, in 1757, and
Lee, in 1760, called the attention of English readers to Linnæus.
Sir J. Hill, (the king's gardener at Kew,) in his _Flora
Britannica_, published in 1760, had employed the classes and generic
characters, but not the nomenclature; but the latter was adopted by
Hudson, in 1762, in the _Flora Anglica_.

[Note 107\16: Pref. to _Language of Botany_, 3rd edit. 1807.]

Two young Swedes, pupils of Linnæus, Dryander and Solander, settled in
England, and were in intimate intercourse with the most active
naturalists, especially with Sir Joseph Banks, of whom the former was
librarian, and the latter a fellow-traveller in Cook's celebrated
voyage. James Edward Smith was also one of the most zealous disciples
of the Linnæan school; and, after the death of Linnæus, purchased his
Herbariums and Collections. It is related,[108\16] as a curious proof
of the high estimation in which Linnæus was held, that when the
Swedish government heard of this bargain, they tried, though too late,
to prevent these monuments of their countryman's labor and glory being
carried from his native land, and even went so far as to send a
frigate in pursuit of the ship which conveyed them to England. Smith
had, however, the triumph of bringing them home in safety. On his
death they were purchased by the Linnæan Society. Such relics serve,
as will easily be imagined, not only to warm the reverence of his
admirers, but to illustrate his writings: and since they have been in
this country, they have been the object of the pilgrimage of many a
botanist, from every part of Europe.

[Note 108\16: Trapp's _Transl. of Stower's Life of Linnæus_, p. 314.]

I have purposely confined myself to the history of the Linnæan system
in the cases in which it is most easily applicable, omitting all
consideration of more obscure and disputed kinds of vegetables, as
ferns, mosses, fungi, lichens, sea-weeds, and the like. The nature and
progress of a classificatory science, which it is our main purpose to
bring into view, will best be understood by attending, in the first
place, to the cases in which such a science has been pursued with the
most decided success; and the advances which have been made in the
knowledge of the more obscure vegetables, are, in fact, advances in
artificial classification, only in as far as they are advances in
natural classification, and in physiology.

To these subjects we now proceed. {404}




CHAPTER V.

PROGRESS TOWARDS A NATURAL SYSTEM OF BOTANY.

WE have already said, that the formation of a Natural System of
classification must result from a comparison of _all_ the
resemblances and differences of the things classed; but that, in
acting upon this maxim, the naturalist is necessarily either guided
by an obscure and instinctive feeling, which is, in fact, an
undeveloped recognition of physiological relations, or else
acknowledges physiology for his guide, though he is obliged to
assume arbitrary rules in order to interpret its indications. Thus
all Natural Classification of organized beings, either begins or
soon ends in Physiology; and can never advance far without the aid
of that science. Still, the progress of the Natural Method in botany
went to such a length before it was grounded entirely on the anatomy
of plants, that it will be proper, and I hope instructive, to
attempt a sketch of it here.

As I have already had occasion to remark, the earlier systems of
plants were natural; and they only ceased to be so, when it appeared
that the problem of constructing a _system_ admitted of a very
useful solution, while the problem of devising a _natural system_
remained insoluble. But many botanists did not so easily renounce
the highest object of their science. In France, especially, a
succession of extraordinary men labored at it with no inconsiderable
success: and they were seconded by worthy fellow-laborers in Germany
and elsewhere.

The precept of taking into account all the parts of plants according
to their importance, may be applied according to arbitrary rules. We
may, for instance, assume that the fruit is the most important part;
or we may make a long list of parts, and look for agreement in the
greatest possible number of these, in order to construct our natural
orders. The former course was followed by Gærtner;[109\16] the
latter by Adanson. Gærtner's principles, deduced from the dissection
of more than a thousand kinds of fruits,[110\16] exercised, in the
sequel, a great and {405} permanent influence on the formation of
natural classes. Adanson's attempt, bold and ingenious, belonged,
both in time and character, to a somewhat earlier stage of the
subject.[111\16] Enthusiastic and laborious beyond belief but
self-confident, and contemptuous of the labors of others, Michael
Adanson had collected, during five years spent in Senegal, an
enormous mass of knowledge and materials; and had formed plans for
the systems which he conceived himself thus empowered to reach, far
beyond the strength and the lot of man.[112\16] In his _Families of
Plants_, however, all agree that his labors were of real value to
the science. The method which he followed is thus described by his
eloquent and philosophical eulogist.[113\16]

[Note 109\16: _De Fructibus et Seminibus Plantarum_. Stuttg.
1788-1791.]

[Note 110\16: Sprengel, ii. 290.]

[Note 111\16: _Familles des Plantes_, 1763.]

[Note 112\16: Cuvier's _Eloge_.]

[Note 113\16: Cuv. _Eloges_, tom. i. p. 282.]

Considering each organ by itself, he formed, by pursuing its various
modifications, a system of division, in which he arranged all known
species according to that organ alone. Doing the same for another
organ, and another, and so for many, he constructed a collection of
systems of arrangement, each artificial,--each founded upon one
assumed organ. The species which come together in all these systems
are, of all, naturally the nearest to each other; those which are
separated in a few of the systems, but contiguous in the greatest
number, are naturally near to each other, though less near than the
former; those which are separated in a greater number, are further
removed from each other in nature; and they are the more removed,
the fewer are the systems in which they are associated.

Thus, by this method, we obtain the means of estimating precisely
the degree of natural affinity of all the species which our systems
include, independent of a physiological knowledge of the influence
of the organs. But the method has, Cuvier adds, the inconvenience of
presupposing another kind of knowledge, which, though it belongs
only to descriptive natural history, is no less difficult to
obtain;--the knowledge, namely, of all species, and of all the
organs of each. A single one neglected, may lead to relations the
most false; and Adanson himself, in spite of the immense number of
his observations, exemplifies this in some instances.

We may add, that in the division of the structure into organs, and
in the estimation of the gradations of these in each artificial
system, there is still room for arbitrary assumption.

In the mean time, the two Jussieus had presented to the world a
"Natural Method," which produced a stronger impression than the
{406} "Universal Method" of Adanson. The first author of the system
was Bernard de Jussieu, who applied it in the arrangement of the
garden of the Trianon, in 1759, though he never published upon it.
His nephew, Antoine Laurent de Jussieu, in his _Treatise of the
Arrangement of the Trianon_,[114\16] gave an account of the
principles and orders of his uncle, which he adopted when he
succeeded him; and, at a later period, published his _Genera
Plantarum secundum Ordines Naturales disposita_; a work, says
Cuvier, which perhaps forms as important an epoch in the sciences of
observation, as the _Chimie_ of Lavoisier does in the sciences of
experiment. The object of the Jussieus was to obtain a system which
should be governed by the natural affinities of the plants, while,
at the same time, the characters by which the orders were ostensibly
determined, should be as clear, simple, and precise, as those of the
best artificial system. The main points in these characters were the
number of the cotyledons, and the structure of the seed: and
subordinate to this, the insertion of the stamina, which they
distinguished as _epigynous_, _perigynous_, and _hypogynous_,
according as they were inserted over, about, or under, the germen.
And the classes which were formed by the Jussieus, though they have
since been modified by succeeding writers, have been so far retained
by the most profound botanists, notwithstanding all the new care and
new light which have been bestowed upon the subject, as to show that
what was done at first, was a real and important step in the
solution of the problem.

[Note 114\16: _Mém. Ac. P._ 1774.]

The merit of the formation of this natural method of plants must be
divided between the two Jussieus. It has been common to speak of the
nephew, Antoine Laurent, as only the publisher of his uncle's
work.[115\16] But this appears, from a recent statement,[116\16] to
be highly unjust. Bernard left nothing in writing but the catalogues
of the garden of the Trianon, which he had arranged according to his
own views; but these catalogues consist merely of a series of names
without explanation or reason added. The nephew, in 1773, undertook
and executed for himself the examination of a natural family, the
_Ranunculaceæ_; and he was wont to relate (as his son informs us)
that it {407} was this employment which first opened his eyes and
rendered him a botanist. In the memoir which he wrote, he explained
fully the relative importance of the characters of plants, and the
subordination of some to others;--an essential consideration, which
Adanson's scheme had failed to take account of. The uncle died in
1777; and his nephew, in speaking of him, compares his arrangement
to the _Ordines Naturales_ of Linnæus: "Both these authors," he
says, "have satisfied themselves with giving a catalogue of genera
which approach each other in different points, without explaining
the motives which induced them to place one order before another, or
to arrange a genus under a certain order. These two arrangements may
be conceived as problems which their authors have left for botanists
to solve. Linnæus published his; that of M. de Jussieu is only known
by the manuscript catalogues of the garden of the Trianon."

[Note 115\16: _Prodromus Floræ Penins. Ind. Orient._ Wight and
Walker-Arnott, Introd. p. xxxv.]

[Note 116\16: By Adrien de Jussieu, son of Antoine Laurent, in the
_Annales des Sc. Nat._, Nov. 1834.]

It was not till the younger Jussieu had employed himself for
nineteen years upon botany, that he published, in 1789, his _Genera
Plantarum_; and by this time he had so entirely formed his scheme in
his head, that he began the impression without having written the
book, and the manuscript was never more than two pages in advance of
the printer's type.

When this work appeared, it was not received with any enthusiasm;
indeed, at that time, the revolution of states absorbed the thoughts
of all Europe, and left men little leisure to attend to the
revolutions of science. The author himself was drawn into the vortex
of public affairs, and for some years forgot his book. The method
made its way slowly and with difficulty: it was a long time before
it was comprehended and adopted in France, although the botanists of
that country had, a little while before, been so eager in pursuit of
a natural system. In England and Germany, which had readily received
the Linnæan method, its progress was still more tardy.

There is only one point, on which it appears necessary further to
dwell. A main and fundamental distinction in all natural systems, is
that of the Monocotyledonous and Dicotyledonous plants; that is,
plants which unfold themselves from an embryo with two little
leaves, or with one leaf only. This distinction produces its effects
in the systems which are regulated by numbers; for the flowers and
fruit of the monocotyledons are generally referrible to some law in
which the number _three_ prevails; a type which rarely occurs in
dicotyledons, these affecting most commonly an arrangement founded
on the number _five_. But it appears, when we attempt to rise
towards a natural {408} method, that this division according to the
cotyledons is of a higher order than the other divisions according
to number; and corresponds to a distinction in the general structure
and organization of the plant. The apprehension of the due rank of
this distinction has gradually grown clearer. Cuvier[117\16]
conceives that he finds such a division clearly marked in Lobel, in
1581, and employed by Ray as the basis of his classification a
century later. This difference has had its due place assigned it in
more recent systems of arrangement; but it is only later still that
its full import has been distinctly brought into view. Desfontaines
discovered[118\16] that the ligneous fibre is developed in an
opposite manner in vegetables with one and with two
cotyledons;--towards the inside in the former case, and towards the
outside in the latter; and hence these two great classes have been
since termed _endogenous_ and _exogenous_.

[Note 117\16: _Hist. Sc. Nat._ ii. 197.]

[Note 118\16: _Hist. Sc. Nat._ i. pp. 196, 290.]

Thus this division, according to the cotyledons, appears to have the
stamp of reality put upon it, by acquiring a physiological meaning.
Yet we are not allowed to forget, even at this elevated point of
generalization, that _no one_ character can be imperative in a natural
method. Lamarck, who employed his great talents on botany, before he
devoted himself exclusively to other branches of natural history,
published his views concerning methods, systems,[119\16] and
characters. His main principle is, that no single part of a plant,
however essential, can be an absolute rule for classification; and
hence he blames the Jussieuian method, as giving this inadmissible
authority to the cotyledons. Roscoe[120\16] further urges that some
plants, as _Orchis morio_, and _Limodorum verecundum_, have no visible
cotyledons. Yet De Candolle, who labored along with Lamarck, in the
new edition of the _Flore Française_, has, as we have already
intimated, been led, by the most careful application of the wisest
principles, to a system of Natural Orders, of which Jussieu's may be
looked upon as the basis; and we shall find the greatest botanists, up
to the most recent period, recognizing, and employing themselves in
improving, Jussieu's Natural Families; so that in the progress of this
part of our knowledge, vague and perplexing as it is, we have no
exception to our general aphorism, that no real acquisition in science
is ever discarded. {409}

[Note 119\16: Sprengel, ii. 296; and, there quoted, _Flore
Française_, t. i. 3, 1778. _Mém. Ac. P._ 1785. _Journ. Hist. Nat._
t. i. For Lamarck's _Méthode Analytique_, see Dumeril, _Sc. Nat._ i.
Art. 390.]

[Note 120\16: Roscoe, _Linn. Tr._ vol. xi. _Cuscuta_ also has no
cotyledons.]

The reception of the system of Jussieu in this country was not so
ready and cordial as that of Linnæus. As we have already noticed,
the two systems were looked upon as rivals. Thus Roscoe, in
1810,[121\16] endeavored to show that Jussieu's system was not more
natural than the Linnæan, and was inferior as an artificial system:
but he argues his points as if Jussieu's characters were the grounds
of his distribution; which, as we have said, is to mistake the
construction of a natural system. In 1803, Salisbury[122\16] had
already assailed the machinery of the system, maintaining that there
are no cases of perigynous stamens, as Jussieu assumes; but this he
urges with great expressions of respect for the author of the
method. And the more profound botanists of England soon showed that
they could appreciate and extend the natural method. Robert Brown,
who had accompanied Captain Flinders to New Holland in 1801, and
who, after examining that country, brought home, in 1805, nearly
four thousand species of plants, was the most distinguished example
of this. In his preface to the _Prodromus Floræ Novæ Hollandiæ_, he
says, that he found himself under the necessity of employing the
natural method, as the only way of avoiding serious error, when he
had to deal with so many new genera as occur in New Holland; and
that he has, therefore, followed the method of Jussieu; the greater
part of whose orders are truly natural, "although their arrangement
in classes, as is," he says, "conceded by their author, no less
candid than learned, is often artificial, and, as appears to me,
rests on doubtful grounds."

[Note 121\16: _Linn. Tr._ vol. xi. p. 50.]

[Note 122\16: Ibid. vol. viii.]

From what has already been said, the reader will, I trust, see what
an extensive and exact knowledge of the vegetable world, and what
comprehensive views of affinity, must be requisite in a person who
has to modify the natural system so as to make it suited to receive
and arrange a great number of new plants, extremely different from
the genera on which the arrangement was first formed, as the New
Holland genera for the most part were. He will also see how
impossible it must be to convey by extract or description any notion
of the nature of these modifications: it is enough to say, that they
have excited the applause of botanists wherever the science is
studied, and that they have induced M. de Humboldt and his
fellow-laborers, themselves botanists of the first rank, to dedicate
one of their works to him in terms of the strongest
admiration.[123\16] Mr. Brown has also published {410} special
disquisitions on parts of the Natural System; as on Jussieu's
_Proteaceæ_;[124\16] on the _Asclepiadeæ_, a natural family of
plants which must be separated from Jussieu's _Apocyneæ_;[125\16]
and other similar labors.

[Note 123\16: Roberto Brown, Britanniarum gloriæ atque ornamento,
totam Botanices scientiam ingenio mirifico complectenti. &c.]

[Note 124\16: _Linn. Tr._ vol. x. 1809.]

[Note 125\16: _Mem. of Wernerian N. H. Soc._ vol. i. 1809.]

We have, I think, been led, by our survey of the history of Botany,
to this point;--that a Natural Method directs us to the study of
Physiology, as the only means by which we can reach the object. This
conviction, which in botany comes at the end of a long series of
attempts at classification, offers itself at once in the natural
history of animals, where the physiological signification of the
resemblances and differences is so much more obvious. I shall not,
therefore, consider any of these branches of natural history in
detail as examples of mere classification. They will come before us,
if at all, more properly when we consider the classifications which
depend on the functions of organs, and on the corresponding
modifications which they necessarily undergo; that is, when we trace
the results of Physiology. But before we proceed to sketch the
history of that part of our knowledge, there are a few points in the
progress of Zoology, understood as a mere classificatory science,
which appear to me sufficiently instructive to make it worth our
while to dwell upon them.

[2nd Ed.] [Mr. Lindley's recent work, _The Vegetable Kingdom_ (1846),
may be looked upon as containing the best view of the recent history
of Systematic Botany. In the Introduction to this work, Mr. Lindley
has given an account of various recent works on the subject; as
Agardh's _Classes Plantarum_ (1826); Perleb's _Lehrbuch der
Naturgeschichte der Pflanzenreich_ (1826); Dumortier's _Florula
Belgica_ (1827); Bartling's _Ordines Naturales Plantarum_ (1830);
Hess's _Uebersicht der Phanerogenischen Natürlichen Pflanzenfamilien_
(1832); Schulz's _Natürliches System des Pflanzenreich's_ (1832);
Horaninow's _Primæ Lineæ Systematis Naturæ_ (1834); Fries's _Corpus
Florarum provincialium Sueciæ_ (1835); Martins's _Conspectus Regni
Vegetablis secundum Characteres Morphologicos_ (1835); Sir Edward F.
Bromhead's System, as published in the _Edinburgh Journal_ and other
Journals (1836-1840); Endlicher's _Genera Plantarum secundum Ordines
Naturales disposita_ (1836-1840); Perleb's _Clavis Classicum Ordinum
et Familiarum_ (1838); Adolphe Brongniart's _Enumération des Genres de
Plantes_ (1843); Meisner's _Plantarum vascularium Genera secundum
Ordines Naturales digesta_ (1843); Horaninow's _Tetractys Naturæ, seu
Systema quinquemembre omnium Naturalium_ {411} (1843); Adrien de
Jussieu's _**Cours Elémentaire d'Histoire Naturelle. Botanique_
(1844).

Mr. Lindley, in this as in all his works, urges strongly the
superior value of natural as compared with artificial systems; his
principles being, I think, nearly such as I have attempted to
establish in the _Philosophy of the Sciences_, Book viii., Chapter
ii. He states that the leading idea which has been kept in view in
the compilation of his work is this maxim of Fries: "Singula sphæra
(sectio) _ideam quandam_ exponit, indeque ejus character notione
simplici optime exprimitur;" and he is hence led to think that the
true characters of all natural assemblages are extremely simple.

One of the leading features in Mr. Lindley's system is that he has
thrown the Natural Orders into groups subordinate to the higher
divisions of Classes and Sub-classes. He had already attempted this,
in imitation of Agardh and Bartling, in his _Nixus Plantarum_
(1838). The groups of Natural Orders were there called _Nixus_
(tendencies); and they were denoted by names ending in _ales_; but
these groups were further subordinated to _Cohorts_. Thus the first
member of the arrangement was Class 1. EXOGENÆ. Sub-class 1.
POLYPETALÆ. Cohort 1. ALBUMINOSÆ. _Nixus_ 1. _Ranales_. Natural
Orders included in this _Nixus_, Ranunculaceæ, Saraceniceæ,
Papaveraceæ, &c. In the _Vegetable Kingdom_, the groups of Natural
Orders are termed _Alliances_. In this work, the Sub-classes of the
EXOGENS are four: I. DICLINOUS; II. HYPOGYNOUS; III. PERIGYNOUS; IV.
EPIGYNOUS; and the Alliances are subordinated to these without the
intervention of _Cohorts_.

Mr. Lindley has also, in this as in other works, given English names
for the Natural Orders. Thus for _Nymphaceæ_, _Ranunculaceæ_,
_Tamaricaceæ_, _Zygophyllaceæ_, _Eleatrinaceæ_, he substitutes
Water-Lilies, Crowfoots, Tamarisks, Bean-Capers, and Water-Peppers;
for _Malvaceæ_, _Aurantiaceæ_, _Gentianaceæ_, _Primulaceæ_,
_Urtiaceæ_, _Euphorbiaceæ_, he employs Mallow-worts, Citron-worts,
Gentian-worts, Prim-worts, Nettle-worts, Spurge-worts; and the terms
Orchids, Hippurids, Amaryllids, Irids, Typhads, Arads, Cucurbits,
are taken as English equivalents for _Orchidaceæ_, _Haloragaceæ_,
_Amaryllidaceæ_, _Iridaceæ_, _Typhaceæ_, _Araceæ_, _Cucurbitaceæ_.
All persons who wish success to the study of botany in England must
rejoice to see it tend to assume this idiomatic shape.] {412}




CHAPTER VI.

THE PROGRESS OF SYSTEMATIC ZOOLOGY.


THE history of Systematic Botany, as we have presented it, may be
considered as a sufficient type of the general order of progression
in the sciences of classification. It has appeared, in the survey
which we have had to give, that this science, no less than those
which we first considered, has been formed by a series of inductive
processes, and has, in its history, Epochs at which, by such
processes, decided advances were made. The important step in such
cases is, the seizing upon some artificial mark which conforms to
natural resemblances;--some basis of arrangement and nomenclature by
means of which true propositions of considerable generality can be
enunciated. The advance of other classificatory sciences, as well as
botany, must consist of such steps; and their course, like that of
botany, must (if we attend only to the real additions made to
knowledge,) be gradual and progressive, from the earliest times to
the present.

To exemplify this continued and constant progression in the whole
range of Zoology, would require vast knowledge and great labor; and
is, perhaps, the less necessary, after we have dwelt so long on the
history of Botany, considered in the same point of view. But there
are a few observations respecting Zoology in general which we are
led to make in consequence of statements recently promulgated; for
these statements seem to represent the history of Zoology as having
followed a course very different from that which we have just
ascribed to the classificatory sciences in general. It is held by
some naturalists, that not only the formation of a systematic
classification in Zoology dates as far back as Aristotle; but that
his classification is, in many respects, superior to some of the
most admired and recent attempts of modern times.

If this were really the case, it would show that at least the idea
of a Systematic Classification had been formed and developed long
previous to the period to which we have assigned such a step; and it
would be difficult to reconcile such an early maturity of Zoology
with the conviction, which we have had impressed upon us by the
other {413} parts of our history, that not only labor but time, not
only one man of genius but several, and those succeeding each other,
are requisite to the formation of any considerable science.

But, in reality, the statements to which we refer, respecting the
scientific character of Aristotle's Zoological system, are
altogether without foundation; and this science confirms the lessons
taught us by all the others. The misstatements respecting
Aristotle's doctrines are on this account so important, and are so
curious in themselves, that I must dwell upon them a little.

Aristotle's nine Books _On Animals_ are a work enumerating the
differences of animals in almost all conceivable respects;--in the
organs of sense, of motion, of nutrition, the interior anatomy, the
exterior covering, the manner of life, growth, generation, and many
other circumstances. These differences are very philosophically
estimated. "The corresponding parts of animals," he says,[126\16]
"besides the differences of quality and circumstance, differ in
being more or fewer, greater or smaller, and, speaking generally, in
excess and defect. Thus some animals have crustaceous coverings,
others hard shells; some have long beaks, some short; some have many
wings, some have few; Some again have parts which others want, as
crests and spurs." He then makes the following important remark:
"Some animals have parts which correspond to those of others, not as
being the same in species, nor by excess and defect, but by
_analogy_; thus a claw is analogous to a thorn, and a nail to a
hoof, and a hand to the nipper of a lobster, and a feather to a
scale; for what a feather is in a bird, that is a scale in a fish."

[Note 126\16: Lib. i. c. i.]

It will not, however, be necessary, in order to understand Aristotle
for our present purpose, that we should discuss his notion of
Analogy. He proceeds to state his object,[127\16] which is, as we
have said, to describe the differences of animals in their structure
and habits. He then observes, that for structure, we may take Man
for our type,[128\16] as being best known to us; and the remainder
of the first Book is occupied with a description of man's body,
beginning from the head, and proceeding to the extremities.

[Note 127\16: Lib. i. c. ii.]

[Note 128\16: c. iii.]

In the next Book, (from which are taken the principal passages in
which his modern commentators detect his system,) he proceeds to
compare the differences of parts in different animals, according to
the order which he had observed in man. In the first chapter he
speaks {414} of the head and neck of animals; in the second, of the
parts analogous to arms and hands; in the third, of the breast and
paps, and so on; and thus he comes, in the seventh chapter, to the
legs, feet, and toes: and in the eleventh, to the teeth, and so to
other parts.

The construction of a classification consists in the selection of
certain parts, as those which shall eminently and peculiarly
determine the place of each species in our arrangement. It is clear,
therefore, that such an enumeration of differences as we have
described, supposing it complete, contains the materials of all
possible classifications. But we can with no more propriety say that
the author of such an enumeration of differences is the author of
any classification which can be made by means of them, than we can
say that a man who writes down the whole alphabet writes down the
solution of a given riddle or the answer to a particular question.

Yet it is on no other ground than this enumeration, so far as I can
discover, that Aristotle's "System" has been so decidedly spoken
of,[129\16] and exhibited in the most formal tabular shape. The
authors of this _Systema Aristotelicum_, have selected, I presume,
the following passages from the work _On Animals_, as they might
have selected any other; and by arranging them according to a
subordination unknown to Aristotle himself have made for him a
scheme which undoubtedly bears a great resemblance to the most
complete systems of modern times.

[Note 129\16: _Linnæan Transactions_, vol. xvi. p. 24.]

Book I., chap. v.--"Some animals are viviparous, some oviparous,
some vermiparous. The viviparous are such as man, and the horse, and
all those animals which have hair; and of aquatic animals, the whale
kind, as the dolphin and cartilaginous fishes."

Book II., chap. vii.--"Of quadrupeds which have blood and are
viviparous, some are (as to their extremities,) many-cloven, as the
hands and feet of man. For some are many-toed, as the lion, the dog,
the panther; some are bifid, and have hoofs instead of nails, as the
sheep, the goat, the elephant, the hippopotamus; and some have
undivided feet, as the solid-hoofed animals, the horse and ass. The
swine kind share both characters."

Chap. ii.--"Animals have also great differences in the teeth, both
when compared with each other and with man. For all quadrupeds which
have blood and are viviparous, have teeth. And in the first place,
some are ambidental,[130\16] (having teeth in both jaws;) and some
{415} are not so, wanting the front teeth in the upper jaw. Some
have neither front teeth nor horns, as the camel; some have
tusks,[131\16] as the boar, some have not. Some have
serrated[132\16] teeth, as the lion, the panther, the dog; some have
the teeth unvaried,[133\16] as the horse and the ox; for the animals
which vary their cutting-teeth have all serrated teeth. No animal
has both tusks and horns; nor has any animal with serrated teeth
either of those weapons. The greater part have the front teeth
cutting, and those within broad."

[Note 130\16: Ἀμφόδοντα.]

[Note 131\16: Χαυλιόδοντα.]

[Note 132\16: Καρχαρόδοντα.]

[Note 133\16: Ἀνεπάλλακτα.]

These passages undoubtedly contain most of the differences on which
the asserted Aristotelian classification rests; but the
classification is formed by using the characters drawn from the
teeth, in order to subdivide those taken from the feet; whereas in
Aristotle these two sets of characters stand side by side, along
with dozens of others; any selection of which, employed according to
any arbitrary method of subordination, might with equal justice be
called Aristotle's system.

Why, for instance, in order to form subdivisions of animals, should
we not go on with Aristotle's continuation of the second of the
above quoted passages, instead of capriciously leaping to the third?
"Of these some have horns, some have none . . . Some have a
fetlock-joint,[134\16] some have none . . . Of those which have
horns, some have them solid throughout, as the stag; others, for the
most part, hollow . . . Some cast their horns, some do not." If it
be replied, that we could not, by means of such characters, form a
tenable zoological system; we again ask by what right we assume
Aristotle to have made or attempted a systematic arrangement, when
what he has written, taken in its natural order, does not admit of
being construed into a system.

[Note 134\16: Ἀστράγαλον.]

Again, what is the object of any classification? This, at least,
among others. To enable the person who uses it to study and describe
more conveniently the objects thus classified. If, therefore,
Aristotle had formed or adopted any system of arrangement, we should
see it in the order of the subjects in his work. Accordingly, so far
as he has a system, he professes to make this use of it. At the
beginning of the fifth Book, where he is proceeding to treat of the
different modes of generation of animals, he says, "As we formerly
made a Division of animals according to their kinds, we must now, in
the same manner, give a general survey of their History (θεωρίαν).
Except, indeed, that in the former case we made our commencement by
a description {416} of man, but in the present instance we must
speak of him last, because he requires most study. We must begin
then with those animals which have shells; we must go on to those
which have softer coverings, as crustacea, soft animals, and
insects; after these, fishes, both viviparous and oviparous; then
birds; then land animals, both viviparous and oviparous."

It is clear from this passage that Aristotle had certain wide and
indefinite views of classification, which though not very exact, are
still highly creditable to him; but it is equally clear that he was
quite unconscious of the classification that has been ascribed to
him. If he had adopted that or any other system, this was precisely
the place in which he must have referred to and employed it.

The honor due to the stupendous accumulation of zoological knowledge
which Aristotle's works contain, cannot be tarnished by our denying
him the credit of a system which he never dreamt of and which, from
the nature of the progress of science, could not possibly be
constructed at that period. But, in reality, we may exchange the
mistaken claims which we have been contesting for a better, because
a truer praise. Aristotle does show, as far as could be done at his
time, a perception of the need of groups, and of names of groups, in
the study of the animal kingdom; and thus may justly be held up as
the great figure in the Prelude to the Formation of Systems which
took place in more advanced scientific times.

This appears, in some measure, from the passage last quoted. For not
only is there, in that, a clear recognition of the value and object
of a method in natural history; but the general arrangement of the
animal kingdom there proposed has considerable scientific merit, and
is, for the time, very philosophical. But there are passages in his
work in which he shows a wish to carry the principle of arrangement
more into detail. Thus, in the first Book, before proceeding to his
survey of the differences of animals,[135\16] after speaking of such
classes as Quadrupeds. Birds, Fishes, Cetaceous, Testaceous,
Crustaceous Animals, Mollusks, Insects, he says, (chap. vii.)
"Animals cannot be divided into large genera, in which one kind
includes many kinds. For some kinds are unique, and have no
difference of species, as _man_. Some have such kinds, but have no
names for them. Thus all quadrupeds which have not wings, have
blood. But of these, some are viviparous, some oviparous. Those
which are {417} viviparous have not all hair; those which are
oviparous have scales." We have here a manifestly intentional
subordination of characters: and a kind of regret that we have not
names for the classes here indicated; such, for instance, as
viviparous quadrupeds having hair. But he follows the subject into
further detail. "Of the class of viviparous quadrupeds," he
continues, "there are many genera,[136\16] but these again are
without names, except specific names, such as _man_, _lion_, _stag_,
_horse_, _dog_, and the like. Yet there is a genus of animals that
have names, as the horse, the ass, the _oreus_, the _ginnus_, the
_innus_, and the animal which in Syria is called _heminus_ (mule);
for these are called _mules_, from their resemblance only; not being
mules, for they breed of their own kind. Wherefore," he adds, that
is, because we do not possess recognized genera and generic names of
this kind, "we must take the species separately, and study the
nature of each."

[Note 135\16: Γένη.]

[Note 136\16: **Εἴδη.]

These passages afford us sufficient ground for placing Aristotle at
the head of those naturalists to whom the first views of the
necessity of a zoological system are due. It was, however, very long
before any worthy successor appeared, for no additional step was
made till modern times. When Natural History again came to be
studied in Nature, the business of Classification, as we have seen,
forced itself upon men's attention, and was pursued with interest in
animals, as in plants. The steps of its advance were similar in the
two cases;--by successive naturalists, various systems of artificial
marks were selected with a view to precision and convenience;--and
these artificial systems assumed the existence of certain natural
groups, and of a natural system to which they gradually tended. But
there was this difference between botany and zoology:--the reference
to physiological principles, which, as we have remarked, influenced
the natural systems of vegetables in a latent and obscure manner,
botanists being guided by its light, but hardly aware that they were
so, affected the study of systematic zoology more directly and
evidently. For men can neither overlook the general physiological
features of animals, nor avoid being swayed by them in their
judgments of the affinities of different species. Thus the
classifications of zoology tended more and more to a union with
comparative anatomy, as the science was more and more
improved.[137\16] But comparative anatomy belongs to the subject of
the next Book; and anything it may be proper to say respecting its
influence upon zoological arrangements, will properly find a place
there. {418}

[Note 137\16: Cuvier, _Leç. d'Anat. Comp._ vol. i. p. 17.]

It will appear, and indeed it hardly requires to be proved, that
those steps in systematic zoology which are due to the light thrown
upon the subject by physiology, are the result of a long series of
labors by various naturalists, and have been, like other advances in
science, led to and produced by the general progress of such
knowledge. We can hardly expect that the classificatory sciences can
undergo any material improvement which is not of this kind. Very
recently, however, some authors have attempted to introduce into
these sciences certain principles which do not, at first sight,
appear as a continuation and extension of the previous researches of
comparative anatomists. I speak, in particular, of the doctrines of
a _Circular Progression_ in the series of affinity; of a _Quinary
Division_ of such circular groups; and of a relation of _Analogy_
between the members of such groups, entirely distinct from the
relation of _Affinity_.

The doctrine of Circular Progression has been propounded principally
by Mr. Macleay; although, as he has shown,[138\16] there are
suggestions of the same kind to be found in other writers. So far as
this view negatives the doctrine of a mere linear progression in
nature, which would place each genus in contact only with the
preceding and succeeding ones, and so far as it requires us to
attend to more varied and ramified resemblances, there can be no
doubt that it is supported by the result of all the attempts to form
natural systems. But whether that assemblage of circles of
arrangement which is now offered to naturalists, be the true and
only way of exhibiting the natural relations of organized bodies, is
a much more difficult question, and one which I shall not here
attempt to examine; although it will be found, I think, that those
analogies of science which we have had to study, would not fail to
throw some light upon such an inquiry. The prevalence of an
invariable numerical law in the divisions of natural groups, (as the
number _five_ is asserted to prevail by Mr. Macleay, the number
_ten_ by Fries, and other numbers by other writers), would be a
curious fact, if established; but it is easy to see that nothing
short of the most consummate knowledge of natural history, joined
with extreme clearness of view and calmness of judgment, could
enable any one to pronounce on the attempts which have been made to
establish such a principle. But the doctrine of a relation of
_Analogy_ distinct from Affinity, in the manner which has recently
been taught, seems to be obviously at variance with that gradual
approximation of the classificatory to the {419} physiological
sciences, which has appeared to us to be the general tendency of
real knowledge. It seems difficult to understand how a reference to
such relations as those which are offered as examples of
analogy[139\16] can be otherwise than a retrograde step in science.

[Note 138\16: _Linn. Trans._ vol. xvi. p. 9.]

[Note 139\16: For example, the goatsucker has an _affinity_ with the
swallow; but it has an _analogy_ with the bat, because both fly at
the same hour of the day, and feed in the same manner.--Swainson,
_Geography and Classification of Animals_, p. 129.]

Without, however, now dwelling upon these points, I will treat a
little more in detail of one of the branches of Zoology.

[2nd Ed.] [For the more recent progress of Systematic Zoology, see
in the _Reports_ of the British Association, in 1834, Mr. L.
Jenyns's _Report an the Recent Progress and Present State of
Zoology_, and in 1844, Mr. Strickland's _Report on the Recent
Progress and Present State of Ornithology_. In these Reports, the
questions of the Circular Arrangement, the Quinary System, and the
relation of Analogy and Affinity are discussed.]




CHAPTER VII.

THE PROGRESS OF ICHTHYOLOGY.


IF it had been already observed and admitted that sciences of the
same kind follow, and must follow, the same course in the order of
their development, it would be unnecessary to give a history of any
special branch of Systematic Zoology; since botany has already
afforded us a sufficient example of the progress of the
classificatory sciences. But we may be excused for introducing a
sketch of the advance of one department of zoology, since we are led
to the attempt by the peculiar advantage we possess in having a
complete history of the subject written with great care, and brought
up to the present time, by a naturalist of unequalled talents and
knowledge. I speak of Cuvier's _Historical View of Ichthyology_,
which forms the first chapter of his great work on that part of
natural history. The place and office in the progress of this
science, which is assigned to each person by Cuvier, will probably
not be lightly contested. It will, therefore, be no small
confirmation of the justice of the views on which the {420}
distribution of the events in the history of botany was founded, if
Cuvier's representation of the history of ichthyology offers to us
obviously a distribution almost identical.

We shall find that this is so;--that we have, in zoology as in botany,
a period of unsystematic knowledge; a period of misapplied erudition;
an epoch of the discovery of fixed characters; a period in which many
systems were put forward; a struggle of an artificial and a natural
method; and a gradual tendency of the natural method to a manifestly
physiological character. A few references to Cuvier's history will
enable us to illustrate these and other analogies.

_Period of Unsystematic Knowledge._--It would be easy to collect a
number of the fabulous stories of early times, which formed a
portion of the imaginary knowledge of men concerning animals as well
as plants. But passing over these, we come to a long period and a
great collection of writers, who, in various ways, and with various
degrees of merit, contributed to augment the knowledge which existed
concerning fish, while as yet there was hardly ever any attempt at a
classification of that province of the animal kingdom. Among these
writers, Aristotle is by far the most important. Indeed he carried
on his zoological researches under advantages which rarely fall to
the lot of the naturalist; if it be true, as Athenæus and Pliny
state,[140\16] that Alexander gave him sums which amounted to nine
hundred talents, to enable him to collect materials for his history
of animals, and put at his disposal several thousands of men to be
employed in hunting, fishing, and procuring information for him. The
works of his on Natural History which remain to us are, nine Books
_Of the History of Animals_; four, _On the Parts of Animals_; five,
_On the Generation of Animals_; one, _On the Going of Animals_; one,
_Of the Sensations, and the Organs of them_; one, _On Sleeping and
Waking_; one, _On the Motion of Animals_; one, _On the Length and
Shortness of Life_; one, _On Youth and Old Age_; one, _On Life and
Death_; one, _On Respiration_. The knowledge of the external and
internal conformation of animals, their habits, instincts, and uses,
which Aristotle displays in these works, is spoken of as something
wonderful even to the naturalists of our own time. And he may be
taken as a sufficient representative of the whole of the period of
which we speak; for he is, says Cuvier,[141\16] not only the first,
but the only one of the ancients who has treated of the natural
history of fishes (the province to which {421} we now confine
ourselves,) in a scientific point of view, and in a way which shows
genius.

[Note 140\16: Cuv. _Hist. Nat. des Poissons_, i. 13.]

[Note 141\16: Cuv. p. 18.]

We may pass over, therefore, the other ancient authors from whose
writings Cuvier, with great learning and sagacity, has levied
contributions to the history of ichthyology; as Theophrastus, Ovid,
Pliny, Oppian, Athenæus, Ælian, Ausonius, Galen. We may, too, leave
unnoticed the compilers of the middle ages, who did little but
abstract and disfigure the portions of natural history which they
found in the ancients. Ichthyological, like other knowledge, was
scarcely sought except in books, and on that very account was not
understood when it was found.

_Period of Erudition._--Better times at length came, and men began to
observe nature for themselves. The three great authors who are held to
be the founders of modern ichthyology, appeared in the middle of the
sixteenth century; these were Bélon, Rondelet, and Salviani, who all
published about 1555. All the three, very different from the compilers
who filled the interval from Aristotle to them, themselves saw and
examined the fishes which they describe, and have given faithful
representations of them. But, resembling in that respect the founders
of modern botany, Briassavola, Ruellius, Tragus, and others, they
resembled them in this also, that they attempted to make their own
observations a commentary upon the ancient writers. Faithful to the
spirit of their time, they are far more careful to make out the names
which each fish bore in the ancient world, and to bring together
scraps of their history from the authors in whom these names occur,
than to describe them in a lucid manner; so that without their
figures, says Cuvier, it would be almost as difficult to discover
their species as those of the ancients.

The difficulty of describing and naming species so that they can be
recognized, is little appreciated at first, although it is in
reality the main-spring of the progress of the sciences of
classification. Aristotle never dreamt that the nomenclature which
was in use in his time could ever become obscure;[142\16] hence he
has taken no precaution to enable his readers to recognize the
species of which he speaks; and in him and in other ancient authors,
it requires much labor and great felicity of divination to determine
what the names mean. The perception of this difficulty among modern
naturalists led to systems, and to nomenclature founded upon system;
but these did not come into {422} being immediately at the time of
which we speak; nor till the evil had grown to a more inconvenient
magnitude.

[Note 142\16: Cuvier, p. 17.]

_Period of Accumulation of Materials. Exotic Collections._--The
fishes of Europe were for some time the principal objects of study;
but those of distant regions soon came into notice.[143\16] In the
seventeenth century the Dutch conquered Brazil, and George Margrave,
employed by them, described the natural productions of the country,
and especially the fishes. Bontius, in like manner, described some
of those of Batavia. Thus these writers correspond to Romphius and
Rheede in the history of botany. Many others might be mentioned; but
we must hasten to the formation of systems, which is our main object
of attention.

[Note 143\16: Cuv. p. 43.]

_Epoch of the Fixation of Characters. Ray and Willoughby._--In
botany, as we have seen, though Ray was one of the first who
invented a connected system, he was preceded at a considerable
interval by Cæsalpinus, who had given a genuine solution of the same
problem. It is not difficult to assign reasons why a sound
classification should be discovered for plants at an earlier period
than for fishes. The vastly greater number of the known species, and
the facilities which belong to the study of vegetables, give the
botanist a great advantage; and there are numerical relations of a
most definite kind (for instance, the number of parts of the
seed-vessel employed by Cæsalpinus as one of the bases of his
system), which are tolerably obvious in plants, but which are not
easily discovered in animals. And thus we find that in ichthyology,
Ray, with his pupil and friend Willoughby, appears as the first
founder of a tenable system.[144\16]

[Note 144\16: Francisci Willoughbeii, Armigeri, _de Historia
Piscium_, libri iv. jussu et sumptibus Societatis Regiæ Londinensis
editi, &c. Totum opus recognovit, coaptavit, supplevit, librum etiam
primum et secundum adjecit Joh. Raius. Oxford, 1668.]

The first great division in this system is into _cartilaginous_ and
_bony_ fishes; a primary division, which had been recognized by
Aristotle, and is retained by Cuvier in his latest labors. The
subdivisions are determined by the general form of the fish (as long
or flat), by the teeth, the presence or absence of ventral fins, the
number of dorsal fins, and the nature of the spines of the fins, as
soft or prickly. Most of these characters have preserved their
importance in later systems; especially the last, which, under the
terms _malacopterygian_ and _acanthopterygian_, holds a place in the
best recent arrangements. {423}

That this system was a true first approximation to a solution of the
problem, appears to be allowed by naturalists. Although, says
Cuvier,[145\16] there are in it no genera well defined and well
limited, still in many places the species are brought together very
naturally, and in such a way that a few words of explanation would
suffice to form, from the groups thus presented to us, several of
the genera which have since been received. Even in botany, as we
have seen, genera were hardly maintained with any degree of
precision, till the binary nomenclature of Linnæus made this
division a matter of such immense convenience.

[Note 145\16: Cuvier, p. 57.]

The amount of this convenience, the value of a brief and sure
nomenclature, had not yet been duly estimated. The work of Willoughby
forms an epoch,[146\16] and a happy epoch, in the history of
ichthyology; for the science, once systematized, could distinguish the
new from the old, arrange methodically, describe clearly. Yet, because
Willoughby had no nomenclature of his own, and no fixed names for his
genera, his immediate influence was not great. I will not attempt to
trace this influence in succeeding authors, but proceed to the next
important step in the progress of system.

[Note 146\16: p. 58.]

_Improvement of the System. Artedi._--Peter Artedi was a countryman
and intimate friend of Linnæus; and rendered to ichthyology nearly
the same services which Linnæus rendered to botany. In his
_Philosophia Ichthyologica_, he analysed[147\16] all the interior
and exterior parts of animals; he created a precise terminology for
the different forms of which these parts are susceptible; he laid
down rules for the nomenclature of genera and species; besides his
improvements of the subdivisions of the class. It is impossible not
to be struck with the close resemblance between these steps, and
those which are due to the _Fundamenta Botanica_. The latter work
appeared in 1736, the former was published by Linnæus, after the
death of the author, in 1738; but Linnæus had already, as early as
1735, made use of Artedi's manuscripts in the ichthyological part of
his _Systema Naturæ_. We cannot doubt that the two young naturalists
(they were nearly of the same age), must have had a great influence
upon each other's views and labors; and it would be difficult now to
ascertain what portion of the peculiar merits of the Linnæan reform
was derived from Artedi. But we may remark that, in ichthyology at
least, Artedi appears to have been a naturalist of more original
views and profounder philosophy than his friend and editor, who
afterwards himself took up the subject. {424} The reforms of
Linnæus, in all parts of natural history, appear as if they were
mainly dictated by a love of elegance, symmetry, clearness, and
definiteness; but the improvement of the ichthyological system by
Artedi seems to have been a step in the progress to a natural
arrangement. His genera,[148\16] which are forty-five in number, are
so well constituted, that they have almost all been preserved; and
the subdivisions which the constantly-increasing number of species
has compelled his successors to introduce, have very rarely been
such that they have led to the transposition of his genera.

[Note 147\16: p. 20.]

[Note 148\16: Cuvier, p. 71.]

In its bases, however, Artedi's was an artificial system. His
characters were positive and decisive, founded in general upon the
number of rays of the membrane of the gills, of which he was the
first to mark the importance;--upon the relative position of the
fins, upon their number, upon the part of the mouth where the teeth
are found, upon the conformation of the scales. Yet, in some cases,
he has recourse to the interior anatomy.

Linnæus himself at first did not venture to deviate from the
footsteps of a friend, who, in this science, had been his master.
But in 1758, in the tenth edition of the _Systema Naturæ_, he chose
to depend upon himself and devised a new ichthyological method. He
divided some genera, united others, gave to the species trivial
names and characteristic phrases, and added many species to those of
Artedi. Yet his innovations are for the most part disapproved of by
Cuvier; as his transferring the _chondropterygian_ fishes of Artedi
to the class of reptiles, under the title of _Amphybia nantes_; and
his rejecting the distinction of acanthopterygian and
malacopterygian, which, as we have seen, had prevailed from the time
of Willoughby, and introducing in its stead a distribution founded
on the presence or absence of the ventral fins, and on their
situation with regard to the pectoral fins. "Nothing," says Cuvier,
"more breaks the true connexions of genera than these orders of
_apodes_, _jugulares_, _thoracici_, and _abdominales_."

Thus Linnæus, though acknowledging the value and importance of
natural orders, was not happy in his attempts to construct a system
which should lead to them. In his detection of good characters for
an artificial system he was more fortunate. He was always attentive
to number, as a character; and he had the very great merit[149\16]
of introducing into the classification the number of rays of the
fins of each species. This mark is one of great importance and use.
And this, as well as {425} other branches of natural history,
derived incalculable advantages from the more general merits of the
illustrious Swede;[150\16]--the precision of the characters, the
convenience of a well-settled terminology, the facility afforded by
the binary nomenclature. These recommendations gave him a
pre-eminence which was acknowledged by almost all the naturalists of
his time, and displayed by the almost universal adoption of his
nomenclature, in zoology, as well as in botany; and by the almost
exclusive employment of his distributions of classes, however
imperfect and artificial they might be.

[Note 149\16: p. 74.]

[Note 150\16: Cuvier, p. 85.]

And even[151\16] if Linnæus had had no other merit than the impulse
he gave to the pursuit of natural science, this alone would suffice
to immortalize his name. In rendering natural history easy, or at
least in making it appear so, he diffused a general taste for it.
The great took it up with interest; the young, full of ardor, rushed
forwards in all directions, with the sole intention of completing
his system. The civilized world was eager to build the edifice which
Linnæus had planned.

[Note 151\16: Ib. p. 88.]

This spirit, among other results, produced voyages of natural
historical research, sent forth by nations and sovereigns. George
the Third of England had the honor of setting the example in this
noble career, by sending out the expeditions of Byron, Wallis, and
Carteret, in 1765. These were followed by those of Bougainville,
Cook, Forster, and others. Russia also scattered several scientific
expeditions through her vast dominions; and pupils of Linnæus sought
the icy shores of Greenland and Iceland, in order to apply his
nomenclature to the productions of those climes. But we need not
attempt to convey any idea of the vast stores of natural historical
treasures which were thus collected from every part of the globe.

I shall not endeavor to follow Cuvier in giving an account of the
great works of natural history to which this accumulation of materials
gave rise; such as the magnificent work of Bloch on Fishes, which
appeared in 1782-1785; nor need I attempt, by his assistance, to
characterize or place in their due position the several systems of
classification proposed about this time. But in the course of these
various essays, the distinction of the artificial and natural methods
of classification came more clearly into view than before; and this is
a point so important to the philosophy of the subject, that we must
devote a few words to it. {426}

_Separation of the Artificial and Natural Methods in Ichthyology._--It
has already been said that all so-called _artificial methods_ of
classification must be natural, at least as to the narrowest members
of the system; thus the artificial Linnæan method is natural as to
species, and even as to genera. And on the other hand, all proposed
natural methods, so long as they remain unmodified, are artificial as
to their characteristic marks. Thus a Natural Method is an attempt to
provide positive and distinct _characters_ for the _wider_ as well as
for the narrower _natural groups_. These considerations are applicable
to zoology as well as to botany. But the question, how we know natural
groups before we find marks for them, was, in botany, as we have seen,
susceptible only of vague and obscure answers:--the mind forms them,
it was said, by taking the aggregate of all the characters; or by
establishing a subordination of characters. And each of these answers
had its difficulty, of which the solution appeared to be, that in
attempting to form natural orders we are really guided by a latent
undeveloped estimate of physiological relations. Now this principle,
which was so dimly seen in the study of vegetables, shines out with
much greater clearness when we come to the study of animals, in which
the physiological relations of the parts are so manifest that they
cannot be overlooked, and have so strong an attraction for our
curiosity that we cannot help having our judgments influenced by them.
Hence the superiority of natural systems in zoology would probably be
far more generally allowed than in botany; and no arrangement of
animals which, in a large number of instances, violated strong and
clear natural affinities, would be tolerated because it answered the
purpose of enabling us easily to find the name and place of the animal
in the artificial system. Every system of zoological arrangement may
be supposed to aspire to be a natural system. But according to the
various habits of the minds of systematizers, this object was pursued
more or less steadily and successfully; and these differences came
more and more into view with the increase of knowledge and the
multiplication of attempts.

Bloch, whose ichthyological labors have been mentioned, followed in
his great work the method of Linnæus. But towards the end of his
life he had prepared a general system, founded upon one single
numerical principle;--the number of fins; just as the sexual system
of Linnæus is founded upon the number of stamina; and he made his
subdivisions according to the position of the ventral and pectoral
fins; the same character which Linnæus had employed for his primary
{427} division. He could not have done better, says Cuvier,[152\16]
if his object had been to turn into ridicule all artificial methods,
and to show to what absurd combinations they may lead.

[Note 152\16: p. 108.]

Cuvier himself who always pursued natural systems with a singularly
wise and sagacious consistency, attempted to improve the
ichthyological arrangements which had been proposed before him. In
his _Règne Animal_, published in 1817, he attempts the problem of
arranging this class; and the views suggested to him, both by his
successes and his failures, are so instructive and philosophical,
that I cannot illustrate the subject better than by citing some of
them.

"The class of fishes," he says,[153\16] "is, of all, that which
offers the greatest difficulties, when we wish to subdivide it into
orders, according to fixed and obvious characters. After many
trials, I have determined on the following distribution, which in
some instances is wanting in precision, but which possesses the
advantage of keeping the natural families entire.

[Note 153\16: _Règne Animal_, vol. ii. p. 110.]

"Fish form two distinct series;--that of _chondropterygians_ or
_cartilaginous fish_, and that of _fish_ properly so called.

"The _first_ of these series has for its character, that the
palatine bones replace, in it, the bones of the upper jaw: moreover
the whole of its structure has evident analogies, which we shall
explain.

"It divides itself into three ORDERS:
"The CYCLOSTOMES, in which the jaws are soldered (_soudées_) into an
immovable ring, and the bronchiæ are open in numerous holes.

"The SELACIANS, which have the bronchiæ like the preceding, but not
the jaws.

"The STURONIANS, in which the bronchiæ are open as usual by a slit
furnished with an operculum.

"The second series, or that of _ordinary fishes_, offers me, in the
first place, a primary division, into those of which the maxillary
bone and the palatine arch are dovetailed (_engrenés_) to the skull.
Of these I make an order of PECTOGNATHS, divided into two families;
the _gymnodonts_ and the _scleroderms_.

"After these I have the fishes with complete jaws, but with bronchiæ
which, instead of having the form of combs, as in all the others,
have the form of a series of little tufts (_houppes_). Of these I
again form an order, which I call LOPHOBRANCHS, which only includes
one family. {428}

"There then remains an innumerable quantity of fishes, to which we
can no longer apply any characters except those of the exterior
organs of motion. After long examination, I have found that the
least bad of these characters is, after all, that employed by Ray
and Artedi, taken from the nature of the first rays of the dorsal
and of the anal fin. Thus ordinary fishes are divided into
MALACOPTERYGIANS, of which all the rays are soft, except sometimes
the first of the dorsal fin or the pectorals;--and
ACANTHOPTERYGIANS, which have always the first portion of the
dorsal, or of the first dorsal when there are two, supported by
spinous rays, and in which the anal has also some such rays, and the
ventrals, at least, each one.

"The former may be subdivided without inconvenience, according to
their ventral fins, which are sometimes situate behind the abdomen,
sometimes adherent to the apparatus of the shoulder, or, finally,
are sometimes wanting altogether.

"We thus arrive at the three orders of ABDOMINAL MALACOPTERYGIANS,
of SUBBRACHIANS, and of APODES; each of which includes some natural
families which we shall explain: the first, especially, is very
numerous.

"But this basis of division is absolutely impracticable with the
Acanthopterygians; and the problem of establishing among these any
other subdivision than that of the natural families has hitherto
remained for me insoluble. Fortunately several of these families
offer characters almost as precise as those which we could give to
true orders.

"In truth, we cannot assign to the families of fishes, ranks as
marked, as for example, to those of mammifers. Thus the
Chondropterygians on the one hand hold to reptiles by the organs of
the senses, and by those of generation in some; and they are related
to mollusks and worms by the imperfection of the skeleton in others.

"As to Ordinary Fishes, if any part of the organization is found
more developed in some than in others, there does not result from
this any pre-eminence sufficiently marked, or of sufficient
influence upon their whole system, to oblige us to consult it in the
methodical arrangement.

"We shall place them, therefore, nearly in the order in which we
have just explained their characters."

I have extracted the whole of this passage, because, though it is
too technical to be understood in detail by the general reader,
those who have followed with any interest the history of the
attempts at a natural classification in any department in nature,
will see here a fine example of the problems which such attempts
propose, of the {429} difficulties which it may present, and of the
reasonings, labors, cautions, and varied resources, by means of
which its solution is sought, when a great philosophical naturalist
girds himself to the task. We see here, most instructively, how
different the endeavor to frame such a natural system, is from the
procedure of an artificial system, which carries imperatively
through the whole of a class of organized beings, a system of marks
either arbitrary, or conformable to natural affinities in a partial
degree. And we have not often the advantage of having the reasons
for a systematic arrangement so clearly and fully indicated, as is
done here, and in the descriptions of the separate orders.

This arrangement Cuvier adhered to in all its main points, both in
the second edition of the _Règne Animal_, published in 1821, and in
his _Histoire Naturelle des Poissons_, of which the first volume was
published in 1828, but which unfortunately was not completed at the
time of his death. It may be supposed, therefore, to be in
accordance with those views of zoological philosophy, which it was
the business of his life to form and to apply; and in a work like
the present, where, upon so large a question of natural history, we
must be directed in a great measure by the analogy of the history of
science, and by the judgments which seem most to have the character
of wisdom, we appear to be justified in taking Cuvier's
ichthyological system as the nearest approach which has yet been
made to a natural method in that department.

The true natural method is only one: artificial methods, and even
good ones, there may be many, as we have seen in botany; and each of
these may have its advantages for some particular use. On some
methods of this kind, on which naturalists themselves have hardly
yet had time to form a stable and distinct opinion, it is not our
office to decide. But judging, as I have already said, from the
general analogy of the natural sciences, I find it difficult to
conceive that the ichthyological method of M. Agassiz, recently
propounded with an especial reference to fossil fishes, can be
otherwise than an artificial method. It is founded entirely on one
part of the animal, its scaly covering, and even on a single scale.
It does not conform to that which almost all systematic
ichthyologists hitherto have considered as a permanent natural
distinction of a high order; the distinction of bony and
cartilaginous fishes; for it is stated that each order contains
examples of both.[154\16] I do not know what general anatomical or
physiological {430} truths it brings into view; but they ought to be
very important and striking ones, to entitle them to supersede those
which led Cuvier to his system. To this I may add, that the new
ichthyological classification does not seem to form, as we should
expect that any great advance towards a natural system would form, a
connected sequel to the past history of ichthyology;--a step to
which anterior discoveries and improvements have led, and in which
they are retained.

[Note 154\16: Dr. Buckland's _Bridgewater Treatise_, p. 270.]

But notwithstanding these considerations, the method of M. Agassiz
has probably very great advantages for his purpose; for in the case
of fossil fish, the parts which are the basis of his system often
remain, when even the skeleton is gone. And we may here again refer
to a principle of the classificatory sciences which we cannot make
too prominent;--all arrangements and nomenclatures are good, which
enable us to assert general propositions. Tried by this test, we
cannot fail to set a high value on the arrangement of M. Agassiz;
for propositions of the most striking generality respecting fossil
remains of fish, of which geologists before had never dreamt, are
enunciated by means of his groups and names. Thus only the two first
orders, the _Placoïdians_ and _Ganoïdians_, existed before the
commencement of the cretaceous formation: the third and fourth
orders, the _Ctenoïdians_ and _Cycloïdians_, which contain
three-fourths of the eight thousand known species of living Fishes,
appear for the first time in the cretaceous formation: and other
geological relations of these orders, no less remarkable, have been
ascertained by M. Agassiz.

But we have now, I trust, pursued these sciences of classification
sufficiently far; and it is time for us to enter upon that higher
domain of Physiology to which, as we have said. Zoology so
irresistibly directs us.

[2nd Ed.] [I have retained the remarks which I ventured at first to
make on the System of M. Agassiz; but I believe the opinion of the
most philosophical ichthyologists to be that Cuvier's System was too
exclusively based on the internal skeleton, as Agassiz's was on the
external skeleton. In some degree both systems have been superseded,
while all that was true in each has been retained. Mr. Owen, in his
_Lectures on Vertebrata_ (1846), takes Cuvierian characters from the
endo-skeleton, Agassizian ones from the exo-skeleton, Linnæan ones
from the ventral fins, Müllerian ones from the air-bladder, and
combines them by the light of his own researches, with the view of
forming a system more truly natural than any preceding one.

As I have said above, naturalists, in their progress towards a
Natural {431} System, are guided by physiological relations,
latently in Botany, but conspicuously in Zoology. From the epoch of
Cuvier's _Règne Animal_, the progress of Systematic Zoology is
inseparably dependent on the progress of Comparative Anatomy. Hence
I have placed Cuvier's Classification of animal forms in the next
Book, which treats of Physiology.]



{{433}}
BOOK XVII.


_ORGANICAL SCIENCES._


HISTORY OF PHYSIOLOGY
AND
COMPARATIVE ANATOMY.


  Fearful and wondrous is the skill which moulds
    Our body's vital plan,
  And from the first dim hidden germ unfolds
    The perfect limbs of man.
  Who, who can pierce the secret? tell us how
    Something is drawn from naught,
  Life from the inert mass? Who, Lord! but thou,
    Whose hand the whole has wrought?
  Of this corporeal substance, still to be,
    Thine eye a survey took;
  And all my members, yet unformed by thee,
    Were written in thy book.
          PSALM cxxxix. 13-16.



{{435}}
INTRODUCTION.


_Of the Organical Sciences_

THOUGH the general notion of _life_ is acknowledged by the most
profound philosophers to be dim and mysterious, even up to the
present time; and must, in the early stages of human speculation,
have been still more obscure and confused; it was sufficient, even
then, to give interest and connexion to men's observations upon
their own bodies and those of other animals. It was seen, that in
living things, certain peculiar processes were constantly repeated,
as those of breathing and of taking food, for example; and that a
certain conformation of the parts of the animal was subservient to
these processes; and thus were gradually formed the notions of
_Function_ and of _Organization_. And the sciences of which these
notions formed the basis are clearly distinguishable from all those
which we have hitherto considered. We conceive an _organized_ body
to be one in which the parts are there for the sake of the whole, in
a manner different from any mechanical or chemical connexion; we
conceive a _function_ to be not merely a process of change, but of
change connected with the general vital process. When mechanical or
chemical processes occur in the living body, they are instrumental
to, and directed by, the peculiar powers of life. The sciences which
thus consider organization and vital functions may be termed
_organical_ sciences.

When men began to speculate concerning such subjects, the general
mode of apprehending the process in the cases of some functions,
appeared to be almost obvious; thus it was conceived that the growth
of animals arose from their frame appropriating to itself a part of
the substance of the food through the various passages of the body.
Under the influence of such general conceptions, speculative men
were naturally led to endeavor to obtain more clear and definite
views of the course of each of such processes, and of the mode in
which the separate parts contributed to it. Along with the
observation of the living person, the more searching examination
which could be carried on in the dead body, and the comparison of
various kinds of animals, soon showed that this pursuit was rich in
knowledge and in interest. {436} Moreover, besides the interest
which the mere speculative faculty gave to this study, the Art of
Healing added to it a great practical value; and the effects of
diseases and of medicines supplied new materials and new motives for
the reasonings of the philosopher.

In this manner anatomy or physiology may be considered as a science
which began to be cultivated in the earliest periods of civilization.
Like most other ancient sciences, its career has been one of perpetual
though variable progress; and as in others, so in this, each step has
implied those which had been previously made, and cannot be understood
aright except we understand them. Moreover, the steps of this advance
have been very many and diverse; the cultivators of anatomy have in
all ages been numerous and laborious; the subject is one of vast
extent and complexity; almost every generation had added something to
the current knowledge of its details; and the general speculations of
physiologists have been subtle, bold, and learned. It must, therefore,
be difficult or impossible for a person who has not studied the
science with professional diligence and professional advantages, to
form just judgments of the value of the discoveries of various ages
and persons, and to arrange them in their due relation to each other.
To this we may add, that though all the discoveries which have been
made with respect to particular functions or organizations are
understood to be subordinate to one general science, the Philosophy of
Life, yet the principles and doctrines of this science nowhere exist
in a shape generally received and assented to among physiologists; and
thus we have not, in this science, the advantage which in some others
we have possessed;--of discerning the true direction of its first
movements, by knowing the point to which they ultimately tend;--of
running on beyond the earlier discoveries, and thus looking them in
the face, and reading their true features. With these disadvantages,
all that we can have to say respecting the history of Physiology must
need great indulgence on the part of the reader.

Yet here, as in other cases, we may, by guiding our views by those
of the greatest and most philosophical men who have made the subject
their study, hope to avoid material errors. Nor can we well evade
making the attempt. To obtain some simple and consistent view of the
progress of physiological science, is in the highest degree
important to the completion of our views of the progress of physical
science. For the physiological or organical sciences form a class to
which the classes already treated of, the mechanical, chemical, and
classificatory sciences, are subordinate and auxiliary. Again,
another {437} circumstance which makes physiology an important part
of our survey of human knowledge is, that we have here a science
which is concerned, indeed, about material combinations, but in
which we are led almost beyond the borders of the material world,
into the region of sensation and perception, thought and will. Such
a contemplation may offer some suggestions which may prepare us for
the transition from physical to metaphysical speculations.

In the survey which we must, for such purposes, take of the progress
of physiology, it is by no means necessary that we should exhaust
the subject, and attempt to give the history of every branch of the
knowledge of the phenomena and laws of living creatures. It will be
sufficient, if we follow a few of the lines of such researches,
which may be considered as examples of the whole. We see that life
is accompanied and sustained by many processes, which at first offer
themselves to our notice as separate functions, however they may
afterwards be found to be connected and identified; such are
feeling, digestion, respiration, the action of the heart and pulse,
generation, perception, voluntary motion. The analysis of any one of
these functions may be pursued separately. And since in this, as in
all genuine sciences, our knowledge becomes real and scientific,
only in so far as it is verified in particular facts, and thus
established in general propositions, such an original separation of
the subjects of research is requisite to a true representation of
the growth of real knowledge. The loose hypotheses and systems,
concerning the connexion of different vital faculties and the
general nature of living things, which have often been promulgated,
must be excluded from this part of our plan. We do not deny all
value and merit to such speculations; but they cannot be admitted in
the earlier stages of the history of physiology, treated of as an
inductive science. If the doctrine so propounded have a solid and
permanent truth, they will again come before us when we have
travelled through the range of more limited truths, and are prepared
to ascend with security and certainty into the higher region of
general physiological principles. If they cannot be arrived at by
such a road, they are then, however plausible and pleasing, no
portion of that real and progressive science with which alone our
history is concerned.

We proceed, therefore, to trace the establishment of some of the
more limited but certain doctrines of physiology. {438}




CHAPTER I.

DISCOVERY OF THE ORGANS OF VOLUNTARY MOTION.


_Sect._ 1.--_Knowledge of Galen and his Predecessors._

IN the earliest conceptions which men entertained of their power of
moving their own members, they probably had no thought of any
mechanism or organization by which this was effected. The foot and
the hand, no less than the head, were seen to be endowed with life;
and this pervading life seemed sufficiently to explain the power of
motion in each part of the frame, without its being held necessary
to seek out a special seat of the will, or instruments by which its
impulses were made effective. But the slightest inspection of
dissected animals showed that their limbs were formed of a curious
and complex collection of cordage, and communications of various
kinds, running along and connecting the bones of the skeleton. These
cords and communications we now distinguish as muscles, nerves,
veins, arteries, &c.; and among these, we assign to the muscles the
office of moving the parts to which they are attached, as cords move
the parts of a machine. Though this action of the muscles on the
bones may now appear very obvious, it was, probably, not at first
discerned. It is observed that Homer, who describes the wounds which
are inflicted in his battles with so much apparent anatomical
precision, nowhere employs the word _muscle_. And even Hippocrates
of Cos, the most celebrated physician of antiquity, is held to have
had no distinct conception of such an organ.[1\17] He always employs
the word _flesh_ when he means _muscle_, and the first explanation
of the latter word (μῦς) occurs in a spurious work ascribed to him.
For nerves, sinews, ligaments,[2\17] he used indiscriminately the
same terms; (τόνος or νεῦρον;) and of these nerves (νεῦρα) he
asserts that they contract the limbs. Nor do we find much more
distinctness on this subject even in Aristotle, a generation or two
later. "The origin of the νεῦρα," he says,[3\17] "is from the heart;
they connect {439} the bones, and surround the joints." It is clear
that he means here the muscles, and therefore it is with injustice
that he has been accused of the gross error of deriving the nerves
from the heart. And he is held to have really had the merit[4\17] of
discovering the nerves of sensation, which he calls the "canals of
the brain" (πόροι τοῦ ἐγκεφάλου); but the analysis of the mechanism
of motion is left by him almost untouched. Perhaps his want of sound
mechanical notions, and his constant straining after verbal
generalities, and systematic classifications of the widest kind,
supply the true account of his thus missing the solution of one of
the simplest problems of Anatomy.

[Note 1\17: Sprengel, _Geschichte der Arzneikunde_, i. 382.]

[Note 2\17: Sprengel, _Gesch. Arz._ i. 385.]

[Note 3\17: _Hist. Anim._ iii. 5.]

[Note 4\17: Ib. i. 456.]

In this, however, as in other subjects, his immediate predecessors
were far from remedying the deficiencies of his doctrines. Those who
professed to study physiology and medicine were, for the most part,
studious only to frame some general system of abstract principles,
which might give an appearance of connexion and profundity to their
tenets. In this manner the successors of Hippocrates became a
medical school, of great note in its day, designated as the
_Dogmatic_ school;[5\17] in opposition to which arose an _Empiric_
sect, who professed to deduce their modes of cure, not from
theoretical dogmas, but from experience. These rival parties
prevailed principally in Asia Minor and Egypt, during the time of
Alexander's successors,--a period rich in names, but poor in
discoveries; and we find no clear evidence of any decided advance in
anatomy, such as we are here attempting to trace.

[Note 5\17: Sprengel, _Gesch. Arz._ i. 583.]

The victories of Lucullus and Pompeius, in Greece and Asia, made the
Romans acquainted with the Greek philosophy; and the consequence
soon was, that shoals of philosophers, rhetoricians, poets, and
physicians[6\17] streamed from Greece, Asia Minor, and Egypt, to
Rome and Italy, to traffic their knowledge and their arts for Roman
wealth. Among these, was one person whose name makes a great figure
in the history of medicine, Asclepiades of Prusa in Bithynia. This
man appears to have been a quack, with the usual endowments of his
class;--boldness, singularity, a contemptuous rejection of all
previously esteemed opinions, a new classification of diseases, a
new list of medicines, and the assertion of some wonderful cures. He
would not, on such accounts, deserve a place in the history of
science, but that he became the founder of a new school, the
_Methodic_, which professed to hold itself separate both from the
Dogmatics and the Empirics. {440}

[Note 6\17: Sprengel, _Gesch. Arz._ ii. 5.]

I have noticed these schools of medicine, because, though I am not
able to state distinctly their respective merits in the cultivation
of anatomy, a great progress in that science was undoubtedly made
during their domination, of which the praise must, I conceive, be in
some way divided among them. The amount of this progress we are able
to estimate, when we come to the works of Galen, who flourished
under the Antonines, and died about A.D. 203. The following passage
from his works will show that this progress in knowledge was not
made without the usual condition of laborious and careful
experiment, while it implies the curious fact of such experiment
being conducted by means of family tradition and instruction, so as
to give rise to a _caste_ of dissectors. In the opening of his
Second Book _On Anatomical Manipulations_, he speaks thus of his
predecessors: "I do not blame the ancients, who did not write books
on anatomical manipulation; though I praise Marinus, who did. For it
was superfluous for them to compose such records for themselves or
others, while they were, from their childhood, exercised by their
parents in dissecting, just as familiarly as in writing and reading;
so that there was no more fear of their forgetting their anatomy,
than of forgetting their alphabet. But when grown men, as well as
children, were taught, this thorough discipline fell off; and, the
art being carried out of the family of the Asclepiads, and declining
by repeated transmission, books became necessary for the student."

That the general structure of the animal frame, as composed of bones
and muscles, was known with great accuracy before the time of Galen,
is manifest from the nature of the mistakes and deficiencies of his
predecessors which he finds it necessary to notice. Thus he
observes, that some anatomists have made one muscle into two, from
its having two heads;--that they have overlooked some of the muscles
in the face of an ape, in consequence of not skinning the animal
with their own hands;--and the like. Such remarks imply that the
current knowledge of this kind was tolerably complete. Galen's own
views of the general mechanical structure of an animal are very
clear and sound. The skeleton, he observes, discharges[7\17] the
office of the pole of a tent, or the walls of a house. With respect
to the action of the muscles, his views were anatomically and
mechanically correct; in some instances, he showed what this action
was, by severing the muscle.[8\17] He himself added considerably to
the existing knowledge of {441} this subject; and his discoveries
and descriptions, even of very minute parts of the muscular system,
are spoken of with praise by modern anatomists.[9\17]

[Note 7\17: _De Anatom. Administ._ i. 2.]

[Note 8\17: Sprengel, ii. 157.]

[Note 9\17: Sprengel, ii. 150.]

We may consider, therefore, that the doctrine of the muscular
system, as a collection of cords and sheets, by the contraction of
which the parts of the body are moved and supported, was firmly
established, and completely followed into detail, by Galen and his
predecessors. But there is another class of organs connected with
voluntary motion, the nerves, and we must for a moment trace the
opinions which prevailed respecting these. Aristotle, as we have
said, noticed some of the nerves of sensation. But Herophilus, who
lived in Egypt in the time of the first Ptolemy, distinguished
nerves as the organs of the will,[10\17] and Rufus, who lived in the
time of Trajan,[11\17] divides the nerves into sensitive and motive,
and derives them all from the brain. But this did not imply that men
had yet distinguished the nerves from the muscles. Even Galen
maintained that every muscle consists of a bundle of nerves and
sinews.[12\17] But the important points, the necessity of the nerve,
and the origination of all this apparatus of motion from the brain,
he insists upon with great clearness and force. Thus he proved the
necessity experimentally, by cutting through some of the bundles of
nerves,[13\17] and thus preventing the corresponding motions. And it
is, he says,[14\17] allowed by all, both physicians and
philosophers, that where the origin of the nerve is, there the seat
of the soul (ἡγημονικὸν τῆς ψυχῆς) must be: now this, he adds, is in
the brain, and not in the heart.

[Note 10\17: Ib. i. 534.]

[Note 11\17: Ib. ii. 67.]

[Note 12\17: Ibid. ii. 152. Galen, _De Motu Musc._, p. 553.]

[Note 13\17: Ib. 157.]

[Note 14\17: _De Hippocr. et Plat. Dog._ viii. 1.]

Thus the general construction and arrangement of the organization by
which voluntary motion is effected, was well made out at the time of
Galen, and is found distinctly delivered in his works. We cannot,
perhaps, justly ascribe any large portion of the general discovery
to him: indeed, the conception of the mechanism of the skeleton and
muscles was probably so gradually unfolded in the minds of
anatomical students, that it would be difficult, even if we knew the
labors of each person, to select one, as peculiarly the author of
the discovery. But it is clear that all those who did materially
contribute to the establishment of this doctrine, must have
possessed the qualifications which we find in Galen for such a task;
namely, clear mechanical views of what the {442} tensions of
collections of strings could do, and an exact practical acquaintance
with the muscular cordage which exists in the animal frame;--in
short, in this as in other instances of real advance in science,
there must have been clear ideas and real facts, unity of thought
and extent of observation, brought into contact.


_Sect._ 2.--_Recognition of Final Causes in Physiology. Galen._

THERE is one idea which the researches of the physiologist and the
anatomist so constantly force upon him, that he cannot help assuming
it as one of the guides of his speculations; I mean, the idea of a
_purpose_, or, as it is called in Aristotelian phrase, a _final
cause_, in the arrangements of the animal frame. It is impossible to
doubt that the motive nerves run along the limbs, _in order that_
they may convey to the muscles the impulses of the will; and that
the muscles are attached to the bones, _in order that_ they may move
and support them. This conviction prevails so steadily among
anatomists, that even when the use of any part is altogether
unknown, it is still taken for granted that it has some use. The
developement of this conviction,--of a purpose in the parts of
animals,--of a function to which each portion of the organization is
subservient,--contributed greatly to the progress of physiology; for
it constantly urged men forwards in their researches respecting each
organ, till some definite view of its purpose was obtained. The
assumption of hypothetical final causes in Physics may have been, as
Bacon asserts it to have been, prejudicial to science; but the
assumption of unknown final causes in Physiology, has given rise to
the science. The two branches of speculation, Physics and
Physiology, were equally led, by every new phenomenon, to ask their
question, "Why?" But, in the former case, "why" meant "through what
cause?" in the latter, "for what end?" And though it may be possible
to introduce into physiology the doctrine of efficient causes, such
a step can never obliterate the obligations which the science owes
to the pervading conception of a purpose contained in all
organization.

This conception makes its appearance very early. Indeed, without any
special study of our structure, the thought, that we are fearfully and
wonderfully made, forces itself upon men, with a mysterious
impressiveness, as a suggestion of our Maker. In this bearing, the
thought is developed to a considerable extent in the well-known
passage in Xenophon's _Conversations of Socrates_. Nor did it ever
lose its hold on sober-minded and instructed men. The Epicureans,
indeed, {443} held that the eye was not made for seeing, nor the ear
for hearing; and Asclepiades, whom we have already mentioned as an
impudent pretender, adopted this wild dogma.[15\17] Such assertions
required no labor. "It is easy," says Galen,[16\17] "for people like
Asclepiades, when they come to any difficulty, to say that Nature has
worked to no purpose." The great anatomist himself pursues his subject
in a very different temper. In a well-known passage, he breaks out
into an enthusiastic scorn of the folly of the atheistical
notions.[17\17] "Try," he says, "if you can imagine a shoe made with
half the skill which appears in the skin of the foot." Some one had
spoken of a structure of the human body which he would have preferred
to that which it now has. "See," Galen exclaims, after pointing out
the absurdity of the imaginary scheme, "see what brutishness there is
in this wish. But if I were to spend more words on such cattle,
reasonable men might blame me for desecrating my work, which I regard
as a religious hymn in honor of the Creator."

[Note 15\17: Sprengel, ii. 15.]

[Note 16\17: _De Usu Part._ v. 5, (on the kidneys.)]

[Note 17\17: _De Usu Part._ iii. 10.]

Galen was from the first highly esteemed as an anatomist. He was
originally of Pergamus; and after receiving the instructions of many
medical and philosophical professors, and especially of those of
Alexandria, which was then the metropolis of the learned and
scientific world, he came to Rome, where his reputation was soon so
great as to excite the envy and hatred of the Roman physicians. The
emperors Marcus Aurelius and Lucius Verus would have retained him
near them; but he preferred pursuing his travels, directed
principally by curiosity. When he died, he left behind him numerous
works, all of them of great value for the light they throw on the
history of anatomy and medicine; and these were for a long period
the storehouse of all the most important anatomical knowledge which
the world possessed. In the time of intellectual barrenness and
servility, among the Arabians and the Europeans of the dark ages,
the writings of Galen had almost unquestioned authority;[18\17] and
it was only by an uncommon effort of independent thinking that
Abdollatif ventured to assert, that even Galen's assertions must
give way to the evidence of the senses. In more modern times, when
Vesalius, in the sixteenth century, accused Galen of mistakes, he
drew upon himself the hostility of the whole body of physicians. Yet
the mistakes were such as might have {444} been pointed out and
confessed[19\17] without acrimony, if, in times of revolution,
mildness and moderation were possible; but an impatience of the
superstition of tradition on the part of the innovators, and an
alarm of the subversion of all recognized truths on the part of the
established teachers, inflame and pervert all such discussions.
Vesalius's main charge against Galen is, that his dissections were
performed upon animals, and not upon the human body. Galen himself
speaks of the dissection of apes as a very familiar employment, and
states that he killed them by drowning. The natural difficulties
which, in various ages, have prevented the unlimited prosecution of
human dissection, operated strongly among the ancients, and it would
have been difficult, under such circumstances, to proceed more
judiciously than Galen did.

[Note 18\17: Sprengel, ii. 359.]

[Note 19\17: Cuv. _Leçons sur l'Hist. des Sc. Nat._ p. 25.]

I shall now proceed to the history of the discovery of another and
less obvious function, the circulation of the blood, which belongs
to modern times.




CHAPTER II.

DISCOVERY OF THE CIRCULATION OF THE BLOOD.


_Sect._ 1.--_Prelude to the Discovery._

THE blood-vessels, the veins and arteries, are as evident and
peculiar in their appearance as the muscles; but their function is
by no means so obvious. Hippocrates[20\17] did not discriminate
Veins and Arteries; both are called by the same name (φλέβες) and
the word from which artery comes (ἀρτηρίη) means, in his works, the
windpipe. Aristotle, scanty as was his knowledge of the vessels of
the body, has yet the merit of having traced the origin of all the
veins to the heart. He expressly contradicts those of his
predecessors who had derived the veins from the head;[21\17] and
refers to dissection for the proof. If the book _On the Breath_ be
genuine (which is doubted), Aristotle was aware of the distinction
between veins and arteries. "Every artery," {445} it is there
asserted, "is accompanied by a vein; the former are filled only with
breath or air."[22\17] But whether or no this passage be
Aristotle's, he held opinions equally erroneous; as, that the
windpipe conveys air into the heart.[23\17] Galen[24\17] was far
from having views respecting the blood-vessels, as sound as those
which he entertained concerning the muscles. He held the liver to be
the origin of the veins, and the heart of the arteries. He was,
however, acquainted with their junctions, or _anastomoses_. But we
find no material advance in the knowledge of this subject, till we
overleap the blank of the middle ages, and reach the dawn of modern
science.

[Note 20\17: Sprengel, i. 383.]

[Note 21\17: _Hist. Animal._ iii. 3.]

[Note 22\17: _De Spiritu_, v. 1078.]

[Note 23\17: Spr. i. 501.]

[Note 24\17: Ib. ii. 152.]

The father of modern anatomy is held to be Mondino,[25\17] who
dissected and taught at Bologna in 1315. Some writers have traced in
him the rudiments of the doctrine of the circulation of the blood;
for he says that the heart transmits blood to the lungs. But it is
allowed, that he afterwards destroys the merit of his remark, by
repeating the old assertion that the left ventricle ought to contain
spirit or air, which it generates from the blood.

[Note 25\17: _Encyc. Brit._ 692. Anatomy.]

Anatomy was cultivated with great diligence and talent in Italy by
Achillini, Carpa, and Messa, and in France by Sylvius and Stephanus
(Dubois and Etienne). Yet still these empty assumptions respecting
the heart and blood-vessels kept their ground. Vesalius, a native of
Brussels, has been termed the founder of human anatomy, and his
great work _De Humani Corporis Fabricâ_ is, even yet, a splendid
monument of art, as well as science. It is said that his figures
were designed by Titian; and if this be not exactly true, says
Cuvier,[26\17] they must, at least, be from the pencil of one of the
most distinguished pupils of the great painter; for to this day,
though we have more finished drawings, we have no designs that are
more artist-like. Fallopius, who succeeded Vesalius at Padua, made
some additions to the researches of his predecessor; but in his
treatise _De Principio Venarum_, it is clearly seen[27\17] that the
circulation of the blood was unknown to him. Eustachius also, whom
Cuvier groups with Vesalius and Fallopius, as the three great
founders of modern anatomy, wrote a treatise on the vein
_azygos_[28\17] which is a little treatise on comparative anatomy;
but the discovery of the functions of the veins came from a
different quarter. {446}

[Note 26\17: _Leçons sur l'Hist. des Sc. Nat._ p. 21.]

[Note 27\17: Cuv. _Sc. Nat._ p. 32.]

[Note 28\17: Ib. p. 34.]

The unfortunate Servetus, who was burnt at Geneva as a heretic in
1553, is the first person who speaks distinctly of the small
circulation, or that which carries the blood from the heart to the
lungs, and back again to the heart. His work entitled _Christianismi
Restitutio_ was also burnt; and only two copies are known to have
escaped the flames. It is in this work that he asserts the doctrine
in question, as a collateral argument or illustration of his
subject. "The communication between the right and left ventricle of
the heart, is made," he says, "not as is commonly believed, through
the partition of the heart, but by a remarkable artifice (_magno
artificio_) the blood is carried from the right ventricle by a long
circuit through the lungs; is elaborated by the lungs, made yellow,
and transfused from the _vena arteriosa_ into the _arteria venosa_."
This truth is, however, mixed with various of the traditional
fancies concerning the "_vital spirit_, which has its origin in the
left ventricle." It may be doubted, also, how far Servetus formed
his opinion upon conjecture, and on a hypothetical view of the
formation of this vital spirit. And we may, perhaps, more justly
ascribe the real establishment of the pulmonary circulation as an
inductive truth, to Realdus Columbus, a pupil and successor of
Vesalius at Padua, who published a work _De Re Anatomicâ_ in 1559,
in which he claims this discovery as his own.[29\17]

[Note 29\17: _Encyc. Brit._]

Andrew Cæsalpinus, who has already come under our notice as one of
the fathers of modern inductive science, both by his metaphysical
and his physical speculations, described the pulmonary circulation
still more completely in his _Quæstiones Peripateticæ_, and even
seemed to be on the eve of discovering the great circulation; for he
remarked the swelling of veins below ligatures, and inferred from it
a refluent motion of blood in these vessels.[30\17] But another
discovery of structure was needed, to prepare the way for this
discovery of function; and this was made by Fabricius of
Acquapendente, who succeeded in the grand list of great professors
at Padua, and taught there for fifty years.[31\17] Sylvius had
discovered the existence of the valves of the veins; but Fabricius
remarked that they are all turned towards the heart. Combining this
disposition with that of the valves of the heart, and with the
absence of valves in the arteries, he might have come to the
conclusion[32\17] that the blood moves in a different direction in
the arteries and in the veins, and might thus have discovered the
circulation: but this glory was reserved for William Harvey: so true
{447} is it, observes Cuvier, that we are often on the brink of a
discovery without suspecting that we are so;--so true is it, we may
add, that a certain succession of time and of persons is generally
necessary to familiarize men with one thought, before they can
advance to that which is the next in order.

[Note 30\17: Ib.]

[Note 31\17: Cuv. p. 44.]

[Note 32\17: p. 45.]


_Sect._ 2.--_The Discovery of the Circulation made by Harvey._

WILLIAM HARVEY was born in 1578, at Folkestone in Kent.[33\17] He
first studied at Cambridge: he afterwards went to Padua, where the
celebrity of Fabricius of Acquapendente attracted from all parts
those who wished to be instructed in anatomy and physiology. In this
city, excited by the discovery of the valves of the veins, which his
master had recently made, and reflecting on the direction of the
valves which are at the entrance of the veins into the heart, and at
the exit of the arteries from it, he conceived the idea of making
experiments, in order to determine what is the course of the blood
in its vessels. He found that when he tied up veins in various
animals, they swelled below the ligature, or in the part furthest
from the heart; while arteries, with a like ligature, swelled on the
side next the heart. Combining these facts with the direction of the
valves, he came to the conclusion that the blood is impelled, by the
left side of the heart, in the arteries to the extremities, and
thence returns by the veins into the right side of the heart. He
showed, too, how this was confirmed by the phenomena of the pulse,
and by the results of opening the vessels. He proved, also, that the
circulation of the lungs is a continuation of the larger
circulation; and thus the whole doctrine of the double circulation
was established.

[Note 33\17: Cuv. p. 51.]

Harvey's experiments had been made in 1616 and 1618; it is commonly
said that he first promulgated his opinion in 1619; but the
manuscript of the lectures, delivered by him as lecturer to the
College of Physicians, is extant in the British Museum, and,
containing the propositions on which the doctrine is founded, refers
them to April, 1616. It was not till 1628 that he published, at
Frankfort, his _Exercitatio Anatomica de Motu Cordis et Sanguinis_;
but he there observes that he had for above nine years confirmed and
illustrated his opinion in his lectures, by arguments grounded upon
ocular demonstrations. {448}


_Sect._ 3.--_Reception of the Discovery._

WITHOUT dwelling long upon the circumstances of the general reception
of this doctrine, we may observe that it was, for the most part,
readily accepted by his countrymen, but that abroad it had to
encounter considerable opposition. Although, as we have seen, his
predecessors had approached so near to the discovery, men's minds were
by no means as yet prepared to receive it. Several physicians denied
the truth of the opinion, among whom the most eminent was Riolan,
professor at the Collège de France. Other writers, as usually happens
in the case of great discoveries, asserted that the doctrine was
ancient, and even that it was known to Hippocrates. Harvey defended
his opinion with spirit and temper; yet he appears to have retained a
lively recollection of the disagreeable nature of the struggles in
which he was thus involved. At a later period of his life, Ent,[34\17]
one of his admirers, who visited him, and urged him to publish the
researches on generation, on which he had long been engaged, gives
this account of the manner in which he received the proposal: "And
would you then advise me, (smilingly replies the doctor,) to quit the
tranquillity of this haven, wherein I now calmly spend my days, and
again commit myself to the unfaithful ocean? You are not ignorant how
great troubles my lucubrations, formerly published, have raised.
Better it is, certainly, at some time, to endeavor to grow wise at
home in private, than by the hasty divulgation of such things to the
knowledge whereof you have attained with vast labor, to stir up
tempests that may deprive you of your leisure and quiet for the
future."

[Note 34\17: Epist. Dedic. to _Anatom. Exercit._]

His merits were, however, soon generally recognized. He was[35\17]
made physician to James the First, and afterwards to Charles the
First, and attended that unfortunate monarch in the civil war. He
had the permission of the parliament to accompany the king on his
leaving London; but this did not protect him from having his house
plundered in his absence, not only of its furniture, but, which he
felt more, of the records of his experiments. In 1652, his brethren
of the College of Physicians placed a marble bust of him in their
hall, with an inscription recording his discoveries; and two years
later, he was nominated to the office of President of the College,
which however he {449} declined in consequence of his age and
infirmities. His doctrine soon acquired popular currency; it was,
for instance, taken by Descartes[36\17] as the basis of his
physiology in his work _On Man_; and Harvey had the pleasure, which
is often denied to discoverers, of seeing his discovery generally
adopted during his lifetime.

[Note 35\17: _Biog. Brit._]

[Note 36\17: Cuv. 53.]


_Sect._ 4.--_Bearing of the Discovery on the Progress of Physiology._

IN considering the intellectual processes by which Harvey's
discoveries were made, it is impossible not to notice, that the
recognition of a creative purpose, which, as we have said, appears
in all sound physiological reasonings, prevails eminently here. "I
remember," says Boyle, "that when I asked our famous Harvey what
were the things that induced him to think of a circulation of the
blood, he answered me, that when he took notice that the valves in
the veins of so many parts of the body were so placed, that they
gave a free passage to the blood towards the heart, but opposed the
passage of the venal blood the contrary way; he was incited to
imagine that so provident a cause as Nature had not placed so many
valves without design; and no design seemed more probable than that
the blood should be sent through the arteries, and return through
the veins, whose valves did not oppose its course that way."

We may notice further, that this discovery implied the usual
conditions, distinct general notions, careful observation of many
facts, and the mental act of bringing together these elements of
truth. Harvey must have possessed clear views of the motions and
pressures of a fluid circulating in ramifying tubes, to enable him
to see how the position of valves, the pulsation of the heart, the
effects of ligatures, of bleeding, and of other circumstances, ought
to manifest themselves in order to confirm his view. That he
referred to a multiplied and varied experience for the evidence that
it was so confirmed, we have already said. Like all the best
philosophers of his time, he insists rigidly upon the necessity of
such experience. "In every science," he says,[37\17] "be it what it
will, a diligent observation is requisite, and sense itself must be
frequently consulted. We must not rely upon other men's experience,
but our own, without which no man is a proper disciple of any part
of natural knowledge." And by publishing his experiments, he trusts,
he adds, that he has enabled his reader "to be an equitable {450}
umpire between Aristotle and Galen;" or rather, he might have said,
to see how, in the promotion of science, sense and reason,
observation and invention, have a mutual need of each other.

[Note 37\17: _Generation of Animals_, Pref.]

We may observe further, that though Harvey's glory, in the case now
before us, rested upon his having proved the reality of certain
mechanical movements and actions in the blood, this discovery, and
all other physiological truths, necessarily involved the assumption
of some peculiar agency belonging to living things, different both
from mechanical agency, and from chemical; and in short, something
_vital_, and not physical merely. For when it was seen that the
pulsation of the heart, its _systole_ and _diastole_, caused the
circulation of the blood, it might still be asked, what force caused
this constantly-recurring contraction and expansion. And again,
circulation is closely connected with respiration; the blood is, by
the circulation, carried to the lungs, and is there, according to
the expression of Columbus and Harvey, mixed with air. But by what
mechanism does this _mixture_ take place, and what is the real
nature of it? And when succeeding researches had enabled
physiologists to give an answer to this question, as far as chemical
relations go, and to say, that the change consists in the
abstraction of the carbon from the blood by means of the oxygen of
the atmosphere; they were still only led to ask further, how this
chemical change was effected, and how such a change of the blood
fitted it for its uses. Every function of which we explain the
course, the mechanism, or the chemistry, is connected with other
functions,--is subservient to them, and they to it; and all together
are parts of the general vital system of the animal, ministering to
its life, but deriving their activity from the life. Life is not a
collection of forces, or polarities, or affinities, such as any of
the physical or chemical sciences contemplate; it has powers of its
own, which often supersede those subordinate relations; and in the
cases where men have traced such agents in the animal frame, they
have always seen, and usually acknowledged, that these agents were
ministerial to some higher agency, more difficult to trace than
these, but more truly the cause of the phenomena.

The discovery of the mechanical and chemical conditions of the vital
functions, as a step in physiology, may be compared to the discovery
of the laws of phenomena in the heavens by Kepler and his
predecessors, while the discovery of the force by which they were
produced was still reserved in mystery for Newton to bring to light.
The subordinate relation of the facts, their **dependence on space
and time, their reduction to order and cycle, had been fully
performed; but the {451} reference of them to distinct ideas of
causation, their interpretation as the results of mechanical force,
was omitted or attempted in vain. The very notion of such Force, and
of the manner in which motions were determined by it, was in the
highest degree vague and vacillating; and a century was requisite,
as we have seen, to give to the notion that clearness and fixity
which made the Mechanics of the Heavens a possible science. In like
manner, the notion of Life, and of Vital Forces, is still too
obscure to be steadily held. We cannot connect it distinctly with
severe inductions from facts. We can trace the motions of the animal
fluids as Kepler traced the motions of the planets; but when we seek
to render a reason for these motions, like him, we recur to terms of
a wide and profound, but mysterious import; to Virtues, Influences,
undefined Powers. Yet we are not on this account to despair. The
very instance to which I am referring shows us how rich is the
promise of the future. Why, says Cuvier,[38\17] may not Natural
History one day have its Newton? The idea of the vital forces may
gradually become so clear and definite as to be available in
science; and future generations may include, in their physiology,
propositions elevated as far above the circulation of the blood, as
the doctrine of universal gravitation goes beyond the explanation of
the heavenly motions by epicycles.

[Note 38\17: _Ossem. Foss._ Introd.]

If, by what has been said, I have exemplified sufficiently the
nature of those steps in physiology, which, like the discovery of
the Circulation, give an explanation of the process of some of the
animal functions, it is not necessary for me to dwell longer on the
subject; for to write a history, or even a sketch of the history of
Physiology, would suit neither my powers nor my purpose. Some
further analysis of the general views which have been promulgated by
the most eminent physiologists, may perhaps be attempted in treating
of the Philosophy of Inductive Science; but the estimation of the
value of recent speculations and investigations must be left to
those who have made this vast subject the study of their lives. A
few brief notices may, however, be here introduced. {452}




CHAPTER III.

DISCOVERY OF THE MOTION OF THE CHYLE, AND CONSEQUENT SPECULATIONS.


_Sect._ 1.--_The Discovery of the Motion of the Chyle._

IT may have been observed in the previous course of this History of
the Sciences, that the discoveries in each science have a peculiar
physiognomy: something of a common type may be traced in the
progress of each of the theories belonging to the same department of
knowledge. We may notice something of this common form in the
various branches of physiological speculation. In most, or all of
them, we have, as we have noticed the case to be with respect to the
circulation of the blood, clear and certain discoveries of
mechanical and chemical processes, succeeded by speculations far
more obscure, doubtful, and vague, respecting the relation of these
changes to the laws of life. This feature in the history of
physiology may be further instanced, (it shall be done very
briefly), in one or two other cases. And we may observe, that the
lesson which we are to collect from this narrative, is by no means
that we are to confine ourselves to the positive discovery, and
reject all the less clear and certain speculations. To do this,
would be to lose most of the chances of ulterior progress; for
though it may be, that our conceptions of the nature of organic life
are not yet sufficiently precise and steady to become the guides to
positive inductive truths, still the only way in which these
peculiar physiological ideas can be made more distinct and precise,
and thus brought more nearly into a scientific form, is by this
struggle with our ignorance or imperfect knowledge. This is the
lesson we have learnt from the history of physical astronomy and
other sciences. We must strive to refer facts which are known and
understood, to higher principles, of which we cannot doubt the
existence, and of which, in some degree, we can see the place;
however dim and shadowy may be the glimpses we have hitherto been
able to obtain of their forms. We may often fail in such attempts,
but without the attempt we can never succeed. {453}

That the food is received into the stomach, there undergoes a change
of its consistence, and is then propelled along the intestines, are
obvious facts in the animal economy. But a discovery made in the
course of the seventeenth century brought into clearer light the
sequel of this series of processes, and its connexion with other
functions. In the year 1622, Asellius or Aselli[39\17] discovered
certain minute vessels, termed _lacteals_, which absorb a white
liquid (the _chyle_) from the bowels, and pour it into the blood.
These vessels had, in fact, been discovered by Eristratus, in the
ancient world,[40\17] in the time of Ptolemy; but Aselli was the
first modern who attended to them. He described them in a treatise
entitled _De Venis Lacteis, cum figuris elegantissimis_, printed at
Milan in 1627, the year after the death of the author. The work is
remarkable as the first which exhibits _colored_ anatomical figures;
the arteries and veins are represented in red, the lacteals in black.

[Note 39\17: Mayo, _Physiology_, p. 156.]

[Note 40\17: Cuv. _Hist. Sc._ p. 50.]

Eustachius,[41\17] at an earlier period, had described (in the
horse) the thoracic duct by which the chyle is poured into the
subclavian vein, on the right side of the neck. But this description
did not excite so much notice as to prevent its being forgotten, and
rediscovered in 1550, after the knowledge of the circulation of the
blood had given more importance to such a discovery. Up to this
time,[42\17] it had been supposed that the lacteals carried the
chyle to the liver, and that the blood was manufactured there. This
opinion had prevailed in all the works of the ancients and moderns;
its falsity was discovered by Pecquet, a French physician, and
published in 1651, in his _New Anatomical Experiments_; in which are
discovered a receptacle of the chyle, unknown till then, and the
vessel which conveys it to the subclavian vein. Pecquet himself and
other anatomists, soon connected this discovery with the doctrine,
then recently promulgated, of the circulation of the blood. In 1665,
these vessels, and the _lymphatics_ which are connected with them,
were further illustrated by Ruysch in his exhibition of their
valves. (_Dilucidatio valvularum in vasis lymphaticis et lacteis_.)

[Note 41\17: Cuv. _Hist._ p. 34.]

[Note 42\17: Ib. p. 365.]


_Sect._ 2.--_The Consequent Speculations. Hypotheses of Digestion._

THUS it was shown that aliments taken into the stomach are, by its
action, made to produce _chyme_; from the chyme, gradually changed
{454} in its progress through the intestines, _chyle_ is absorbed by
the lacteals; and this, poured into the blood by the thoracic duct,
repairs the waste and nourishes the growth of the animal. But by
what powers is the food made to undergo these transformations? Can
we explain them on mechanical or on chemical principles? Here we
come to a part of physiology less certain than the discovery of
vessels, or of the motion of fluids. We have a number of opinions on
this subject, but no universally acknowledged truth. We have a
collection of _Hypotheses of Digestion_ and _Nutrition_.

I shall confine myself to the former class; and without dwelling
long upon these, I shall mention some of them. The philosophers of
the Academy _del Cimento_, and several others, having experimented
on the stomach of gallinaceous birds, and observed the astonishing
force with which it breaks and grinds substances, were led to
consider the digestion which takes place in the stomach as a kind of
_trituration_.[43\17] Other writers thought it was more properly
described as _fermentation_; others again spoke of it as a
_putrefaction_. Varignon gave a merely physical account of the first
part of the process, maintaining that the division of the aliments
was the effect of the disengagement of the air introduced into the
stomach, and dilated by the heat of the body. The opinion that
digestion is a _solution_ of the food by the gastric juice has been
more extensively entertained.

[Note 43\17: Bourdon, _Physiol. Comp._ p. 514.]

Spallanzani and others made many experiments on this subject. Yet it
is denied by the best physiologists, that the changes of digestion
can be adequately represented as chemical changes only. The nerves
of the stomach (the _pneumo-gastric_) are said to be essential to
digestion. Dr. Wilson Philip has asserted that the influence of
these nerves, when they are destroyed, may be replaced by a galvanic
current.[44\17] This might give rise to a supposition that digestion
depends on galvanism. Yet we cannot doubt that all these
hypotheses,--mechanical, physical, chemical, galvanic--are
altogether insufficient. "The stomach must have," as Dr. Prout
says,[45\17] "the power of {455} organizing and vitalizing the
different elementary substances. It is impossible to imagine that
this organizing agency of the stomach can be chemical. This agency
is _vital_, and its nature completely unknown."

[Note 44\17: Müller (_Manual of Physiology_, B. iii. Sect. 1, Chap.
iii.) speaks of Dr. Wilson Philip's assertion that the nerves of the
stomach being cut, and a galvanic current kept up in them, digestion
is still accomplished. He states that he and other physiologists
have repeated such experiments on an extensive scale, and have found
no effect of this kind.]

[Note 45\17:  _Bridgewater Tr._ p. 493.]




CHAPTER IV.

EXAMINATION OF THE PROCESS OF REPRODUCTION IN ANIMALS AND PLANTS,
AND CONSEQUENT SPECULATIONS.


_Sect._ 1.--_The Examination of the Process of Reproduction in
Animals._

IT would not, perhaps, be necessary to give any more examples of
what has hitherto been the general process of investigations on each
branch of physiology; or to illustrate further the combination which
such researches present, of certain with uncertain knowledge;--of
solid discoveries of organs and processes, succeeded by indefinite
and doubtful speculation concerning vital forces. But the
reproduction of organized beings is not only a subject of so much
interest as to require some notice, but also offers to us laws and
principles which include both the vegetable and the animal kingdom;
and which, therefore, are requisite to render intelligible the most
general views to which we can attain, respecting the world of
organization.

The facts and laws of reproduction were first studied in detail in
animals. The subject appears to have attracted the attention of some
of the philosophers of antiquity in an extraordinary degree: and
indeed we may easily imagine that they hoped, by following this
path, if any, to solve the mystery of creation. Aristotle appears to
have pursued it with peculiar complacency; and his great work _On
animals_ contains[46\17] an extraordinary collection of curious
observations relative to this subject. He had learnt the modes of
reproduction of most of the animals with which he was acquainted;
and his work is still, as a writer of our own times has said,[47\17]
"original after so many copies, and young after two thousand years."
His observations referred principally to the external circumstances
of generation: the anatomical examination was {456} left to his
successors. Without dwelling on the intermediate labors, we come to
modern times, and find that this examination owes its greatest
advance to those who had the greatest share in the discovery of the
circulation of the blood;--Fabricius of Acquapendente, and Harvey.
The former[48\17] published a valuable work on the Egg and the
Chick. In this are given, for the first time, figures representing
the developement of the chick, from its almost imperceptible
beginning, to the moment when it breaks the shell. Harvey pursued
the researches of his teacher. Charles[49\17] the First had supplied
him with the means of making the experiments which his purpose
required, by sacrificing a great number of the deer in Windsor Park
in the state of gestation: but his principal researches were those
respecting the egg, in which he followed out the views of Fabricius.
In the troubles which succeeded the death of the unfortunate Charles
the house of Harvey was pillaged; and he lost the whole of the
labors he had bestowed on the generation of insects. His work,
_Exercitationes de Generatione Animalium_, was published at London
in 1651; it is more detailed and perfect than that of Fabricius; but
the author was prevented by the unsettled condition of the country
from getting figures engraved to accompany his descriptions.

[Note 46\17: Bourdon, p. 161.]

[Note 47\17: Ib. p. 101.]

[Note 48\17: Cuv. _Hist. Sc. Nat._ p. 46.]

[Note 49\17: Ib. p. 53.]

Many succeeding anatomists pursued the examination of the series of
changes in generation, and of the organs which are concerned in
them, especially Malpighi, who employed the microscope in this
investigation, and whose work on the Chick was published in 1673. It
is impossible to give here any general view of the result of these
laborious series of researches: but we may observe, that they led to
an extremely minute and exact survey of all the parts of the fœtus,
its envelopes and appendages, and, of course, to a designation of
these by appropriate names. These names afterwards served to mark
the attempts which were made to carry the analogy of animal
generation into the vegetable kingdom.

There is one generalization of Harvey which deserves notice.[50\17]
He was led by his researches to the conclusion, that all living
things may be properly said to come from eggs: "Omne vivum ex ovo."
Thus not only do oviparous animals produce by means of eggs, but in
those which are viviparous, the process of generation begins with
the developement of a small vesicle, which comes from the ovary, and
which exists before the embryo: and thus viviparous or
suckling-beasts, {457} notwithstanding their name, are born from
eggs, as well as birds, fishes, and reptiles.[51\17] This principle
also excludes that supposed production of organized beings without
parents (of worms in corrupted matter, for instance,) which was
formerly called _spontaneous generation_; and the best physiologists
of modern times agree in denying the reality of such a mode of
generation.[52\17]

[Note 50\17: Exerc. lxiii.]

[Note 51\17: Bourdon, p. 221.]

[Note 52\17: Ib. p. 49.]


_Sect._ 2.--_The Examination of the Process of Reproduction in
Vegetables._

THE extension of the analogies of animal generation to the vegetable
world was far from obvious. This extension was however made;--with
reference to the embryo plant, principally by the microscopic
observers, Nehemiah Grew, Marcello Malpighi, and Antony
Leeuwenhoek;--with respect to the existence of the sexes, by Linnæus
and his predecessors.

The microscopic labors of Grew and Malpighi were patronized by the
Royal Society of London in its earliest youth. Grew's book, _The
Anatomy of Plants_, was ordered to be printed in 1670. It contains
plates representing extremely well the process of germination in
various seeds, and the author's observations exhibit a very clear
conception of the relation and analogies of different portions of
the seed. On the day on which the copy of this work was laid before
the Society, a communication from Malpighi of Bologna, _Anatomes
Plantarum Idea_, stated his researches, and promised figures which
should illustrate them. Both authors afterwards went on with a long
train of valuable observations, which they published at various
times, and which contain much that has since become a permanent
portion of the science.

Both Grew and Malpighi were, as we have remarked, led to apply to
vegetable generation many terms which imply an analogy with the
generation of animals. Thus, Grew terms the innermost coat of the
seed, the _secundine_; speaks of the _navel-fibres_, &c. Many more
such terms have been added by other writers. And, as has been
observed by a modern physiologist,[53\17] the resemblance is
striking. Both in the vegetable seed and in the fertilized animal
egg, we have an _embryo_, _chalazæ_, a _placenta_, an _umbilical
cord_, a _cicatricula_, an _amnios_, _membranes_, _nourishing
vessels_. The _cotyledons_ of the seed are the equivalent of the
_vitellus_ of birds, or of the _umbilical vesicle_ of
**suckling-beasts: {458} the _albumen_ or _perisperm_ of the grain is
analogous to the _white of the egg_ of birds, or the _allantoid_ of
viviparous animals.

[Note 53\17: Ib. p. 384.]

_Sexes of Plants._--The attribution of sexes to plants, is a notion
which was very early adopted; but only gradually unfolded into
distinctness and generality.[54\17] The ancients were acquainted
with the fecundation of vegetables. Empedocles, Aristotle,
Theophrastus, Pliny, and some of the poets, make mention of it; but
their notions were very incomplete, and the conception was again
lost in the general shipwreck of human knowledge. A Latin poem,
composed in the fifteenth century by Jovianus Pontanus, the
preceptor of Alphonso, King of Naples, is the first modern work in
which mention is made of the sex of plants. Pontanus sings the loves
of two date-palms, which grew at the distance of fifteen leagues
from each other: the male at Brundusium, the female at Otranto. The
distance did not prevent the female from becoming fruitful, as soon
as the palms had raised their heads above the surrounding trees, so
that nothing intervened directly between them, or, to speak with the
poet, so that they were able to see each other.

[Note 54\17: Mirbel, _El._ ii. 538.]

Zaluzian, a botanist who lived at the end of the fifteenth century,
says that the greater part of the species of plants are
_androgynes_, that is, have the properties of the male and of the
female united in the same plant; but that some species have the two
sexes in separate individuals; and he adduces a passage of Pliny
relative to the fecundation of the date-palm. John Bauhin, in the
middle of the seventeenth century, cites the expressions of
Zaluzian; and forty years later, a professor of Tübingen, Rudolph
Jacob Camerarius, pointed out clearly the organs of generation, and
proved by experiments on the mulberry, on maize, and on the plant
called Mercury (_mercurialis_), that when by any means the action of
the stamina upon the pistils is intercepted, the seeds are barren.
Camerarius, therefore, a philosopher in other respects of little
note, has the honor assigned him of being the author of the
discovery of the sexes of plants in modern times.[55\17]

[Note 55\17: Mirbel, ii. 539.]

The merit of this discovery will, perhaps, appear more considerable
when it is recollected that it was rejected at first by very eminent
botanists. Thus Tournefort, misled by insufficient experiments,
maintained that the stamina are excretory organs; and Reaumur, at
the beginning of the eighteenth century, inclined to the same
doctrine. {459} Upon this, Geoffroy, an apothecary at Paris,
scrutinized afresh the sexual organs; he examined the various forms
of the pollen, already observed by Grew and Malpighi; he pointed out
the excretory canal, which descends through the style, and the
_micropyle_, or minute orifice in the coats of the ovule, which is
opposite to the extremity of this canal; though he committed some
mistakes with regard to the nature of the pollen. Soon afterwards,
Sebastian Vaillant, the pupil of Tournefort, but the corrector of
his error on this subject, explained in his public lectures the
phenomenon of the fecundation of plants, described the explosion of
the anthers, and showed that the _florets_ of composite flowers,
though formed on the type of an _androgynous_ flower, are sometimes
male, sometimes female, and sometimes neuter.

But though the sexes of plants had thus been noticed, the subject
drew far more attention when Linnæus made the sexual parts the basis
of his classification. Camerarius and Burkard had already
entertained such a thought, but it was Linnæus who carried into
effect, and thus made the notion of the sexes of vegetables almost
as familiar to us as that of the sexes of animals.


_Sect._ 3.--_The Consequent Speculations.--Hypotheses of Generation._

THE views of the processes of generation, and of their analogies
throughout the whole of the organic world, which were thus
established and diffused, form an important and substantial part of
our physiological knowledge. That a number of curious but doubtful
hypotheses should be put forward, for the purpose of giving further
significance and connexion to these discoveries, was to be expected.
We must content ourselves with speaking of these very briefly. We
have such hypotheses in the earliest antiquity of Greece; for as we
have already said, the speculations of cosmogony were the source of
the Greek philosophy; and the laws of generation appeared to offer
the best promise of knowledge respecting the mystery of creation.
Hippocrates explained the production of a new animal by the _mixture
of seed_ of the parents; and the offspring was male or female as the
seminal principle of the father or of the mother was the more
powerful. According to Aristotle, the mother supplied the _matter_,
and the father the _form_. Harvey's doctrine was, that the ovary of
the female is fertilized by a _seminal contagion_ produced by the
seed of the male. But an opinion which obtained far more general
reception was, that {460} the _embryo pre-existed_ in the mother,
before any union of the sexes.[56\17] It is easy to see that this
doctrine is accompanied with great difficulties;[57\17] for if the
mother, at the beginning of life, contain in her the embryos of all
her future children; these embryos again must contain the children
which they are capable of producing; and so on indefinitely; and
thus each female of each species contains in herself the germs of
infinite future generations. The perplexity which is involved in
this notion of an endless series of creatures, thus encased one
within another, has naturally driven inquirers to attempt other
suppositions. The microscopic researches of Leeuwenhoek and others
led them to the belief that there are certain animalcules contained
in the seed of the male, which are the main agents in the work of
reproduction. This system ascribes almost everything to the male, as
the one last mentioned does to the female. Finally, we have the
system of Buffon;--the famous hypothesis of _organic molecules_.
That philosopher asserted that he found, by the aid of the
microscope, all nature full of moving globules, which he conceived
to be, not animals as Leeuwenhoek imagined, but bodies capable of
producing, by their combination, either animals or vegetables, in
short, all organized bodies. These globules he called _organic
molecules_.[58\17] And if we inquire how these organic molecules,
proceeding from all parts of the two parents, unite into a whole, as
perfect as either of the progenitors, Buffon answers, that this is
the effect of the _interior mould_; that is, of a system of internal
laws and tendencies which determine the form of the result as an
external mould determines the shape of the cast.

[Note 56\17: Bourdon, p. 204.]

[Note 57\17: Ib. p. 209.]

[Note 58\17: Ib. p. 219.]

An admirer of Buffon, who has well shown the untenable character of
this system, has urged, as a kind of apology for the promulgation of
the hypothesis,[59\17] that at the period when its author wrote, he
could not present his facts with any hope of being attended to, if he
did not connect them by some common tie, some dominant idea which
might gratify the mind; and that, acting under this necessity, he did
well to substitute for the extant theories, already superannuated and
confessedly imperfect, conjectures more original and more probable.
Without dissenting from this view, we may observe, that Buffon's
theory, like those which preceded it, is excusable, and even deserving
of admiration, so far as it groups the facts consistently; because in
doing this, it exhibits the necessity, which the physiological
speculator ought to feel, of aspiring to definite and solid general
principles; and that thus, though {461} the theory may not be
established as true, it may be useful by bringing into view the real
nature and application of such principles.

[Note 59\17: Ib. p. 221.]

It is, therefore, according to our views, unphilosophical to derive
despair, instead of hope, from the imperfect success of Buffon and
his predecessors. Yet this is what is done by the writer to whom we
refer. "For me," says he,[60\17] "I vow that, after having long
meditated on the system of Buffon,--a system so remarkable, so
ingenious, so well matured, so wonderfully connected in all its
parts, at first sight so probable;--I confess that, after this long
study, and the researches which it requires, I have conceived in
consequence, a distrust of myself a skepticism, a disdain of
hypothetical systems, a decided predilection and exclusive taste for
pure and rational observation, in short, a disheartening, which I
had never felt before."

[Note 60\17: Bourdon, p. 274.]

The best remedy of such feelings is to be found in the history of
science. Kepler, when he had been driven to reject the solid
epicycles of the ancients, or a person who had admired Kepler as M.
Bourdon admires Buffon, but who saw that his magnetic virtue was an
untenable fiction, might, in the same manner, have thrown up all
hope of a sound theory of the causes of the celestial motions. But
astronomers were too wise and too fortunate to yield to such
despondency. The predecessors of Newton substituted a solid science
of Mechanics for the vague notions of Kepler; and the time soon came
when Newton himself reduced the motions of the heavens to a Law as
distinctly conceived as the Motions had been before.




CHAPTER V.

EXAMINATION OF THE NERVOUS SYSTEM, AND CONSEQUENT SPECULATIONS.


_Sect._ 1.--_The Examination of the Nervous System._

IT is hardly necessary to illustrate by further examples the manner
in which anatomical observation has produced conjectural and
hypothetical attempts to connect structure and action with some
{462} higher principle, of a more peculiarly physiological kind. But
it may still be instructive to notice a case in which the principle,
which is thus brought into view, is far more completely elevated
above the domain of matter and mechanism than in those we have yet
considered;--a case where we have not only Irritation, but
Sensation;--not only Life, but Consciousness and Will. A part of
science in which suggestions present themselves, brings us, in a
very striking manner, to the passage from the physical to the
hyperphysical sciences.

We have seen already (chap. i.) that Galen and his predecessors had
satisfied themselves that the nerves are the channels of perception; a
doctrine which had been distinctly taught by Herophilus[61\17] in the
Alexandrian school. Herophilus, however, still combined, under the
common name of Nerves, the Tendons; though he distinguished such
Nerves from those which arise from the brain and the spinal marrow,
and which are subservient to the will. In Galen's time this subject
had been prosecuted more into detail. That anatomist has left a
Treatise expressly upon _The Anatomy of the Nerves_; in which he
describes the successive _Pairs_ of Nerves: thus, the First Pair are
the visual nerves: and we see, in the language which Galen uses, the
evidence of the care and interest with which he had himself examined
them. "These nerves," he says, "are not resolved into many fibres,
like all the other nerves, when they reach the organs to which they
belong; but spread out in a different and very remarkable manner,
which it is not easy to describe or to believe, without actually
seeing it." He then gives a description of the retina. In like manner
he describes the Second Pair, which is distributed to the muscles of
the eyes; the Third and Fourth Pairs, which go to the tongue and
palate; and so on to the Seventh Pair. This division into Seven Pairs
was established by Marinus,[62\17] but Vesalius found it to be
incomplete. The examination which is the basis of the anatomical
enumeration of the Nerves at present recognized was that of Willis.
His book, entitled _Cerebri Anatome, cui accessit Nervorum descriptio
et usus_, appeared at London in 1664. He made important additions to
the knowledge of this subject.[63\17] Thus he is the first who
describes in a distinct manner what has been called the _Nervous
Centre_,[64\17] the pyramidal eminences which, according to more
recent anatomists, are the communication of the brain with the spinal
marrow: and of which the _Decussation_, described by Santorini,
affords the explanation of the action of a part {463} of the brain
upon the nerves of the opposite side. Willis proved also that the
_Rete Mirabile_, the remarkable net-work of arteries at the base of
the brain, observed by the ancients in ruminating animals, does not
exist in man. He described the different Pairs of Nerves with more
care than his predecessors; and his mode of numbering them is employed
up to the present time. He calls the Olfactory Nerves the First Pair;
previously to him, these were not reckoned a Pair: and thus the optic
nerves were, as we have seen, called the first. He added the Sixth and
the Ninth Pairs, which the anatomists who preceded him did not reckon.
Willis also examined carefully the different _Ganglions_, or knots
which occur upon the nerves. He traced them wherever they were to be
found, and he gave a general figure of what Cuvier calls the _nervous
skeleton_, very superior to that of Vesalius, which was coarse and
inexact. Willis also made various efforts to show the connexion of the
parts of the brain. In the earlier periods of anatomy, the brain had
been examined by slicing it, so as to obtain a section. Varolius
endeavored to unravel it, and was followed by Willis. Vicq d'Azyr, in
modern times, has carried the method of section to greater perfection
than had before been given it;[65\17] as Vieussens and Gall have done
with respect to the method of Varolius and Willis. Recently Professor
Chaussier[66\17] makes three kinds of Nerves:--the _Encephalic_, which
proceed from the head, and are twelve on each side;--the _Rachidian_,
which proceed from the spinal marrow, and are thirty on each
side;--and _Compound Nerves_, among which is the _Great Sympathetic_
Nerve.

[Note 61\17: Spr. i. 534.]

[Note 62\17: _Dic. Sc. Med._ xxxv. 467.]

[Note 63\17: Cuv. _Sc. Nat._ p. 385.]

[Note 64\17: Ibid.]

[Note 65\17: Cuv. p. 40.]

[Note 66\17: _Dict. Sc. Nat._ xxxv. 467.]

One of the most important steps ever made in our knowledge of the
nerves is, the distinction which Bichat is supposed to have
established, of a _ganglionic system_, and a _cerebral system_. And
we may add, to the discoveries in nervous anatomy, the remarkable
one, made in our own time, that the two offices--of conducting the
motive impressions from the central seat of the will to the muscles,
and of propagating sensations from the surface of the body and the
external organs of sense to the sentient mind--reside in two
distinct portions of the nervous substance:--a discovery which has
been declared[67\17] to be "doubtless the most important accession
to physiological (anatomical) knowledge since the time of Harvey."
This doctrine was first published and taught by Sir Charles Bell:
after an interval of some {464} years, it was more distinctly
delivered in the publications of Mr. John Shaw, Sir C. Bell's pupil.
Soon afterwards it was further confirmed, and some part of the
evidence corrected, by Mr. Mayo, another pupil of Sir C. Bell, and
by M. Majendie.[68\17]

[Note 67\17: Dr. Charles Henry's _Report of Brit. Assoc._ iii.
p. 62.]

[Note 68\17: As authority for the expressions which I have now used
in the text, I will mention Müller's _Manual of Physiology_ (4th
edition, 1844). In Book iii. Section 2, Chap. i., "On the Nerves of
Sensation and Motion," Müller says, "Charles Bell was the first who
had the ingenious thought that the posterior roots of the nerves of
the spine--those which are furnished with a ganglion--govern
sensation only; that the anterior roots are appointed for motion;
and that the primitive fibres of these roots, after being united in
a single nervous cord, are mingled together in order to supply the
wants of the skin and muscles. He developed this idea in a little
work (_An Idea of a new Anatomy of the Brain_, London, 1811), which
was not intended to travel beyond the circle of his friends." Müller
goes on to say, that eleven years later, Majendie prosecuted the
same theory. But Mr. Alexander Shaw, in 1839, published _A Narrative
of the Discoveries of Sir Charles Bell in the Nervous System_, in
which it appears that Sir Charles Bell had further expounded his
views in his lectures to his pupils (p. 89), and that one of these,
Mr. John Shaw, had in various publications, in 1821 and 1822,
further insisted upon the same views; especially in a Memoir _On
Partial Paralysis_ (p. 75). MM. Mayo and Majendie both published
Memoirs in August, 1822; and these and subsequent works confirmed
the doctrine of Bell. Mr. Alexander Shaw states (p. 97), that a
mistake of Sir Charles Bell's, in an experiment which he had made to
prove his doctrine, was discovered through the joint labors of M.
Majendie and Mr. Mayo.]


_Sect._ 2.--_The Consequent Speculations. Hypotheses respecting
Life, Sensation, and Volition._

I SHALL not attempt to explain the details of these anatomical
investigations; and I shall speak very briefly of the speculations
which have been suggested by the obvious subservience of the nerves
to life, sensation, and volition. Some general inferences from their
distribution were sufficiently obvious; as, that the seat of
sensation and volition is in the brain. Galen begins his work, _On
the Anatomy of the Nerves_, thus: "That none of the members of the
animal either exercises voluntary motion, or receives sensation, and
that if the nerve be cut, the part immediately becomes inert and
insensible, is acknowledged by all physicians. But that the origin
of the nerves is partly from the brain, and partly from the spinal
marrow, I proceed to explain." And in his work _On the Doctrines of
Plato and Hippocrates_, he proves at {465} great length[69\17] that
the brain is the origin of sensation and motion, refuting the
opinions of earlier days, as that of Chrysippus,[70\17] who placed
the _hegemonic_ or master-principle of the soul, in the heart. But
though Galen thought that the rational soul resides in the brain, he
was disposed to agree with the poets and philosophers, according to
whom the heart is the seat of courage and anger, and the liver the
seat of love.[71\17] The faculties of the soul were by succeeding
physiologists confined to the brain; but the disposition still
showed itself, to attribute to them distinct localities. Thus
Willis[72\17] places the imagination in the _corpus callosum_, the
memory in the folds of the _hemispheres_, the perception in the
_corpus striatum_. In more recent times, a system founded upon a
similar view has been further developed by Gall and his followers.
The germ of Gall's system may be considered as contained in that of
Willis; for Gall represents the hemispheres as the folds of a great
membrane which is capable of being unwrapped and spread out, and
places the different faculties of man in the different regions of
this membrane. The chasm which intervenes between matter and motion
on the one side, and thought and feeling on the other, is brought
into view by all such systems; but none of the hypotheses which they
involve can effectually bridge it over.

[Note 69\17: Lib. vii.]

[Note 70\17: Lib. iii. c. 1.]

[Note 71\17: Lib. vi. c. 8.]

[Note 72\17: Cuv. _Sc. Nat._ p. 384.]

The same observation may be made respecting the attempts to explain
the manner in which the nerves operate as the instruments of
sensation and volition. Perhaps a real step was made by
Glisson,[73\17] professor of medicine in the University of
Cambridge, who distinguished in the fibres of the muscles of motion
a peculiar property, different from any merely mechanical or
physical action. His work _On the Nature of the Energetic Substance,
or on the Life of Nature and of its Three First Faculties, The
Perceptive, Appetitive, and Motive_, which was published in 1672, is
rather metaphysical than physiological. But the principles which he
establishes in this treatise he applies more specially to physiology
in a treatise _On the Stomach and Intestines_ (Amsterdam, 1677). In
this he ascribes to the fibres of the animal body a peculiar power
which he calls _Irritability_. He divides _irritation_ into natural,
vital, and animal; and he points out, though briefly, the gradual
differences of irritability in different organs. "It is hardly
comprehensible," says Sprengel,[74\17] "how this {466} lucid and
excellent notion of the Cambridge teacher was not accepted with
greater alacrity, and further unfolded by his contemporaries." It
has, however, since been universally adopted.

[Note 73\17: Cuv. _Sc. Nat._ p. 434.]

[Note 74\17: Spr. iv. 47.]

But though the discrimination of muscular irritability as a peculiar
power might be a useful step in physiological research, the
explanations hitherto offered, of the way in which the nerves
operate on this irritability, and discharge their other offices,
present only a series of hypotheses. Glisson[75\17] assumed the
existence of certain vital spirits, which, according to him, are a
mild, sweet fluid, resembling the spirituous part of white of egg,
and residing in the nerves.--This hypothesis, of a very subtle humor
or spirit existing in the nerves, was indeed very early taken
up.[76\17] This nervous spirit had been compared to air by
Erasistratus, Asclepiades, Galen, and others. The chemical
tendencies of the seventeenth century led to its being described as
acid, sulphureous or nitrous. At the end of that century, the
hypothesis of an _ether_ attracted much notice as a means of
accounting for many phenomena; and this ether was identified with
the nervous fluid. Newton himself inclines to this view, in the
remarkable Queries which are annexed to his _Opticks_. After
ascribing many physical effects to his ether, he adds (Query 23),
"Is not vision performed chiefly by the vibrations of this medium,
excited in the bottom of the eye by the rays of light, and
propagated through the solid, pellucid, and uniform capillamenta of
the nerves into the place of sensation?" And (Query 24), "Is not
animal motion performed by the vibrations of this medium, excited in
the brain by the power of the will, and propagated from thence
through the capillamenta of the nerves into the muscles for
contracting and dilating them?" And an opinion approaching this has
been adopted by some of the greatest of modern physiologists; as
Haller, who says,[77\17] that, though it is more easy to find what
this nervous spirit is not than what it is, he conceives that, while
it must be far too fine to be perceived by the sense, it must yet be
more gross than fire, magnetism, or electricity; so that it may be
contained in vessels, and confined by boundaries. And Cuvier speaks
to the same effect:[78\17] "There is a great probability that it is
by an imponderable fluid that the nerve acts on the fibre, and that
this nervous fluid is drawn from the blood, and secreted by the
medullary matter."

[Note 75\17: Spr. iv. 38.]

[Note 76\17: Haller, _Physiol._ iv. 365.]

[Note 77\17: _Physiol._ iv. 381, lib. x. sect. viii. § 15.]

[Note 78\17: _Règne Animal_, Introd. p. 30.]

Without presuming to dissent from such authorities on a point of
{467} anatomical probability, we may venture to observe, that these
hypotheses do not tend at all to elucidate the physiological
principle which is here involved; for this principle cannot be
mechanical, chemical, or physical, and therefore cannot be better
understood by embodying it in a fluid; the difficulty we have in
conceiving what the moving force _is_, is not got rid of by explaining
the machinery by which it is merely _transferred_. In tracing the
phenomena of sensation and volition to their cause, it is clear that
we must call in some peculiar and hyperphysical principle. The
hypothesis of a fluid is not made more satisfactory by attenuating
the fluid; it becomes subtle, spirituous, ethereal, imponderable, to
no purpose; it must cease to be a fluid, before its motions can
become sensation and volition. This, indeed, is acknowledged by most
physiologists; and strongly stated by Cuvier.[79\17] "The impression
of external objects upon the ME, the production of a sensation, of
an image, is a mystery impenetrable for our thoughts." And in
several places, by the use of this peculiar phrase, "_the me_," (_le
moi_) for the sentient and volent faculty, he marks, with peculiar
appropriateness and force, that phraseology borrowed from the world
of matter will, in this subject, no longer answer our purpose. We
have here to go from Nouns to Pronouns, from Things to Persons. We
pass from the Body to the Soul, from Physics to Metaphysics. We are
come to the borders of material philosophy; the next step is into
the domain of Thought and Mind. Here, therefore, we begin to feel
that we have reached the boundaries of our present subject. The
examination of that which lies beyond them must be reserved for a
philosophy of another kind, and for the labors of the future; if we
are ever enabled to make the attempt to extend into that loftier and
wider scene, the principles which we gather on the ground we are now
laboriously treading.

[Note 79\17: _Règne Animal_, Introd. p. 47.]

Such speculations as I have quoted respecting the nervous fluid,
proceeding from some of the greatest philosophers who ever lived,
prove only that hitherto the endeavor to comprehend the mystery of
perception and will, of life and thought, have been fruitless and
vain. Many anatomical truths have been discovered, but, so far as
our survey has yet gone, no genuine physiological principle. All the
trains of physiological research which we have followed have begun
in exact examination of organization and function, and have ended in
wide conjectures and arbitrary hypotheses. The stream of knowledge
in all such cases is {468} clear and lively at its outset; but,
instead of reaching the great ocean of the general truths of
science, it is gradually spread abroad among sands and deserts till
its course can be traced no longer.

Hitherto, therefore, we must consider that we have had to tell the
story of the _failures_ of physiological speculation. But of late
there have come into view and use among physiologists certain
principles which may be considered as peculiar to organized
subjects; and of which the introduction forms a real advance in
organical science. Though these have hitherto been very imperfectly
developed, we must endeavor to exhibit, in some measure, their
history and bearing.

[2nd Ed.] [In order to show that I am not unaware how imperfect the
sketch given in this work is, as a History of Physiology, I may
refer to the further discussions on these subjects contained in the
_Philosophy of the Inductive Sciences_, Book ix. I have there (Chap.
ii.) noticed the successive _Biological Hypotheses_ of the Mystical,
the Iatrochemical, and Iatromathematical Schools, the Vital-Fluid
School, and the Psychical School. I have (Chaps. iii., iv., v.)
examined several of the attempts which have been made to analyze the
Idea of Life, to classify Vital Functions, and to form Ideas of
Separate Vital Forces. I have considered in particular, the attempts
to form a distinct conception of Assimilation and Secretion, of
Generation, and of Voluntary Motion; and I have (Chap. vi.) further
discussed the Idea of Final Causes as employed in Biology.]




CHAPTER VI.

INTRODUCTION OF THE PRINCIPLE OF DEVELOPED AND METAMORPHOSED
SYMMETRY.


_Sect._ 1.--_Vegetable Morphology. Göthe. De Candolle._

BEFORE we proceed to consider the progress of principles which
belong to animal and human life, such as have just been pointed at,
we must look round for such doctrines, if any such there be, as
apply alike to all organized beings, conscious or unconscious, fixed
or locomotive;--to the laws which regulate vegetable as well as
animal forms and functions. Though we are very far from being able
to present a {469} clear and connected code of such laws, we may
refer to one law, at least, which appears to be of genuine authority
and validity; and which is worthy our attention as an example of a
properly organical or physiological principle, distinct from all
mechanical, chemical, or other physical forces; and such as cannot
even be conceived to be resolvable into those. I speak of the
tendency which produces such results as have been brought together
in recent speculations upon _Morphology_.

It may perhaps be regarded as indicating how peculiar are the
principles of organic life, and how far removed from any mere
mechanical action, that the leading idea in these speculations was
first strongly and effectively apprehended, not by a laborious
experimenter and reasoner, but by a man of singularly brilliant and
creative fancy; not by a mathematician or chemist, but by a poet.
And we may add further, that this poet had already shown himself
incapable of rightly apprehending the relation of physical facts to
their principles; and had, in trying his powers on such subjects,
exhibited a signal instance of the ineffectual and perverse
operation of the method of philosophizing to which the constitution
of his mind led him. The person of whom we speak, is John Wolfgang
Göthe, who is held, by the unanimous voice of Europe, to have been
one of the greatest poets of our own, or of any time, and whose
_Doctrine of Colors_ we have already had to describe, in the History
of Optics, as an entire failure. Yet his views on the laws which
connect the forms of plants into one simple system, have been
generally accepted and followed up. We might almost be led to think
that this writer's poetical endowments had contributed to this
scientific discovery;--the love of beauty of form, by fixing the
attention upon the symmetry of plants; and the creative habit of
thought, by making constant developement of a familiar
process.[80\17] {470}

[Note 80\17: We may quote some of the poet's own verses as an
illustration of his feelings on this subject. They are addressed to
a lady.

  Dich verwirret, geliebte, die tausendfältige mischung
    Dieses blumengewühls über dem garten umher;
  Viele namen hörest du an, und immer verdränget,
    Mit barbarischem klang, einer den andern im ohr.
  Alle gestalten sind **ähnlich und keine gleichet der andern;
    Und so deutet das chor auf ein geheimes gesetz,
  Auf ein heiliges räthsel. O! könnte ich dich, liebliche freundinn,
    Ueberliefern so gleich glücklich das lösende wort.

  Thou, my love, art perplext with the endless seeming confusion
    Of the luxuriant wealth which in the garden is spread;
  Name upon name thou hearest, and in thy dissatisfied hearing,
    With a barbarian noise one drives another along.
  All the forms resemble, yet none is the same as another;
    Thus the whole of the throng points at a deep hidden law.
  Points at a sacred riddle. Oh! could I to thee, my beloved friend,
    Whisper the fortunate word by which the riddle is read!]

But though we cannot but remark the peculiarity of our being
indebted to a poet for the discovery of a scientific principle, we
must not forget that he himself held, that in making this step, he
had been guided, not by his invention, but by observation. He
repelled, with extreme repugnance, the notion that he had
substituted fancy for fact, or imposed ideal laws on actual things.
While he was earnestly pursuing his morphological speculations, he
attempted to impress them upon Schiller. "I expounded to him, in as
lively a manner as possible, the metamorphosis of plants, drawing on
paper, with many characteristic strokes, a symbolic plant before his
eyes. He heard me," Göthe says,[81\17] "with much interest and
distinct comprehension; but when I had done, he shook his head, and
said, 'That is not Experience; that is an Idea:' I stopt with some
degree of irritation; for the point which separated us was marked
most luminously by this expression." And in the same work he relates
his botanical studies and his habit of observation, from which it is
easily seen that no common amount of knowledge and notice of
details, were involved in the course of thought which led him to the
principle of the Metamorphosis of Plants.

[Note 81\17:_ Zur Morphologie_, p. 24.]

Before I state the history of this principle, I may be allowed to
endeavor to communicate to the reader, to whom this subject is new,
some conception of the principle itself. This will not be difficult,
if he will imagine to himself a flower, for instance, a common
wild-rose, or the blossom of an apple-tree, as consisting of a
series of parts disposed in _whorls_, placed one over another on an
_axis_. The lowest whorl is the calyx with its five sepals; above
this is the corolla with its five petals; above this are a multitude
of stamens, which may be considered as separate whorls of five each,
often repeated; above these is a whorl composed of the ovaries, or
what become the seed-vessels in the fruit, which are five united
together in the apple, but indefinite in number and separate in the
rose. Now the morphological view is {471} this;--that the members of
each of these whorls are in their nature identical, and the same as
if they were whorls of ordinary leaves, brought together by the
shortening their common axis, and modified in form by the successive
elaboration of their nutriment. Further, according to this view, a
whorl of leaves itself is to be considered as identical with several
detached leaves dispersed spirally along the axis, and brought
together because the axis is shortened. Thus all the parts of a
plant are, or at least represent, the successive metamorphoses of
the same elementary member. The root-leaves thus pass into the
common leaves;--these into bracteæ;--these into the sepals;--these
into the petals;--these into the stamens with their anthers;--these
into the ovaries with their styles and stigmas;--these ultimately
become the fruit; and thus we are finally led to the seed of a new
plant.

Moreover the same notion of metamorphosis may be applied to explain
the existence of flowers which are not symmetrical like those we
have just referred to, but which have an irregular corolla or calyx.
The papilionaceous flower of the pea tribe, which is so markedly
irregular, may be deduced by easy gradations from the regular
flower, (through the _mimoseæ_,) by expanding one petal, joining one
or two others, and modifying the form of the intermediate ones.

Without attempting to go into detail respecting the proofs of that
identity of all the different organs, and all the different forms of
plants, which is thus asserted, we may observe, that it rests on
such grounds as these;--the transformations which the parts of
flowers undergo by accidents of nutriment or exposure. Such changes,
considered as monstrosities where they are very remarkable, show the
tendencies and possibilities belonging to the organization in which
they occur. For instance, the single wild-rose, by culture,
transforms many of its numerous stamens into petals, and thus
acquires the deeply folded flower of the double garden-rose. We
cannot doubt of the reality of this change, for we often see stamens
in which it is incomplete. In other cases we find petals becoming
leaves, and a branch growing out of the centre of the flower. Some
pear-trees, when in blossom, are remarkable for their tendencies to
such monstrosities.[82\17] Again, we find that flowers which are
usually irregular, occasionally become regular, and conversely. The
common snap-dragon (_Linaria vulgaris_) affords a curious instance
of this.[83\17] The usual form of this plant is "personate," the
corolla being divided into two lobes, which differ in form, and
{472} together present somewhat the appearance of an animal's face;
and the upper portion of the corolla is prolonged backwards into a
tube-like "spur." No flower can be more irregular; but there is a
singular variety of this plants termed _Peloria_, in which the
corolla is strictly symmetrical, consisting of a conical tube,
narrowed in front, elongated behind into five equal spurs, and
containing five stamens of equal length, instead of the two unequal
pairs of the didynamous Linaria. These and the like appearances show
that there is in nature a capacity for, and tendency to, such
changes as the doctrine of metamorphosis asserts.

[Note 82\17: Lindley, _Nat. Syst._ p. 84.]

[Note 83\17: Henslow, _Principles of Botany_, p. 116.]

Göthe's _Metamorphosis of Plants_ was published 1790: and his system
was the result of his own independent course of thoughts. The view
which it involved was not, however, absolutely new, though it had
never before been unfolded in so distinct and persuasive a manner.
Linnæus considered the leaves, calyx, corolla, stamens, each as
evolved in succession from the other; and spoke of it as _prolepsis_
or _anticipation_,[84\17] when the leaves changed accidentally into
bracteæ, these into a calyx, this into a corolla, the corolla into
stamens, or these into the pistil. And Caspar Wolf apprehended in a
more general manner the same principle. "In the whole plant," says
he,[85\17] "we see nothing but leaves and stalk;" and in order to
prove what is the situation of the leaves in all their later forms,
he adduces the cotyledons as the first leaves.

[Note 84\17: Sprengel, _Bot._ ii. 302. _Amœn. Acad._ vi. 324, 365.]

[Note 85\17: _Nov. Con. Ac. Petrop._ xii. 403, xiii. 478.]

Göthe was led to his system on this subject by his general views of
nature. He saw, he says,[86\17] that a whole life of talent and
labor was requisite to enable any one to arrange the infinitely
copious organic forms of a single kingdom of nature. "Yet I felt,"
he adds, "that for me there must be another way, analogous to the
rest of my habits. The appearance of the changes, round and round,
of organic creatures had taken strong hold on my mind. Imagination
and Nature appeared to me to vie with each other which could go on
most boldly yet most consistently." His observation of nature,
directed by such a thought, led him to the doctrine of the
metamorphosis.

[Note 86\17: _Zur Morph._ i. 30.]

In a later republication of his work (_Zur Morphologie_, 1817,) he
gives a very agreeable account of the various circumstances which
affected the reception and progress of his doctrine.
Willdenow[87\17] quoted {473} him thus:--"The life of plants is, as
Mr. Göthe very prettily says, an expansion and contraction, and
these alternations make the various periods of life." "This
'_prettily_,'" says Göthe, "I can be well content with, but the
'_egregie_,' of Usteri is much more pretty and obliging." Usteri had
used this term respecting Göthe in an edition of Jussieu.

[Note 87\17: _Zur Morph._ i. 121.]

The application of the notion of metamorphosis to the explanation of
double and monstrous flowers had been made previously by Jussieu.
Göthe's merit was, to have referred to it the _regular_ formation of
the flower. And as Sprengel justly says,[88\17] his view had so
profound a meaning, made so strong an appeal by its simplicity, and
was so fruitful in the most valuable consequences, that it was not
to be wondered at if it occasioned further examination of the
subject; although many persons pretend to slight it. The task of
confirming and verifying the doctrine by a general application of it
to all cases,--a labor so important and necessary after the
promulgation of any great principle,--Göthe himself did not execute.
At first he collected specimens and made drawings with some such
view,[89\17] but he was interrupted and diverted to other matters.
"And now," says he, in his later publication, "when I look back on
this undertaking, it is easy to see that the object which I had
before my eyes was, for me, in my position, with my habits and mode
of thinking, unattainable. For it was no less than this: that I was
to take that which I had stated in general, and presented to the
conception, to the mental intuition, in words; and that I should, in
a particularly visible, orderly, and gradual manner, present it to
the eye; so as to show to the outward sense that out of the germ of
this idea might grow a tree of physiology fit to overshadow the
world."

[Note 88\17: _Gesch. Botan._ ii. 304.]

[Note 89\17: _Zur Morph._ i. **129.]

Voigt, professor at Jena, was one of the first who adopted Göthe's
view into an elementary work, which he did in 1808. Other botanists
labored in the direction which had thus been pointed out. Of those
who have thus contributed to the establishment and developement of
the metamorphic doctrine. Professor De Candolle, of Geneva, is
perhaps the most important. His Theory of Developement rests upon
two main principles, _abortion_ and _adhesion_. By considering some
parts as degenerated or absent through the abortion of the buds
which might have formed them, and other parts as adhering together,
he holds that all plants may be reduced to perfect symmetry: and the
actual and constant occurrence of such incidents is shown beyond
{474} all doubt. And thus the snap-dragon, of which we have spoken
above, is derived from the Peloria, which is the normal condition of
the flower, by the abortion of one stamen, and the degeneration of
two others. Such examples are too numerous to need to be dwelt on.


_Sect._ 2.--_Application of Vegetable Morphology._

THE doctrine, being thus fully established, has been applied to
solve different problems in botany; for instance, to explain the
structure of flowers which appear at first sight to deviate widely
from the usual forms of the vegetable world. We have an instance of
such an application in Mr. Robert Brown's explanation of the real
structure of various plants which had been entirely misunderstood:
as, for example, the genus _Euphorbia_. In this plant he showed that
what had been held to be a jointed filament, was a pedicel with a
filament above it, the intermediate corolla having evanesced. In
_Orchideæ_ (the orchis tribe), he showed that the peculiar structure
of the plant arose from its having six stamens (two sets of three
each), of which five are usually abortive. In _Coniferæ_ (the
cone-bearing trees), it was made to appear that the seed was naked,
while the accompanying appendage, corresponding to a seed-vessel,
assumed all forms, from a complete leaf to a mere scale. In like
manner it was proved that the _pappus_, or down of _composite_
plants (as thistles), is a transformed calyx.

Along with this successful application of a profound principle, it
was natural that other botanists should make similar attempts. Thus
Mr. Lindley was led to take a view[90\17] of the structure of
_Reseda_ (mignonette) different from that usually entertained;
which, when published, attracted a good deal of attention, and
gained some converts among the botanists of Germany and France. But
in 1833, Mr. Lindley says, with great candor, "Lately, Professor
Henslow has satisfactorily proved, in part by the aid of a
monstrosity in the common _Mignonette_, in part by a severe
application of morphological rules, that my hypothesis must
necessarily be false." Such an agreement of different botanists
respecting the consequences of morphological rules, proves the
reality and universality of the rules.

[Note 90\17: Lindley, _Brit. Assoc. Report_, iii. 50.]

We find, therefore, that a principle which we may call the
_Principle of Developed and Metamorphosed Symmetry_, is firmly
established {475} and recognized, and familiarly and successfully
applied by botanists. And it will be apparent, on reflection, that
though _symmetry_ is a notion which applies to inorganic as well as
to organic things, and is, in fact, a conception of certain
relations of space and position, such _developement_ and
_metamorphosis_ as are here spoken of, are ideas entirely different
from any of those to which the physical sciences have led us in our
previous survey; and are, in short, genuine _organical_ or
_physiological_ ideas;--real elements of the philosophy of _life_.

We must, however imperfectly, endeavor to trace the application of
this idea in the other great department of the world of life; we
must follow the history of Animal Morphology.




CHAPTER VII.

PROGRESS OF ANIMAL MORPHOLOGY.


_Sect._ 1.--_Rise of Comparative Anatomy._

THE most general and constant relations of the form of the organs,
both in plants and animals, are the most natural grounds of
classification. Hence the first scientific classifications of
animals are the first steps in animal morphology. At first, a
_zoology_ was constructed by arranging animals, as plants were at
first arranged, according to their external parts. But in the course
of the researches of the anatomists of the seventeenth century, it
was seen that the internal structure of animals offered resemblances
and transitions of a far more coherent and philosophical kind, and
the Science of _Comparative Anatomy_ rose into favor and importance.
Among the main cultivators of this science[91\17] at the period just
mentioned, we find Francis Redi, of Arezzo; Guichard-Joseph
Duvernay, who was for sixty years Professor of Anatomy at the Jardin
du Roi at Paris, and during this lapse of time had for his pupils
almost all the greatest anatomists of the greater part of the
eighteenth century; Nehemiah Grew, secretary to the Royal Society of
London, whose _Anatomy of Plants_ we have already noticed.

[Note 91\17: Cuv. _Leçons sur l'Hist. des Sc. Nat._ 414, 420.]

But Comparative Anatomy, which had been cultivated with ardor {476}
to the end of the seventeenth century, was, in some measure,
neglected during the first two-thirds of the eighteenth. The
progress of botany was, Cuvier sagaciously suggests,[92\17] one
cause of this; for that science had made its advances by confining
itself to external characters, and rejecting anatomy; and though
Linnæus acknowledged the dependence of zoology upon anatomy[93\17]
so far as to make the number of teeth his characters, even this was
felt, in his method, as a bold step. But his influence was soon
opposed by that of Buffon, Daubenton, and Pallas; who again brought
into view the importance of comparative anatomy in Zoology; at the
same time that Haller proved how much might be learnt from it in
Physiology. John Hunter in England, the two Monros in Scotland,
Camper in Holland, and Vicq d'Azyr in France, were the first to
follow the path thus pointed out. Camper threw the glance of genius
on a host of interesting objects, but almost all that he produced
was a number of sketches; Vicq d'Azyr, more assiduous, was stopt in
the midst of a most brilliant career by a premature death.

[Note 92\17: Cuv. _Hist. Sc. Nat._ i. 301.]

[Note 93\17: Ib.]

Such is Cuvier's outline of the earlier history of comparative
anatomy. We shall not go into detail upon this subject; but we may
observe that such studies had fixed in the minds of naturalists the
conviction of the possibility and the propriety of considering large
divisions of the animal kingdom as modifications of one common
_type_. Belon, as early as 1555, had placed the skeleton of a man
and a bird side by side, and shown the correspondence of parts. So
far as the case of vertebrated animals extends, this correspondence
is generally allowed; although it required some ingenuity to detect
its details in some cases; for instance, to see the analogy of parts
between the head of a man and a fish.

In tracing these less obvious correspondencies, some curious steps
have been made in recent times. And here we must, I conceive, again
ascribe no small merit to the same remarkable man who, as we have
already had to point out, gave so great an impulse to vegetable
morphology. Göthe, whose talent and disposition for speculating on
all parts of nature were truly admirable, was excited to the study
of anatomy by his propinquity to the Duke of Weimar's cabinet of
natural history. In 1786, he published a little essay, the object of
which was to show that in man, as well as in beasts, the upper jaw
contains an intermaxillary bone, although the sutures are
obliterated. After 1790,[94\17] animated and impelled by the same
passion for natural {477} observation and for general views, which
had produced his Metamorphosis of Plants, he pursued his
speculations on these subjects eagerly and successfully. And in
1795, he published a _Sketch of a Universal Introduction into
Comparative Anatomy, beginning with Osteology_; in which he attempts
to establish an "osteological type," to which skeletons of all
animals may be referred. I do not pretend that Göthe's anatomical
works have had any influence on the progress of the science
comparable with that which has been exercised by the labors of
professional anatomists; but the ingenuity and value of the views
which they contained was acknowledged by the best authorities; and
the clearer introduction and application of the principle of
developed and metamorphosed symmetry may be dated from about this
time. Göthe declares that, at an early period of these speculations,
he was convinced[95\17] that the bony head of beasts is to be
derived from six vertebræ. In 1807, Oken published a "Program" _On
the Signification of the Bones of the Skull_, in which he maintained
that these bones are equivalent to four vertebræ); and Meckel, in
his _Comparative Anatomy_, in 1811, also resolved the skull into
vertebræ. But Spix, in his elaborate work _Cephalogenesis_, in 1815,
reduced the vertebræ of the head to three. "Oken," he says,[96\17]
"published opinions merely theoretical, and consequently contrary to
those maintained in this work, which are drawn from observation."
This resolution of the head into vertebræ is assented to by many of
the best physiologists, as explaining the distribution of the
nerves, and other phenomena. Spix further extended the application
of the vertebral theory to the heads of all classes of vertebrate
animals; and Bojanus published a Memoir expressly on the vertebral
structure of the skulls of fishes in Oken's _Isis_ for 1818.
Geoffroy Saint-Hilaire presented a lithographic plate to the French
Academy in February 1824, entitled _Composition de la Tête **osseuse
chez l'Homme et les Animaux_, and developed his views of the
vertebral composition of the skull in two Memoirs published in the
_Annales des Sciences Naturelles_ for 1824. We cannot fail to
recognize here the attempt to apply to the skeleton of animals the
principle which leads botanists to consider all the parts of a
flower as transformations of the same organs. How far the
application of the principle, as here proposed, is just, I must
leave philosophical physiologists to decide.

[Note 94\17: _Zur Morphologie_, i. 234.]

[Note 95\17: _Zur Morphologie_, 250.]

[Note 96\17:  Spix, _Cephalogenesis_.]

By these and similar researches, it is held by the best
physiologists {478} that the skull of all vertebrate animals is
pretty well reduced to a uniform structure, and the laws of its
variations nearly determined.[97\17]

[Note 97\17: Cuv. _Hist. Sc. Nat._ iii. 442.]

The vertebrate animals being thus reduced to a single type, the
question arises how far this can be done with regard to other
animals, and how many such types there are. And here we come to one
of the important services which Cuvier rendered to natural history.


_Sect._ 2.--_Distinction of the General Types of the Forms of
Animals.--Cuvier._

ANIMALS were divided by Lamarck into vertebrate and invertebrate;
and the general analogies of all vertebrate animals are easily made
manifest. But with regard to other animals, the point is far from
clear. Cuvier was the first to give a really philosophical view of
the animal world in reference to the plan on which each animal is
constructed. There are,[98\17] he says, four such plans;--four forms
on which animals appear to have been modelled; and of which the
ulterior divisions, with whatever titles naturalists have decorated
them, are only very slight modifications, founded on the development
or addition of some parts which do not produce any essential change
in the plan.

[Note 98\17: _Règne Animal_, p. 57.]

These four great branches of the animal world are the _vertebrata_,
_mollusca_, _articulata_, _radiata_; and the differences of these
are so important that a slight explanation of them may be permitted.

The _vertebrata_ are those animals which (as man and other sucklers,
birds, fishes, lizards, frogs, serpents) have a backbone and a skull
with lateral appendages, within which the viscera are included, and
to which the muscles are attached.

The _mollusca_, or soft animals, have no bony skeleton; the muscles
are attached to the skin, which often includes stony plates called
_shells_; such molluscs are shell-fish; others are cuttle-fish, and
many pulpy sea-animals.

The _articulata_ consist of _crustacea_ (lobsters, &c.), _insects_,
_spiders_, and _annulose worms_, which consist of a head and a
number of successive annular portions of the body _jointed_ together
(to the interior of which the muscles are attached), whence the name.

Finally, the _radiata_ include the animals known under the name of
_zoophytes_. In the preceding three branches the organs of motion
and of sense were distributed symmetrically on the two sides of an
axis, {479} so that the animal has a right and a left side. In the
radiata the similar members radiate from the axis in a circular
manner, like the petals of a regular flower.

The whole value of such a classification cannot be understood
without explaining its use in enabling us to give general
descriptions, and general laws of the animal functions of the
classes which it includes; but in the present part of our work our
business is to exhibit it as an exemplification of the reduction of
animals to laws of Symmetry. The bipartite Symmetry of the form of
vertebrate and articulate animals is obvious; and the reduction of
the various forms of such animals to a common type has been
effected, by attention to their anatomy, in a manner which has
satisfied those who have best studied the subject. The molluscs,
especially those in which the head disappears, as oysters, or those
which are rolled into a spiral, as snails, have a less obvious
Symmetry, but here also we can apply certain general types. And the
Symmetry of the radiated zoophytes is of a nature quite different
from all the rest, and approaching, as we have suggested, to the
kind of Symmetry found in plants. Some naturalists have doubted
whether[99\17] these zoophytes are not referrible to two types
(_acrita_ or polypes, and true _radiata_,) rather than to one.

[Note 99\17: _Brit. Assoc. Rep._ iv. 227.]

This fourfold division was introduced by Cuvier.[100\17] Before him,
naturalists followed Linnæus, and divided non-vertebrate animals
into two classes, insects and worms. "I began," says Cuvier, "to
attack this view of the subject, and offered another division, in a
Memoir read at the Society of Natural History of Paris, the 21st of
Floreal, in the year III. of the Republic (May 10, 1795,) printed in
the _Décade Philosophique_: in this, I mark the characters and the
limits of molluscs, insects, worms, echinoderms, and zoophytes. I
distinguish the red-blooded worms or annelides, in a Memoir read to
the Institute, the 11th Nivose, year X. (December 31, 1801.) I
afterwards distributed these different classes into three branches,
each co-ordinate to the branch formed by the vertebrate animals, in
a Memoir read to the Institute in July, 1812, printed in the
_Annales du Muséum d'Histoire Naturelle_, tom. xix." His great
systematic work, the _Règne Animal_, founded on this distribution,
was published in 1817; and since that time the division has been
commonly accepted among naturalists.

[Note 100\17: _Règne A._ 61.]

[2nd Ed.] [The question of the Classification of Animals is
discussed in the first of Prof. Owen's _Lectures on the
Invertebrate_ {480} _Animals_ (1843). Mr. Owen observes that the
arrangement of animals into _Vertebrate_ and _Invertebrate_ which
prevailed before Cuvier, was necessarily bad, inasmuch as no
_negative_ character in Zoology gives true natural groups. Hence the
establishment of the _sub-kingdoms_, _Mollusca_, _Articulata_,
_Radiata_, as co-ordinate with _Vertebrata_, according to the
arrangement of the nervous system, was a most important advance. But
Mr. Owen has seen reason to separate the _Radiata_ of Cuvier into
two divisions; the _Nematoneura_, in which the nervous system can be
traced in a filamentary form (including _Echinoderma_,
_Ciliobrachiata_, _Cœlelmintha_, _Rotifera_,) and the _Acrita_ or
lowest division of the animal kingdom, including _Acalepha_,
_Nudibrachiata_, _Sterelmintha_, _Polygastria_.]


_Sect._ 3.--_Attempts to establish the Identity of the Types of
Animal Forms._

SUPPOSING this great step in Zoology, of which we have given an
account,--the reduction of all animals to four types or plans,--to
be quite secure, we are then led to ask whether any further advance
is possible;--whether several of these types can be referred to one
common form by any wider effort of generalization. On this question
there has been a considerable difference of opinion. Geoffroy
Saint-Hilaire,[101\17] who had previously endeavored to show that
all vertebrate animals were constructed so exactly upon the same
plan as to preserve the strictest analogy of parts in respect to
their osteology, thought to extend this unity of plan by
demonstrating, that the hard parts of crustaceans and insects are
still only modifications of the skeleton of higher animals, and that
therefore the type of vertebrata must be made to include them
also:--the segments of the articulata are held to be strictly
analogous to the vertebras of the higher animals, and thus the
former live _within_ their vertebral column in the same manner as
the latter live _without_ it. Attempts have even been made to reduce
molluscous and vertebrate animals to a community of type, as we
shall see shortly.

[Note 101\17: Mr. Jenyns, _Brit. Assoc. Rep._ iv. 150.]

Another application of the principle, according to which creatures
the most different are developments of the same original type, may
be discerned[102\17] in the doctrine, that the embryo of the higher
forms of animal life passes by gradations through those forms which
are {481} permanent in inferior animals. Thus, according to this
view, the human fœtus assumes successively the plan of the zoophyte,
the worm, the fish, the turtle, the bird, the beast. But it has been
well observed, that "in these analogies we look in vain for the
precision which can alone support the inference that has been
deduced;"[103\17] and that at each step, the higher embryo and the
lower animal which it is supposed to resemble, differ in having each
different organs suited to their respective destinations.

[Note 102\17: Dr. Clark, _Report_, Ib. iv. 113.]

[Note 103\17: Dr. Clark, p. 114.]

Cuvier[104\17] never assented to this view, nor to the attempts to
refer the different divisions of his system to a common type. "He
could not admit," says his biographer, "that the lungs or gills of
the vertebrates are in the same connexion as the branchiæ of
molluscs and crustaceans, which in the one are situated at the base
of the feet, or fixed on the feet themselves, and in the other often
on the back or about the arms. He did not admit the analogy between
the skeleton of the vertebrates and the skin of the articulates; he
could not believe that the tænia and the sepia were constructed on
the same plan; that there was a similarity of composition between
the bird and the echinus, the whale and the snail; in spite of the
skill with which some persons sought gradually to efface their
discrepancies."

[Note 104\17: Laurillard, _Elog. de Cuvier_, p. 66.]

Whether it may be possible to establish, among the four great
divisions of the "Animal Kingdom," some analogies of a higher order
than those which prevail within each division, I do not pretend to
conjecture. If this can be done, it is clear that it must be by
comparing the types of these divisions under their most general
forms: and thus Cuvier's arrangement, so far as it is itself rightly
founded on the unity of composition of each branch, is the surest
step to the discovery of a unity pervading and uniting these
branches. But those who generalize surely, and those who generalize
rapidly, may travel in the same direction, they soon separate so
widely, that they appear to move from each other. The partisans of a
universal "unity of composition" of animals, accused Cuvier of being
too inert in following the progress of physiological and zoological
science. Borrowing their illustration from the political parties of
the times, they asserted that he belonged to the science of
_resistance_, not to the science of the _movement_. Such a charge
was highly honorable to him; for no one acquainted with the history
of zoology can doubt that he had a great share in the impulse by
which the "movement" was occasioned; or that he {482} himself made a
large advance with it; and it was because he was so poised by the
vast mass of his knowledge, so temperate in his love of doubtful
generalizations, that he was not swept on in the wilder part of the
stream. To such a charge, moderate reformers, who appreciate the
value of the good which exists, though they try to make it better,
and who know the knowledge, thoughtfulness, and caution, which are
needful in such a task, are naturally exposed. For us, who can only
decide on such a subject by the general analogies of the history of
science, it may suffice to say, that it appears doubtful whether the
fundamental conceptions of affinity, analogy, transition, and
developement, have yet been fixed in the minds of physiologists with
sufficient firmness and clearness, or unfolded with sufficient
consistency and generality, to make it likely that any great
additional step of this kind can for some time be made.

We have here considered the doctrine of the identity of the
seemingly various types of animal structure, as an attempt to extend
the correspondencies which were the basis of Cuvier's division of
the animal kingdom. But this doctrine has been put forward in
another point of view, as the antithesis to the doctrine of final
causes. This question is so important a one, that we cannot help
attempting to give some view of its state and bearings.




CHAPTER VIII.

THE DOCTRINE OF FINAL CAUSES IN PHYSIOLOGY.


_Sect._ 1.--_Assertion of the Principle of Unity of Plan._

WE have repeatedly seen, in the course of our historical view of
Physiology, that those who have studied the structure of animals and
plants, have had a conviction forced upon them, that the organs are
constructed and combined in subservience to the life and functions
of the whole. The parts have a _purpose_, as well as a _law_;--we
can trace Final Causes, as well as Laws of Causation. This principle
is peculiar to physiology; and it might naturally be expected that,
in the progress of the science, it would come under special
consideration. This accordingly has happened; and the principle has
been drawn {483} into a prominent position by the struggle of two
antagonistic schools of physiologists. On the one hand, it has been
maintained that this doctrine of final causes is altogether
unphilosophical, and requires to be replaced by a more comprehensive
and profound principle: on the other hand, it is asserted that the
doctrine is not only true, but that, in our own time, it has been
fixed and developed so as to become the instrument of some of the
most important discoveries which have been made. Of the views of
these two schools we must endeavor to give some account.

The disciples of the former of the two schools express their tenets
by the phrases _unity_ of _plan_, _unity_ of _composition_; and the
more detailed developement of these doctrines has been termed the
_Theory of Analogies_, by Geoffroy Saint-Hilaire, who claims this
theory as his own creation. According to this theory, the structure
and functions of animals are to be studied by the guidance of their
analogy only; our attention is to be turned, not to the fitness of
the organization for any end of life or action, but to its
resemblance to other organizations by which it is gradually derived
from the original type.

According to the rival view of this subject, we must not assume, and
cannot establish, that the plan of all animals is the same, or their
composition similar. The existence of a single and universal system
of analogies in the construction of all animals is entirely
unproved, and therefore cannot be made our guide in the study of
their properties. On the other hand, the plan of the animal, the
purpose of its organization in the support of its life, the
necessity of the functions to its existence, are truths which are
irresistibly apparent, and which may therefore be safely taken as
the bases of our reasonings. This view has been put forward as the
doctrine of the _conditions of existence_: it may also be described
as the principle of _a purpose in organization_; the structure being
considered as having the function for its end. We must say a few
words on each of these views.

It had been pointed out by Cuvier, as we have seen in the last
chapter, that the animal kingdom may be divided into four great
branches; in each of which the _plan_ of the animal is different,
namely, _vertebrata_, _articulata_, _mollusca_, _radiata_. Now the
question naturally occurs, is there really no resemblance of
construction in these different classes? It was maintained by some,
that there is such a resemblance. In 1820,[105\17] M. Audouin, a
young naturalist of Paris, {484} endeavored to fill up the chasm
which separates insects from other animals; and by examining
carefully the portions which compose the solid frame-work of
insects, and following them through their various transformations in
different classes, he conceived that he found relations of position
and function, and often of number and form, which might be compared
with the relations of the parts of the skeleton in vertebrate
animals. He thought that the first segment of an insect, the
head,[106\17] represents one of the three vertebræ which, according
to Spix and others, compose the vertebrate head: the second segment
of the insects, (the _prothorax_ of Audouin,) is, according to M.
Geoffroy, the second vertebra of the head of the vertebrata, and so
on. Upon this speculation Cuvier[107\17] does not give any decided
opinion; observing only, that even if false, it leads to active
thought and useful research.

[Note 105\17: Cuv. _Hist. Sc. Nat._ iii. 422.]

[Note 106\17: Ib. 437.]

[Note 107\17: Cuv. _Hist. Sc. Nat._ iii. 441.]

But when an attempt was further made to identify the plan of another
branch of the animal world, the mollusca, with that of the
vertebrata, the radical opposition between such views and those of
Cuvier, broke out into an animated controversy.

Two French anatomists, MM. Laurencet and Meyranx, presented to the
Academy of Sciences, in 1830, a Memoir containing their views on the
organization of molluscous animals; and on the sepia or cuttle-fish
in particular, as one of the most complete examples of such animals.
These creatures, indeed, though thus placed in the same division
with shell-fish of the most defective organization and obscure
structure, are far from being scantily organized. They have a
brain,[108\17] often eyes, and these, in the animals of this class,
(_cephalopoda_) are more complicated than in any
vertebrates;[109\17] they have sometimes ears, salivary glands,
multiple stomachs, a considerable liver, a bile, a complete double
circulation, provided with auricles and ventricles; in short, their
vital activity is vigorous, and their senses are distinct.

[Note 108\17: Geoffroy Saint-Hilaire denies this. _Principes de
Phil. Zoologique discutés en_ 1830, p. 68.]

[Note 109\17: Geoffroy Saint-Hilaire, _Principes de Phil. Zoologique
discutés en_ 1830, p. 55.]

But still, though this organization, in the abundance and diversity
of its parts, approaches that of vertebrate animals, it had not been
considered as composed in the same manner, or arranged in the same
order, Cuvier had always maintained that the plan of molluscs is not
a continuation of the plan of vertebrates. {485}

MM. Laurencet and Meyranx, on the contrary, conceived that the sepia
might be reduced to the type of a vertebrate creature, by
considering the back-bone of the latter bent double backwards, so as
to bring the root of the tail to the nape of the neck; the parts
thus brought into contact being supposed to coalesce. By this mode
of conception, these anatomists held that the viscera were placed in
the same connexion as in the vertebrate type, and the functions
exercised in an analogous manner.

To decide on the reality of the analogy thus asserted, clearly
belonged to the jurisdiction of the most eminent anatomists and
physiologists. The Memoir was committed to Geoffroy Saint-Hilaire
and Latreille, two eminent zoologists, in order to be reported on.
Their report was extremely favorable; and went almost to the length
of adopting the views of the authors.

Cuvier expressed some dissatisfaction with this report on its being
read;[110\17] and a short time afterwards,[111\17] represented
Geoffroy Saint-Hilaire as having asserted that the new views of
Laurencet and Meyranx refuted completely the notion of the great
interval which exists between molluscous and vertebrate animals.
Geoffroy protested against such an interpretation of his
expressions; but it soon appeared, by the controversial character
which the discussions on this and several other subjects assumed,
that a real opposition of opinions was in action.

[Note 110\17: _Princ. de Phil. Zool. discutés en_ 1830, p. 36.]

[Note 111\17: p. 50.]

Without attempting to explain the exact views of Geoffroy, (we may,
perhaps, venture to say that they are hardly yet generally
understood with sufficient distinctness to justify the mere
historian of science in attempting such an explanation,) their
general tendency may be sufficiently collected from what has been
said; and from the phrases in which his views are conveyed.[112\17]
_The principle of connexions, the elective affinities of organic
elements, the equilibrization of organs_;--such are the designations
of the leading doctrines which are unfolded in the preliminary
discourse of his _Anatomical Philosophy_. Elective affinities of
organic elements are the forces by which the vital structures and
varied forms of living things are produced; and the principles of
connexion and equilibrium of these forces in the various parts of
the organization prescribe limits and conditions to the variety and
developement of such forms.

[Note 112\17: _Phil. Zool._ 15.]

The character and tendency of this philosophy will be, I think,
{486} much more clear, if we consider what it excludes and denies.
It rejects altogether all conception of a plan and purpose in the
organs of animals, as a principle which has determined their forms,
or can be of use in directing our reasonings. "I take care," says
Geoffroy, "not to ascribe to God any intention."[113\17] And when
Cuvier speaks of the combination of organs in such order that they
may be in consistence with the part which the animal _has to play_
in nature; his rival rejoins,[114\17] I "know nothing of animals
which _have to play_ a part in nature." Such a notion is, he holds,
unphilosophical and dangerous. It is an abuse of final causes which
makes the cause to be engendered by the effect. And to illustrate
still further his own view, he says, "I have read concerning
fishes, that because they live in a medium which resists more than
air, their motive forces are calculated so as to give them the power
of progression under those circumstances. By this mode of reasoning,
you would say of a man who makes use of crutches, that he was
originally destined to the misfortune of having a leg paralysed or
amputated."

[Note 113\17: "Je me garde de prêter à Dieu aucune intention."
_Phil. Zool._ 10.]

[Note 114\17: "Je ne connais point d'animal qui DOIVE jouer un rôle
dans la nature." p. 65.]

How far this doctrine of unity in the plan in animals, is admissible
or probable in physiology when kept within proper limits, that is,
when not put in opposition to the doctrine of a purpose involved in
the plan of animals, I do not pretend even to conjecture. The
question is one which appears to be at present deeply occupying the
minds of the most learned and profound physiologists; and such
persons alone, adding to their knowledge and zeal, judicial sagacity
and impartiality, can tell us what is the general tendency of the
best researches on this subject.[115\17] But when the anatomist
expresses such opinions, and defends them by such illustrations as
those which I have just quoted,[116\17] we perceive that he quits
the entrenchments of his superior science, in which he might {487}
have remained unassailable so long as the question was a
professional one; and the discussion is open to those who possess no
peculiar knowledge of anatomy. We shall, therefore, venture to say a
few words upon it.

[Note 115\17: So far as this doctrine is generally accepted among
the best physiologists, we cannot doubt the propriety of Meckel's
remark, (_Comparative Anatomy_, 1821, Pref. p. xi.) that it cannot
be truly asserted either to be new, or to be peculiarly due to
Geoffroy Saint-Hilaire.]

[Note 116\17: It is hardly worth while answering such illustrations,
but I may remark, that the one quoted above, irrelevant and
unbecoming as it is, tells altogether against its author. The fact
that the wooden leg is of the same length as the other, proves, and
would satisfy the most incredulous man, that it was _intended_ for
walking.]


_Sect._ 2.--_Estimate of the Doctrine of Unity of Plan._

IT has been so often repeated, and so generally allowed in modern
times, that Final Causes ought not to be made our guides in natural
philosophy, that a prejudice has been established against the
introduction of any views to which this designation can be applied,
into physical speculations. Yet, in fact, the assumption of an end
or purpose in the structure of organized beings, appears to be an
intellectual habit which no efforts can cast off. It has prevailed
from the earliest to the latest ages of zoological research; appears
to be fastened upon us alike by our ignorance and our knowledge; and
has been formally accepted by so many great anatomists, that we
cannot feel any scruple in believing the rejection of it to be the
superstition of a false philosophy, and a result of the exaggeration
of other principles which are supposed capable of superseding its
use. And the doctrine of unity of plan of all animals, and the other
principles associated with this doctrine, so far as they exclude the
conviction of an intelligible scheme and a discoverable end, in the
organization of animals, appear to be utterly erroneous. I will
offer a few reasons for an opinion which may appear presumptuous in
a writer who has only a general knowledge of the subject.

1. In the first place, it appears to me that the argumentation on
the case in question, the Sepia, does by no means turn out to the
advantage of the new hypothesis. The arguments in support of the
hypothetical view of the structure of this mollusc were, that by
this view the relative position of the parts was explained, and
confirmations which had appeared altogether anomalous, were reduced
to rule; for example, the beak, which had been supposed to be in a
position the reverse of all other beaks, was shown, by the assumed
posture, to have its upper mandible longer than the lower, and thus
to be regularly placed. "But," says Cuvier,[117\17] "supposing the
posture, in order that the side on which the funnel of the sepia is
folded should be the back of the animal, considered as similar to a
vertebrate, the brain with {488} regard to the beak, and the
œsophagus with regard to the liver, should have positions
corresponding to those in vertebrates; but the positions of these
organs are exactly contrary to the hypothesis. How, then, can you
say," he asks, "that the cephalopods and vertebrates have _identity
of composition_, _unity of composition_, without using words in a
sense entirely different from their common meaning?"

[Note 117\17: _G. S. H. Phil. Zool._ p. 70.]

This argument appears to be exactly of the kind on which the value
of the hypothesis must depend.[118\17] It is, therefore, interesting
to see the reply made to it by the theorist. It is this: "I admit
the facts here stated, but I deny that they lead to the notion of a
different sort of animal composition. Molluscous animals had been
placed too high in the zoological scale; but if they are only the
embryos of its lower stages, if they are only beings in which far
fewer organs come into play, it does not follow that the organs are
destitute of the relations which the power of successive generations
may demand. The organ A will be in an unusual relation with the
organ C, if B has not been produced;--if a stoppage of the
developement has fallen upon this latter organ, and has thus
prevented its production. And thus," he says, "we see how we may
have different arrangements, and divers constructions as they appear
to the eye."

[Note 118\17: I do not dwell on other arguments which were employed.
It was given as a circumstance suggesting the supposed posture of
the type, that in this way the back was colored, and the belly was
white. On this Cuvier observes (_Phil. Zool._ pp. 93, 68), "I must
say, that I do not know any naturalist so ignorant as to suppose
that the back is determined by its dark color, or even by its
position when the animal is in motion; they all know that the badger
has a black belly and a white back; that an infinity of other
animals, especially among insects, are in the same case; and that
many fishes swim on their side, or with their belly upwards."]

It seems to me that such a concession as this entirely destroys the
theory which it attempts to defend; for what arrangement does the
principle of unity of composition _exclude_, if it admits unusual,
that is, various arrangements of some organs, accompanied by the
total absence of others? Or how does this differ from Cuvier's mode
of stating the conclusion, except in the introduction of certain
arbitrary hypotheses of developement and stoppage? "I reduce the
facts," Cuvier says, "to their true expression, by saying that
Cephalopods have several organs which are common to them and
vertebrates, and which discharge the same offices; but that these
organs are in them differently distributed, and often constructed in
a different manner; {489} and they are accompanied by several other
organs which vertebrates have not; while these on the other hand
have several which are wanting in cephalopods."

We shall see afterwards the general principles which Cuvier himself
considered as the best guides in these reasonings. But I will first
add a few words on the disposition of the school now under
consideration, to reject all assumption of an end.

2. That the parts of the bodies of animals are made in order to
discharge their respective offices, is a conviction which we cannot
believe to be otherwise than an irremovable principle of the
philosophy of organization, when we see the manner in which it has
constantly forced itself upon the minds of zoologists and anatomists
in all ages; not only as an inference, but as a guide whose
indications they could not help following. I have already noticed
expressions of this conviction in some of the principal persons who
occur in the history of physiology, as Galen and Harvey. I might add
many more, but I will content myself with adducing a contemporary of
Geoffroy's whose testimony is the more remarkable, because he
obviously shares with his countryman in the common prejudice against
the use of final causes. "I consider," he says, in speaking of the
provisions for the reproduction of animals,[119\17] "with the great
Bacon, the philosophy of final causes as sterile; but I have
elsewhere acknowledged that it was very difficult for the most
cautious man never to have recourse to them in his explanations."
After the survey which we have had to take of the history of
physiology, we cannot but see that the assumption of final causes in
this branch of science is so far from being sterile, that it has had
a large share in every discovery which is included in the existing
mass of real knowledge. The use of every organ has been discovered
by starting from the assumption that it must have _some_ use. The
doctrine of the circulation of the blood was, as we have seen,
clearly and professedly due to the persuasion of a purpose in the
circulatory apparatus. The study of comparative anatomy is the study
of the adaption of animal structures to their purposes. And we shall
soon have to show that this conception of final causes has, in our
own times, been so far from barren, that it has, in the hands of
Cuvier and others, enabled us to become intimately acquainted with
vast departments of zoology to which we have no other mode of
access. It has placed before us in a complete state, {490} animals,
of which, for thousands of years, only a few fragments have existed,
and which differ widely from all existing animals; and it has given
birth, or at least has given the greatest part of its importance and
interest, to a science which forms one of the brightest parts of the
modern progress of knowledge. It is, therefore, very far from being
a vague and empty assertion, when we say that final causes are a
real and indestructible element in zoological philosophy; and that
the exclusion of them, as attempted by the school of which we speak,
is a fundamental and most mischievous error.

[Note 119\17: Cabanis, _Rapports du Physique et du Morale de
l'Homme_, i. **299.]

3. Thus, though the physiologist may persuade himself that he ought
not to refer to final causes, we find that, practically, he cannot
help doing this; and that the event shows that his practical habit
is right and well-founded. But he may still cling to the speculative
difficulties and doubts in which such subjects may be involved by _à
priori_ considerations. He may say, as Saint-Hilaire does
say,[120\17] "I ascribe no intention to God, for I mistrust the
feeble powers of my reason. I observe facts merely, and go no
further. I only pretend to the character of the historian of _what
is_." "I cannot make Nature an intelligent being who does nothing in
vain, who acts by the shortest mode, who does all for the best."

[Note 120\17: _Phil. Zool._ p. 10.]

I am not going to enter at any length into this subject, which, thus
considered, is metaphysical and theological, rather than
physiological. If any one maintain, as some have maintained, that no
manifestation of means apparently used for ends in nature, can prove
the existence of design in the Author of nature, this is not the
place to refute such an opinion in its general form. But I think it
may be worth while to show, that even those who incline to such an
opinion, still cannot resist the necessity which compels men to
assume, in organized beings, the existence of an end.

Among the philosophers who have referred our conviction of the being
of God to our moral nature, and have denied the possibility of
demonstration on mere physical grounds, Kant is perhaps the most
eminent. Yet he has asserted the reality of such a principle of
physiology as we are now maintaining in the most emphatic manner.
Indeed, this assumption of an end makes his very definition of an
organized being. "An organized product of nature is that in which
all the parts are mutually ends and means."[121\17] And this, he
says, is a universal and necessary maxim. He adds, "It is well known
that the {491} anatomizers of plants and animals, in order to
investigate their structure, and to obtain an insight into the
grounds why and to what end such parts, why such a situation and
connexion of the parts, and exactly such an internal form, come
before them, assume, as indispensably necessary, this maxim, that in
such a creature nothing is _in vain_, and proceed upon it in the
same way in which in general natural philosophy we proceed upon the
principle that _nothing happens by chance_. In fact, they can as
little free themselves from this _teleological_ principle as from
the general physical one; for as, on omitting the latter, no
experience would be possible, so on omitting the former principle,
no clue could exist for the observation of a kind of natural objects
which can be considered teleologically under the conception of
natural ends."

[Note 121\17: _Urtheilskraft_, p. 296.]

Even if the reader should not follow the reasoning of this
celebrated philosopher, he will still have no difficulty in seeing
that he asserts, in the most distinct manner, that which is denied
by the author whom we have before quoted, the propriety and
necessity of assuming the existence of an end as our guide in the
study of animal organization.

4. It appears to me, therefore, that whether we judge from the
arguments, the results, the practice of physiologists, their
speculative opinions, or those of the philosophers of a wider field,
we are led to the same conviction, that in the organized world we
may and must adopt the belief that organization exists for its
purpose, and that the apprehension of the purpose may guide us in
seeing the meaning of the organization. And I now proceed to show
how this principle has been brought into additional clearness and
use by Cuvier.

In doing this, I may, perhaps, be allowed to make a reflection of a
kind somewhat different from the preceding remarks, though suggested
by them. In another work,[122\17] I endeavored to show that those
who have been discoverers in science have generally had minds, the
disposition of which was to believe in an intelligent Maker of the
universe; and that the scientific speculations which produced an
opposite tendency, were generally those which, though they might
deal familiarly with known physical truths, and conjecture boldly
with regard to the unknown, did not add to the number of solid
generalizations. In order to judge whether this remark is distinctly
applicable in the case now considered, I should have to estimate
Cuvier in comparison with other physiologists of his time, which I
do not presume to do. But I may {492} observe, that he is allowed by
all to have established, on an indestructible basis, many of the
most important generalizations which zoology now contains; and the
principal defect which his critics have pointed out, has been, that
he did not generalize still more widely and boldly. It appears,
therefore, that he cannot but be placed among the great discoverers
in the studies which he pursued; and this being the case, those who
look with pleasure on the tendency of the thoughts of the greatest
men to an Intelligence far higher than their own, most be gratified
to find that he was an example of this tendency; and that the
acknowledgement of a creative purpose, as well as a creative power,
not only entered into his belief but made an indispensable and
prominent part of his philosophy.

[Note 122\17: _Bridgewater Treatise_, B. iii. c. vii. and viii. On
Inductive Habits of Thought, and on Deductive Habits of Thought.]


_Sect._ 3.--_Establishment and Application of the Principle of the
Conditions of Existence of Animals.--Cuvier._

WE have now to describe more in detail the doctrine which Cuvier
maintained in opposition to such opinions as we have been speaking
of; and which, in his way of applying it, we look upon as a material
advance in physiological knowledge, and therefore give to it a
distinct place in our history. "Zoology has," he says,[123\17] in
the outset of his _Règne Animal_, "a principle of reasoning which is
peculiar to it, and which it employs with advantage on many
occasions: this is the principle of _the Conditions of Existence_,
vulgarly the principle of _Final Causes_. As nothing can exist if it
do not combine all the conditions which render its existence
possible, the different parts of each being must be co-ordinated in
such a manner as to render the total being possible, not only in
itself, but in its relations to those which surround it; and the
analysis of these conditions often leads to general laws, as clearly
demonstrated as those which result from calculation or from
experience."

[Note 123\17: _Règne An._ p. 6.]

This is the enunciation of his leading principle in general terms.
To our ascribing it to him, some may object on the ground of its
being self-evident in its nature,[124\17] and having been very
anciently applied. But to this we reply, that the principle must be
considered as a real discovery in the hands of him who first shows
how to make it an instrument of other discoveries. It is true, in
other cases as well as in this, that some vague apprehension, of
true general principles, such as _à_ {493} _priori_ considerations
can supply, has long preceded the knowledge of them as real and
verified laws. In such a way it was seen, before Newton, that the
motions of the planets must result from attraction; and so, before
Dufay and Franklin, it was held that electrical actions must result
from a fluid. Cuvier's merit consisted, not in seeing that an animal
cannot exist without combining all the conditions of its existence;
but in perceiving that this truth may be taken as a guide in our
researches concerning animals;--that the mode of their existence may
be collected from one part of their structure, and then applied to
interpret or detect another part. He went on the supposition not
only that animal forms have _some_ plan, _some_ purpose, but that
they have an intelligible plan, a discoverable purpose. He proceeded
in his investigations like the decipherer of a manuscript, who makes
out his alphabet from one part of the context, and then applies it
to read the rest. The proof that his principle was something very
different from an identical proposition, is to be found in the fact,
that it enabled him to understand and arrange the structures of
animals with unprecedented clearness and completeness of order; and
to restore the forms of the extinct animals which are found in the
rocks of the earth, in a manner which has been universally assented
to as irresistibly convincing. These results cannot flow from a
trifling or barren principle; and they show us that if we are
disposed to form such a judgment of Cuvier's doctrine, it must be
because we do not fully apprehend its import.

[Note 124\17: Swainson. _Study of Nat. Hist._ p. 85.]

To illustrate this, we need only quote the statement which he makes,
and the uses to which he applies it. Thus in the Introduction to his
great work on _Fossil Remains_ he says, "Every organized being forms
an entire system of its own, all the parts of which mutually
correspond, and concur to produce a certain definite purpose by
reciprocal reaction, or by combining to the same end. Hence none of
these separate parts can change their forms without a corresponding
change in the other parts of the same animal; and consequently each of
these parts, taken separately, indicates all the other parts to which
it has belonged. Thus, if the viscera of an animal are so organized as
only to be fitted for the digestion of recent flesh, it is also
requisite that the jaws should be so constructed as to fit them for
devouring prey; the claws must be constructed for seizing it and
tearing it to pieces; the teeth for cutting and dividing its flesh;
the entire system of the limbs or organs of motion for pursuing and
overtaking it; and the organs of sense for discovering it at a
distance. Nature must also have endowed the brain of the animal with
instincts sufficient for concealing itself and for laying plans to
{494} catch its necessary victims."[125\17] By such considerations he
has been able to reconstruct the whole of many animals of which parts
only were given;--a positive result, which shows both the reality and
the value of the truth on which he wrought.

[Note 125\17: _Theory of the Earth_, p. 90.]

Another great example, equally showing the immense importance of
this principle in Cuvier's hands, is the reform which, by means of
it, he introduced into the classification of animals. Here again we
may quote the view he himself has given[126\17] of the character of
his own improvements. In studying the physiology of the natural
classes of vertebrate animals, he found, he says, "in the respective
quantity of their respiration, the reason of the quantity of their
motion, and consequently of the kind of locomotion. This, again,
furnishes the reason for the forms of their skeletons and muscles;
and the energy of their senses, and the force of their digestion,
are in a necessary proportion to the same quantity. Thus a division
which had till then been established, like that of vegetables, only
upon observation, was found to rest upon causes appreciable, and
applicable to other cases." Accordingly, he applied this view to
invertebrates;--examined the modifications which take place in their
organs of circulation, respiration, and sensation; and having
calculated the necessary results of these modifications, he deduced
from it a new division of those animals, in which they are arranged
according to their true relations.

[Note 126\17: _Hist. Sc. Nat._ i. 293.]

Such have been some of the results of the principle of the
Conditions of Existence, as applied by its great assertor.

It is clear, indeed, that such a principle could acquire its
practical value only in the hands of a person intimately acquainted
with anatomical details, with the functions of the organs, and with
their variety in different animals. It is only by means of such
nutriment that the embryo truth could be developed into a vast tree
of science. But it is not the less clear, that Cuvier's immense
knowledge and great powers of thought led to their results, only by
being employed under the guidance of this master-principle: and,
therefore, we may justly consider it as the distinctive feature of
his speculations, and follow it with a gratified eye, as the thread
of gold which runs through, connects, and enriches his zoological
researches:--gives them a deeper interest and a higher value than
can belong to any view of the organical sciences, in which the very
essence of organization is kept out of sight. {495}

The real philosopher, who knows that all the kinds of truth are
intimately connected, and that all the best hopes and encouragements
which are granted to our nature must be consistent with truth, will be
satisfied and confirmed, rather than surprised and disturbed, thus to
find the Natural Sciences leading him to the borders of a higher
region. To him it will appear natural and reasonable, that after
journeying so long among the beautiful and orderly laws by which the
universe is governed, we find ourselves at last approaching to a
Source of order and law, and intellectual beauty:--that, after
venturing into the region of life and feeling and will, we are led to
believe the Fountain of life and will not to be itself unintelligent
and dead, but to be a living Mind, a Power which aims as well as acts.
To us this doctrine appears like the natural cadence of the tones to
which we have so long been listening; and without such a final strain
our ears would have been left craving and unsatisfied. We have been
lingering long amid the harmonies of law and symmetry, constancy and
development; and these notes, though their music was sweet and deep,
must too often have sounded to the ear of our moral nature, as vague
and unmeaning melodies, floating in the air around us, but conveying
no definite thought, moulded into no intelligible announcement. But
one passage which we have again and again caught by snatches, though
sometimes interrupted and lost, at last swells in our ears full,
clear, and decided; and the religious "Hymn in honor of the Creator,"
to which Galen so gladly lent his voice, and in which the best
physiologists of succeeding times have ever joined, is filled into a
richer and deeper harmony by the greatest philosophers of these later
days, and will roll on hereafter the "perpetual song" of the temple of
science.



{{497}}
BOOK XVIII.


_THE PALÆTIOLOGICAL SCIENCES._


HISTORY OF GEOLOGY.


  Di quibus imperium est animarum, Umbræque silentes,
  Et Chaos, et Phlegethon, loca nocte silentia late,
  Sit mihi fas audita loqui; sit, numine vestro
  Pandere res alta terrâ et caligine mersas.
          VIRGIL. _Æn._ vi. 264.

  Ye Mighty Ones, who sway the Souls that go
  Amid the marvels of the world below!
  Ye, silent Shades, who sit and hear around!
  Chaos! and Streams that burn beneath the ground!
  All, all forgive, if by your converse stirred,
  My lips shall utter what my ears have heard;
  If I shall speak of things of doubtful birth,
  Deep sunk in darkness, as deep sunk in earth.



{{499}}
INTRODUCTION.


_Of the Palætiological Sciences._

WE now approach the last Class of Sciences which enter into the
design of the present work; and of these, Geology is the
representative, whose history we shall therefore briefly follow. By
the Class of Sciences to which I have referred it, I mean to point
out those researches in which the object is, to ascend from the
present state of things to a more ancient condition, from which the
present is derived by intelligible causes.

The sciences which treat of causes have sometimes been termed
_ætiological_, from αἰτία, _a cause_: but this term would not
sufficiently describe the speculations of which we now speak; since
it might include sciences which treat of Permanent Causality, like
Mechanics, as well as inquiries concerning Progressive Causation.
The investigations which I now wish to group together, deal, not
only with the possible, but with the actual past; and a portion of
that science on which we are about to enter, Geology, has properly
been termed _Palæontology_, since it treats of beings which formerly
existed.[1\18] Hence, combining these two notions,[2\18]
_Palætiology_ appears to be a term not inappropriate, to describe
those speculations which thus refer to actual past events, and
attempt to explain them by laws of causation.

[Note 1\18: Πάλαι, ὄντα]

[Note 2\18: Πάλαι, αἰτία]

Such speculations are not confined to the world of inert matter; we
have examples of them in inquiries concerning the monuments of the
art and labor of distant ages; in examinations into the origin and
early progress of states and cities, customs and languages; as well
as in researches concerning the causes and formations of mountains
and rocks, the imbedding of fossils in strata, and their elevation
from the bottom of the ocean. All these speculations are connected
by this bond,--that they endeavor to ascend to a past state of
things, by the aid of the evidence of the present. In asserting,
with Cuvier, that {500} "The geologist is an antiquary of a new
order," we do not mark a fanciful and superficial resemblance of
employment merely, but a real and philosophical connexion of the
principles of investigation. The organic fossils which occur in the
rock, and the medals which we find in the ruins of ancient cities,
are to be studied in a similar spirit and for a similar purpose.
Indeed, it is not always easy to know where the task of the
geologist ends, and that of the antiquary begins. The study of
ancient geography may involve us in the examination of the causes by
which the forms of coasts and plains are changed; the ancient mound
or scarped rock may force upon us the problem, whether its form is
the work of nature or of man; the ruined temple may exhibit the
traces of time in its changed level, and sea-worn columns; and thus
the antiquarian of the earth may be brought into the very middle of
the domain belonging to the antiquarian of art.

Such a union of these different kinds of archæological
investigations has, in fact, repeatedly occurred. The changes which
have taken place in the temple of Jupiter Serapis, near Puzzuoli,
are of the sort which have just been described; and this is only one
example of a large class of objects;--the monuments of art converted
into records of natural events. And on a wider scale, we find
Cuvier, in his inquiries into geological changes, bringing together
historical and physical evidence. Dr. Prichard, in his _Researches
into the Physical History of Man_, has shown that to execute such a
design as his, we must combine the knowledge of the physiological
laws of nature with the traditions of history and the philosophical
comparison of languages. And even if we refuse to admit, as part of
the business of geology, inquiries concerning the origin and
physical history of the present population of the globe; still the
geologist is compelled to take an interest in such inquiries, in
order to understand matters which rigorously belong to his proper
domain; for the ascertained history of the present state of things
offers the best means of throwing light upon the causes of _past_
changes. Mr. Lyell quotes Dr. Prichard's book more frequently than
any geological work of the same extent.

Again, we may notice another common circumstance in the studies
which we are grouping together as palætiological, diverse as they
are in their subjects. In all of them we have the same kind of
manifestations of a number of successive changes, each springing out
of a preceding state; and in all, the phenomena at each step become
more and more complicated, by involving the results of all that has
preceded, modified by supervening agencies. The general aspect of
all these {501} trains of change is similar, and offers the same
features for description. The relics and ruins of the earlier states
are preserved, mutilated and dead, in the products of later times.
The analogical figures by which we are tempted to express this
relation are philosophically true. It is more than a mere fanciful
description, to say that in languages, customs, forms of Society,
political institutions, we see a number of formations super-imposed
upon one another, each of which is, for the most part, an assemblage
of fragments and results of the preceding condition. Though our
comparison might be bold, it would be just, if we were to assert,
that the English language is a conglomerate of Latin words, bound
together in a Saxon cement; the fragments of the Latin being partly
portions introduced directly from the parent quarry, with all their
sharp edges, and partly pebbles of the same material, obscured and
shaped by long rolling in a Norman or some other channel. Thus the
study of palætiology in the materials of the earth, is only a type
of similar studies with respect to all the elements, which, in the
history of the earth's inhabitants, have been constantly undergoing
a series of connected changes.

But, wide as is the view which such considerations give us of the
class of sciences to which geology belongs, they extend still
further. "The science of the changes which have taken place in the
organic kingdoms of nature," (such is the description which has been
given of Geology,[3\18]) may, by following another set of
connexions, be extended beyond "the modifications of the surface of
our own planet." For we cannot doubt that some resemblance of a
closer or looser kind, has obtained between the changes and causes
of change, on other bodies of the universe, and on our own. The
appearances of something of the kind of volcanic action on the
surface of the moon, are not to be mistaken. And the inquiries
concerning the origin of our planet and of our solar system,
inquiries to which Geology irresistibly impels her students, direct
us to ask what information the rest of the universe can supply,
bearing upon this subject. It has been thought by some, that we can
trace systems, more or less like our solar system, in the process of
formation; the nebulous matter, which is at first expansive and
attenuated, condensing gradually into suns and planets. Whether this
_Nebular Hypothesis_ be tenable or not, I shall not here inquire;
but the discussion of such a question would be closely connected
with {502} geology, both in its interests and in its methods. If men
are ever able to frame a science of the past changes by which the
universe has been brought into its present condition, this science
will be properly described as _Cosmical Palætiology_.

[Note 3\18: Lyell, _Principles of Geology_, p. 1.]

These palætiological sciences might properly be called _historical_,
if that term were sufficiently precise: for they are all of the
nature of history, being concerned with the succession of events:
and the part of history which deals with the past causes of events,
is, in fact, a moral palætiology. But the phrase _Natural History_
has so accustomed us to a use of the word _history_ in which we have
nothing to do with time, that, if we were to employ the word
_historical_ to describe the palætiological sciences, it would be in
constant danger of being misunderstood. The fact is, as Mohs has
said, that Natural History, when systematically treated, rigorously
excludes all that is _historical_; for it classes objects by their
permanent and universal properties, and has nothing to do with the
narration of particular and casual facts. And this is an
inconsistency which we shall not attempt to rectify.

All palætiological sciences, since they undertake to refer changes
to their causes, assume a certain classification of the phenomena
which change brings forth, and a knowledge of the operation of the
causes of change. These phenomena, these causes, are very different,
in the branches of knowledge which I have thus classed together. The
natural features of the earth's surface, the works of art, the
institutions of society, the forms of language, taken together, are
undoubtedly a very wide collection of subjects of speculation; and
the kinds of causation which apply to them are no less varied. Of
the causes of change in the inorganic and organic world,--the
peculiar principles of Geology--we shall hereafter have to speak. As
these must be studied by the geologist, so, in like manner, the
tendencies, instincts, faculties, principles, which direct man to
architecture and sculpture, to civil government, to rational and
grammatical speech, and which have determined the circumstances of
his progress in these paths, must be in a great degree known to the
Palætiologist of Art, of Society, and of Language, respectively, in
order that he may speculate soundly upon his peculiar subject. With
these matters we shall not here meddle, confining ourselves, in our
exemplification of the conditions and progress of such sciences, to
the case of Geology.

The journey of survey which we have attempted to perform over the
field of human knowledge, although carefully directed according to
the paths and divisions of the physical sciences, has already {503}
conducted us to the boundaries of physical science, and gives us a
glimpse of the region beyond. In following the history of Life, we
found ourselves led to notice the perceptive and active faculties of
man; it appeared that there was a ready passage from physiology to
psychology, from physics to metaphysics. In the class of sciences
now under notice, we are, at a different point, carried from the
world of matter to the world of thought and feeling,--from things to
men. For, as we have already said, the science of the causes of
change includes the productions of Man as well as of Nature. The
history of the earth, and the history of the earth's inhabitants, as
collected from phenomena, are governed by the same principles. Thus
the portions of knowledge which seek to travel back towards the
origin, whether of inert things or of the works of man, resemble
each other. Both of them treat of events as connected by the thread
of time and causation. In both we endeavor to learn accurately what
the present is, and hence what the past has been. Both are
_historical_ sciences in the same sense.

It must be recollected that I am now speaking of history as
ætiological;--as it investigates causes, and as it does this in a
scientific, that is, in a rigorous and systematic, manner. And I may
observe here, though I cannot now dwell on the subject, that all
ætiological sciences will consist of three portions; the Description
of the facts and phenomena;--the general Theory of the causes of
change appropriate to the case;--and the Application of the theory
to the facts. Thus, taking Geology for our example, we must have,
first _Descriptive_ or _Phenomenal_ Geology; next, the exposition of
the general principles by which such phenomena can be produced,
which we may term _Geological Dynamics_; and, lastly, doctrines
hence derived, as to what have been the causes of the existing state
of things, which we may call _Physical Geology_.

These three branches of geology may be found frequently or
constantly combined in the works of writers on the subject, and it
may not always be easy to discriminate exactly what belongs to each
subject.[4\18] But the analogy of this science with others, its
present {504} condition and future fortunes, will derive great
illustration from such a distribution of its history; and in this
point of view, therefore, we shall briefly treat of it; dividing the
history of Geological Dynamics, for the sake of convenience, into
two Chapters, one referring to inorganic, and one to organic,
phenomena.

[Note 4\18: The Wernerians, in distinguishing their study from
_Geology_, and designating it as _Geognosy_, the _knowledge_ of the
earth, appear to have intended to select Descriptive Geology for
their peculiar field. In like manner, the original aim of the
Geological Society of London, which was formed (1807) "with a view
to record and multiply observations," recognized the possibility of
a Descriptive Geology separate from the other portions of the
science.]



{{505}}
DESCRIPTIVE GEOLOGY.




CHAPTER I.

PRELUDE TO SYSTEMATIC DESCRIPTIVE GEOLOGY.


_Sect._ 1.--_Ancient Notices of Geological Facts._

THE recent history of Geology, as to its most important points, is
bound up with what is doing at present from day to day; and that
portion of the history of the science which belongs to the past, has
been amply treated by other writers.[5\18] I shall, therefore, pass
rapidly over the series of events of which this history consists;
and shall only attempt to mention what may seem to illustrate and
confirm my own view of its state and principles.

[Note 5\18: As MM. Lyell, Fitton, Conybeare, in our own country.]

Agreeably to the order already pointed out, I shall notice, in the
first place, Phenomenal Geology, or the description of the facts, as
distinct from the inquiry into their causes. It is manifest that
such a merely descriptive kind of knowledge may exist; and it
probably will not be contested, that such knowledge ought to be
collected, before we attempt to frame theories concerning the causes
of the phenomena. But it must be observed, that we are here speaking
of the formation of a _science_; and that it is not a collection of
miscellaneous, unconnected, unarranged knowledge that can be
considered as constituting science; but a methodical, coherent, and,
as far as possible, complete body of facts, exhibiting fully the
condition of the earth as regards those circumstances which are the
subject matter of geological speculation. Such a Descriptive Geology
is a pre-requisite to Physical Geology, just as Phenomenal Astronomy
necessarily preceded Physical Astronomy, or as Classificatory Botany
is a necessary accompaniment to Botanical Physiology. We may observe
also that Descriptive Geology, such as we now speak of, is one of
the classificatory sciences, like {506} Mineralogy or Botany: and
will be found to exhibit some of the features of that class of
sciences.

Since, then, our History of Descriptive Geology is to include only
systematic and scientific descriptions of the earth or portions of
it, we pass over, at once, all the casual and insulated statements
of facts, though they may be geological facts, which occur in early
writers; such, for instance, as the remark of Herodotus,[6\18] that
there are shells in the mountains of Egypt; or the general
statements which Ovid puts in the mouth of Pythagoras:[7\18]
    Vidi ego quod fuerat solidissima tellus,
  Esse fretum; vidi factas ex æquore terras,
  Et procul a pelago conchæ jacuere marinæ.

[Note 6\18: ii. 12.]

[Note 7\18: Met. xv. 262.]

We may remark here already how generally there are mingled with
descriptive notices of such geological facts, speculations
concerning their causes. Herodotus refers to the circumstance just
quoted, for the purpose of showing that Egypt was formerly a gulf of
the sea; and the passage of the Roman poet is part of a series of
exemplifications which he gives of the philosophical tenet, that
nothing perishes but everything changes. It will be only by constant
attention that we shall be able to keep our provinces of geology
distinct.


_Sect._ 2.--_Early Descriptions and Collections of Fossils._

IF we look, as we have proposed to do, for systematic and exact
knowledge of geological facts, we find nothing which we can properly
adduce till we come to modern times. But when facts such as those
already mentioned, (that sea-shells and other marine objects are
found imbedded in rocks,) and other circumstances in the structure
of the Earth, had attracted considerable attention, the exact
examination, collection, and record of these circumstances began to
be attempted. Among such steps in Descriptive Geology, we may notice
descriptions and pictures of fossils, descriptions of veins and
mines, collections of organic and inorganic fossils, maps of the
mineral structure of countries, and finally, the discoveries
concerning the superposition of strata, the constancy of their
organic contents, their correspondence in different countries, and
such great general relations of the materials and features of the
earth as have been discovered up to the present time. {507} Without
attempting to assign to every important advance its author, I shall
briefly exemplify each of the modes of contributing to descriptive
geology which I have just enumerated.

The study of organic fossils was first pursued with connexion and
system in Italy. The hills which on each side skirt the
mountain-range of the Apennines are singularly rich in remains of
marine animals. When these remarkable objects drew the attention of
thoughtful men, controversies soon arose whether they really were
the remains of living creatures, or the productions of some
capricious or mysterious power by which the forms of such creatures
were mimicked; and again, if the shells were really the spoils of
the sea, whether they had been carried to the hills by the deluge of
which the Scripture speaks, or whether they indicated revolutions of
the earth of a different kind. The earlier works which contain the
descriptions of the phenomena have, in almost all instances, by far
the greater part of their pages occupied with these speculations;
indeed, the facts could not be studied without leading to such
inferences, and would not have been collected but for the interest
which such reasonings possessed. As one of the first persons who
applied a sound and vigorous intellect to these subjects, we may
notice the celebrated painter Leonardo da Vinci, whom we have
already had to refer to as one of the founders of the modern
mechanical sciences. He strenuously asserts the contents of the
rocks to be real shells, and maintains the reality of the changes of
the domain of land and sea which these spoils of the ocean imply.
"You will tell me," he says, "that nature and the influence of the
stars have formed these shelly forms in the mountains; then show me
a place in the mountains where the stars at the present day make
shelly forms of different ages, and of different species in the same
place. And how, with that, will you explain the gravel which is
hardened in stages at different heights in the mountains?" He then
mentions several other particulars respecting these evidences that
the existing mountains were formerly in the bed of the sea. Leonardo
died in 1519. At present we refer to geological essays like his,
only so far as they are descriptive. Going onwards with this view,
we may notice Fracastoro, who wrote concerning the petrifactions
which were brought to light in the mountains of Verona, when, in
1517, they were excavated for the purpose of repairing the city.
Little was done in the way of collection of facts for some time
after this. In 1669, Steno, a Dane resident in Italy, put forth his
treatise, _De Solido intra Solidum naturaliter contento_; and the
{508} following year, Augustino Scilla, a Sicilian painter,
published a Latin epistle, _De Corporibus Marinis Lapidescentibus_,
illustrated by good engravings of fossil-shells, teeth, and
corals.[8\18] After another interval of speculative controversy, we
come to Antonio Vallisneri, whose letters, _De' Corpi Marini che su'
Monti si trovano_, appeared at Venice in 1721. In these letters he
describes the fossils of Monte Bolca, and attempts to trace the
extent of the marine deposits of Italy,[9\18] and to distinguish the
most important of the fossils. Similar descriptions and figures were
published with reference to our own country at a later period. In
1766, Brander's _Fossilia Hantoniensia_, or Hampshire Fossils,
appeared; containing excellent figures of fossil shells from a part
of the south coast of England; and similar works came forth in other
parts of Europe.

[Note 8\18: Augustine Scilla's original drawings of fossil shells,
teeth, and corals, from which the engravings mentioned in the text
were executed, as well as the natural objects from which the
drawings were made, were bought by Woodward, and are now in the
Woodwardian Museum at Cambridge.]

[Note 9\18: p. 20.]

However exact might be the descriptions and figures thus produced,
they could not give such complete information as the objects
themselves, collected and permanently preserved in museums.
Vallisneri says,[10\18] that having begun to collect fossils for the
purpose of forming a grotto, he selected the best, and preserved
them "as a noble diversion for the more curious." The museum of
Calceolarius at Verona contained a celebrated collection of such
remains. A copious description of it appeared in 1622. Such
collections had been made from an earlier period, and catalogues of
them published. Thus Gessner's work, _De Rerum Fossilium, Lapidum et
Gemmarum Figuris_ (1565), contains a catalogue of the cabinet of
petrifactions collected by John Kentman; many catalogues of the same
kind appeared in the seventeenth century.[11\18] Lhwyd's
_**Lythophylacii Britannici Iconographia_, published at Oxford in
1669, and exhibiting a very ample catalogue of English Fossils
contained in the Ashmolean Museum, may be noticed as one of these.

[Note 10\18: p. 1.]

[Note 11\18: Parkinson, _Organic Remains_, vol. i. p. 20.]

One of the most remarkable occurrences in the progress of
descriptive geology in England, was the formation of a geological
museum by William Woodward as early as 1695. This collection, formed
with great labor, systematically arranged, and carefully catalogued,
he bequeathed to the University of Cambridge; founding and endowing
{509} at the same time a professorship of the study of geology. The
Woodwardian Museum still subsists, a monument of the sagacity with
which its author so early saw the importance of such a collection.

Collections and descriptions of fossils, including in the term
specimens of minerals of all kinds, as well as organic remains, were
frequently made, and especially in places where mining was
cultivated; but under such circumstances, they scarcely tended at
all to that general and complete knowledge of the earth of which we
are now tracing the progress.

In more modern times, collections may be said to be the most
important books of the geologist, at least next to the strata
themselves. The identifications and arrangements of our best
geologists, the immense studies of fossil anatomy by Cuvier and
others, have been conducted mainly by means of collections of
specimens. They are more important in this study than in botany,
because specimens which contain important geological information are
both more rare and more permanent. Plants, though each individual is
perishable, perpetuate and diffuse their kind; while the organic
impression on a stone, if lost, may never occur in a second
instance; but, on the other hand, if it be preserved in the museum,
the individual is almost as permanent in this case, as the species
in the other.

I shall proceed to notice another mode in which such information was
conveyed.


_Sect._ 3.--_First Construction of Geological Maps._

DR. LISTER, a learned physician, sent to the Royal Society, in 1683,
a proposal for maps of soils or minerals; in which he suggested that
in the map of England, for example, each soil and its boundaries
might be distinguished by color, or in some other way. Such a mode
of expressing and connecting our knowledge of the materials of the
earth was, perhaps, obvious, when the mass of knowledge became
considerable. In 1720, Fontenelle, in his observations on a paper of
De Reaumur's, which contained an account of a deposit of
fossil-shells in Touraine, says, that in order to reason on such
cases, "we must have a kind of geographical charts, constructed
according to the collection of shells found in the earth." But he
justly adds, "What a quantity of observations, and what time would
it not require to form such maps!"

The execution of such projects required, not merely great labor, but
{510} several steps in generalization and classification, before it
could take place. Still such attempts were made. In 1743, was
published, _A new Philosophico-chorographical Chart of East Kent,
invented and delineated_ by Christopher Packe, M.D.; in which,
however, the main object is rather to express the course of the
valleys than the materials of the country. Guettard formed the
project of a mineralogical map of France, and Monnet carried this
scheme into effect in 1780,[12\18] "by order of the king." In these
maps, however, the country is not considered as divided into soils,
still less strata; but each part is marked with its predominant
mineral only. The spirit of generalization which constitutes the
main value of such a work is wanting.

[Note 12\18: _Atlas et Description Minéralogique de la France,
entrepris par ordre du Roi_, par MM. Guettard et Monnet, Paris,
1780, pp. 212, with 31 maps.]

Geological maps belong strictly to Descriptive Geology; they are
free from those wide and doubtful speculations which form so large a
portion of the earlier geological books. Yet even geological maps
cannot be usefully or consistently constructed without considerable
steps of classification and generalization. When, in our own time,
geologists were become weary of controversies respecting theory,
they applied themselves with extraordinary zeal to the construction
of stratigraphical maps of various countries; flattering themselves
that in this way they were merely recording incontestable facts and
differences. Nor do I mean to intimate that their facts were
doubtful, or their distinctions arbitrary. But still they were facts
interpreted, associated, and represented, by means of the
classifications and general laws which earlier geologists had
established; and thus even Descriptive Geology has been brought into
existence as a science by the formation of systems and the discovery
of principles. At this we cannot be surprized, when we recollect the
many steps which the formation of Classificatory Botany required. We
must now notice some of the discoveries which tended to the
formation of Systematic Descriptive Geology. {511}




CHAPTER II.

FORMATION OF SYSTEMATIC DESCRIPTIVE GEOLOGY.


_Sect._ 1.--_Discovery of the Order and Stratification of the
Materials of the Earth._

THAT the substances of which the earth is framed are not scattered
and mixed at random, but possess identity and continuity to a
considerable extent, Lister was aware, when he proposed his map. But
there is, in his suggestions, nothing relating to stratification;
nor any order of position, still less of time, assigned to these
materials. Woodward, however, appears to have been fully aware of
the general law of stratification. On collecting information from
all parts, "the result was," he says, "that in time I was abundantly
assured that the circumstances of these things in remoter countries
were much the same with those of ours here: that the stone, and
other terrestrial matter in France, Flanders, Holland, Spain, Italy,
Germany, Denmark, and Sweden, was distinguished into _strata or
layers_, as it is in England; that these strata were divided by
parallel fissures; that there were enclosed in the stone and all the
other denser kinds of terrestrial matter, great numbers of the
shells, and other productions of the sea, in the same manner as in
that of this island."[13\18] So remarkable a truth, thus collected
from a copious collection of particulars by a patient induction, was
an important step in the science.

[Note 13\18: _Natural History of the Earth_, 1723.]

These general facts now began to be commonly recognized, and followed
into detail. **Stukeley the antiquary[14\18] (1724), remarked an
important feature in the strata of England, that their _escarpments_,
or steepest sides, are turned towards the west and north-west; and
Strachey[15\18] (1719), gave a stratigraphical description of certain
coal-mines near Bath.[16\18] Michell, appointed Woodwardian Professor
at Cambridge {512} in 1762, described this stratified structure of the
earth far more distinctly than his predecessors, and pointed out, as
the consequence of it, that "the same kinds of earths, stones, and
minerals, will appear at the surface of the earth in long parallel
slips, parallel to the long ridges of mountains; and so, in fact, we
find them."[17\18]

[Note 14\18: _Itinerarium Curiosum_, 1724.]

[Note 15\18: _Phil. Trans._ 1719, and _Observations on Strata, &c._
1729.]

[Note 16\18: Fitton, _Annals of Philosophy_, N. S. vol. i. and ii.
(1832, '3), p.  157.]

[Note 17\18: _Phil. Trans._ 1760.]

Michell (as appeared by papers of his which were examined after his
death) had made himself acquainted with the series of English strata
which thus occur from Cambridge to York;--that is, from the chalk to
the coal. These relations of position required that geological maps,
to complete the information they conveyed, should be accompanied by
geological _Sections_, or imaginary representations of the order and
mode of superpositions, as well as of the superficial extent of the
strata, as in more recent times has usually been done. The strata,
as we travel from the higher to the lower, come from under each
other into view; and this _out-cropping_, _basseting_, or by
whatever other term it is described, is an important feature in
their description.

It was further noticed that these relations of position were
combined with other important facts, which irresistibly suggested
the notion of a relation in time. This, indeed, was implied in all
theories of the earth; but observations of the facts most require
our notice. Steno is asserted by Humboldt[18\18] to be the first who
(in 1669) distinguished between rocks anterior to the existence of
plants and animals upon the globe, containing therefore no organic
remains; and rocks super-imposed on these, and full of such remains;
"turbidi maris sedimenta sibi invicem imposita".

[Note 18\18: _Essai **Géognostique_.]

Rouelle is stated, by his pupil Desmarest, to have made some
additional and important observations. "He saw," it is said, "that
the shells which occur in rocks were not the same in all countries;
that certain species occur together, while others do not occur in
the same beds; that there is a constant order in the arrangement of
these shells, certain species lying in distinct bands."[19\18]

[Note 19\18: _Encycl. Méthod. Geogr. Phys._ tom. i. p. 416, as
quoted by Fitton as above, p. 159.]

Such divisions as these required to be marked by technical names. A
distinction was made of _l'ancienne terre_ and _la nouvelle terre_,
to which Rouelle added a _travaille intermédiaire_. Rouelle died in
1770, having been known by lectures, not by books. Lehman, in 1756,
claims for himself the credit of being the first to observe and
describe correctly the structure of stratified countries; being
ignorant, {513} probably, of the labors of Strachey in England. He
divided mountains into three classes;[20\18] _primitive_, which were
formed with the world;--those which resulted from a partial
destruction of the primitive rocks;--and a third class resulting
from local or universal deluges. In 1759, also, Arduine,[21\18] in
his Memoirs on the mountains of Padua, Vicenza, and Verona, deduced,
from original observations, the distinction of rocks into _primary_,
_secondary_, and _tertiary_.

[Note 20\18: Lyell, i. 70.]

[Note 21\18: Ib. 72.]

The relations of position and fossils were, from this period,
inseparably connected with opinions concerning succession in time.
Odoardi remarked,[22\18] that the strata of the **Sub-Apennine hills
are _unconformable_ to those of the Apennine, (as Strachey had
observed, that the strata above the coal were unconformable to the
coal;[23\18]) and his work contained a clear argument respecting the
different ages of these two classes of hills. Fuchsel was, in 1762,
aware of the distinctness of strata of different ages in Germany.
Pallas and Saussure were guided by general views of the same kind in
observing the countries which they visited: but, perhaps, the
general circulation of such notions was most due to Werner.

[Note 22\18: Ib. 74.]

[Note 23\18: Fitton, p. 157.]


_Sect._ 2.--_Systematic form given to Descriptive Geology.--Werner._

WERNER expressed the general relations of the strata of the earth by
means of classifications which, so far as general applicability is
concerned, are extremely imperfect and arbitrary; he promulgated a
theory which almost entirely neglected all the facts previously
discovered respecting the grouping of fossils,--which was founded
upon observations made in a very limited district of Germany,--and
which was contradicted even by the facts of this district. Yet the
acuteness of his discrimination in the subjects which he studied,
the generality of the tenets he asserted, and the charm which he
threw about his speculations, gave to Geology, or, as he termed it,
_Geognosy_, a popularity and reputation which it had never before
possessed. His system had asserted certain universal formations,
which followed each other in a constant order;--granite the
lowest,--then mica-slate and clay-slate;--upon these _primitive_
rocks, generally highly inclined, rest other _transition_
strata;--upon these, lie _secondary_ ones, which being more nearly
horizontal, are called _flötz_ or flat. The term _formation_, {514}
which we have thus introduced, indicating groups which, by evidence
of all kinds,--of their materials, their position, and their organic
contents,--are judged to belong to the same period, implies no small
amount of theory: yet this term, from this time forth, is to be
looked upon as a term of classification solely, so far as
classification can be separately attended to.

Werner's distinctions of strata were for the most part drawn from
mineralogical constitution. Doubtless, he could not fail to perceive
the great importance of organic fossils. "I was witness," says M. de
Humboldt, one of his most philosophical followers, "of the lively
satisfaction which he felt when, in 1792, M. de **Schlottheim, one of
the most distinguished geologists of the school of Freiberg, began
to make the relations of fossils to strata the principal object of
his studies." But Werner and the disciples of his school, even the
most enlightened of them, never employed the characters derived from
organic remains with the same boldness and perseverance as those who
had from the first considered them as the leading phenomena: thus M.
de Humboldt expresses doubts which perhaps many other geologists do
not feel when, in 1823, he says, "Are we justified in concluding
that all formations are characterized by particular species? that
the fossil-shells of the chalk, the muschelkalk, the Jura limestone,
and the Alpine limestone, are all different? I think this would be
pushing the induction much too far."[24\18] In Prof. Jamieson's
_Geognosy_, which may be taken as a representation of the Wernerian
doctrines, organic fossils are in no instance referred to as
characters of formations or strata. After the curious and important
evidence, contained in organic fossils, which had been brought into
view by the labors of Italian, English, and German writers, the
promulgation of a system of Descriptive Geology, in which all this
evidence was neglected, cannot be considered otherwise than as a
retrograde step in science.

[Note 24\18: _Gissement des Roches_, p. 41.]

Werner maintained the aqueous deposition of all strata above the
primitive rocks; even of those _trap_ rocks, to which, from their
resemblance to lava and other phenomena, Raspe, Arduino, and others,
had already assigned a volcanic origin. The fierce and long
controversy between the _Vulcanists_ and _Neptunists_, which this
dogma excited, does not belong to this part of our history; but the
discovery of veins of granite penetrating the superincumbent slate,
to which the controversy led, was an important event in descriptive
geology. Hutton, the {515} author of the theory of igneous causation
which was in this country opposed to that of Werner, sought and
found this phenomenon in the Grampian hills, in 1785. This supposed
verification of his system "filled him with delight, and called
forth such marks of joy and exultation, that the guides who
accompanied him were persuaded, says his biographer,[25\18] that he
must have discovered a vein of silver or gold."[26\18]

[Note 25\18: Playfair's _Works_, vol. iv. p. 75.]

[Note 26\18: Lyell, i. 90.]

Desmarest's examination of Auvergne (1768) showed that there was
there an instance of a country which could not even be described
without terms implying that the basalt, which covered so large a
portion of it, had flowed from the craters of extinct volcanoes. His
map of Auvergne was an excellent example of a survey of such a
country, thus exhibiting features quite different from those of
common stratified countries.[27\18]

[Note 27\18: Lyell, i. 86.]

The facts connected with metalliferous veins were also objects of
Werner's attention. A knowledge of such facts is valuable to the
geologist as well as to the miner, although even yet much difficulty
attends all attempts to theorize concerning them. The facts of this
nature have been collected in great abundance in all mining
districts; and form a prominent part of the descriptive geology of
such districts; as, for example, the Hartz, and Cornwall.

Without further pursuing the history of the knowledge of the
inorganic phenomena of the earth, I turn to a still richer
department of geology, which is concerned with organic fossils.


_Sect._ 3.--_Application of Organic Remains as a Geological
Character.--Smith._

ROUELLE and Odoardi had perceived, as we have seen, that fossils
were grouped in bands: but from this general observation to the
execution of a survey of a large kingdom, founded upon this
principle, would have been a vast stride, even if the author of it
had been aware of the doctrines thus asserted by these writers. In
fact, however, William Smith executed such a survey of England, with
no other guide or help than his own sagacity and perseverance. In
his employments as a civil engineer, he noticed the remarkable
continuity and constant order of the strata in the neighborhood of
Bath, as discriminated by their fossils; and about the year 1793,
he[28\18] drew up a Tabular View of the {516} strata of that
district, which contained the germ of his subsequent discoveries.
Finding in the north of England the same strata and associations of
strata with which he had become acquainted in the west, he was led
to name them and to represent them by means of maps, according to
their occurrence over the whole face of England. These maps
appeared[29\18] in 1815; and a work by the same author, entitled
_The English Strata identified by Organic Remains_, came forth
later. But the views on which this identification of strata rests,
belong to a considerably earlier date; and had not only been acted
upon, but freely imparted in conversation many years before.

[Note 28\18: Fitton, p. 148.]

[Note 29\18: Brit. Assoc. 1832. Conybeare, p. 373.]

In the meantime the study of fossils was pursued with zeal in
various countries. Lamarck and Defrance employed themselves in
determining the fossil shells of the neighborhood of Paris;[30\18]
and the interest inspired by this subject was strongly nourished and
stimulated by the memorable work of Cuvier and Brongniart, _On the
Environs of Paris_, published in 1811, and by Cuvier's subsequent
researches on the subjects thus brought under notice. For now, not
only the distinction, succession, and arrangement, but many other
relations among fossil strata, irresistibly arrested the attention
of the philosopher. Brongniart[31\18] showed that very striking
resemblances occurred in their fossil remains, between certain
strata of Europe and of North America; and proved that a rock may be
so much disguised, that the identity of the stratum can only be
recognized by geological characters.[32\18]

[Note 30\18: Humboldt, _Giss. d. R._ p. 35.]

[Note 31\18: _Hist. Nat. des Crustacés Fossiles_, pp. 57, 62.]

[Note 32\18: Humboldt, _Giss. d. R._ p. 45.]

The Italian geologists had found in their hills, for the most part,
the same species of shells which existed in their seas; but the
German and English writers, as Gesner,[33\18] Raspe,[34\18] and
Brander,[35\18] had perceived that the fossil-shells were either of
unknown species, or of such as lived in distant latitudes. To decide
that the animals and plants, of which we find the remains in a
fossil state, were of species now extinct, obviously required an
exact and extensive knowledge of natural history. And if this were
so, to assign the relations of the past to the existing tribes of
beings, and the peculiarities of their vital processes and habits,
were tasks which could not be performed without the most consummate
physiological skill and talent. Such tasks, however, have been the
familiar employments of geologists, and naturalists incited and
{517} appealed to by geologists, ever since Cuvier published his
examination of the fossil inhabitants of the Paris basin. Without
attempting a history of such labors, I may notice a few
circumstances connected with them.

[Note 33\18: Lyell, i. 70.]

[Note 34\18: Ib. 74.]

[Note 35\18: Ib. 76.]


_Sect._ 4.--_Advances in Palæontology.--Cuvier._

SO long as the organic fossils which were found in the strata of the
earth were the remains of marine animals, it was very difficult for
geologists to be assured that the animals were such as did not exist
in any part or clime of the existing ocean. But when large land and
river animals were discovered, different from any known species, the
persuasion that they were of extinct races was forced upon the
naturalist. Yet this opinion was not taken up slightly, nor
acquiesced in without many struggles.

Bones supposed to belong to fossil elephants, were some of the first
with regard to which this conclusion was established. Such remains
occur in vast numbers in the soil and gravel of almost every part of
the world; especially in Siberia, where they are called the bones of
the _mammoth_. They had been noticed by the ancients, as we learn
from Pliny;[36\18] and had been ascribed to human giants, to
elephants imported by the Romans, and to many other origins. But in
1796, Cuvier had examined these opinions with a more profound
knowledge than his predecessors; and he thus stated the result of
his researches.[37\18] "With regard to what have been called the
fossil remains of elephants, from Tentzelius to Pallas, I believe
that I am in the condition to prove, that they belong to animals
which were very clearly different in species from our existing
elephants, although they resembled them sufficiently to be
considered as belonging to the same genera." He had founded this
conclusion principally on the structure of the teeth, which he found
to differ in the Asiatic and African elephant; while, in the fossil
animal, it was different from both. But he also reasoned in part on
the form of the skull, of which the best-known example had been
described in the _Philosophical Transactions_ as early as
1737.[38\18] "As soon," says Cuvier, at a later period, "as I became
acquainted with Messerschmidt's drawing, and joined to the
differences which it presented, those which I had myself observed in
the inferior jaw and the {518} molar teeth, I no longer doubted that
the fossil elephants were of a species different from the Indian
elephant. This idea, which I announced to the Institute in the month
of January, 1796, opened to me views entirely new respecting the
theory of the earth; and determined me to devote myself to the long
researches and to the assiduous labors which have now occupied me
for twenty-five years."[39\18]

[Note 36\18: _Hist. Nat._ lib. xxxvi. 18.]

[Note 37\18: _Mém. Inst. Math. et Phys._ tom. ii. p. 4.]

[Note 38\18: Described by Breyne from a specimen found in Siberia by
Messerschmidt in 1722. _Phil. Trans._ xl. 446.]

[Note 39\18: _Ossemens Fossiles_, second edit. i. 178.]

We have here, then, the starting-point of those researches
concerning extinct animals, which, ever since that time, have
attracted so large a share of notice from geologists and from the
world. Cuvier could hardly have anticipated the vast storehouse of
materials which lay under his feet, ready to supply him occupation
of the most intense interest in the career on which he had thus
entered. The examination of the strata on which Paris stands, and of
which its buildings consist, supplied him with animals, not only
different from existing ones, but some of them of great size and
curious peculiarities. A careful examination of the remains which
these strata contain was undertaken soon after the period we have
referred to. In 1802, Defrance had collected several hundreds of
undescribed species of shells; and Lamarck[40\18] began a series of
Memoirs upon them; remodelling the whole of Conchology, in order
that they might be included in its classifications. And two years
afterwards (1804) appears the first of Cuvier's grand series of
Memoirs containing the restoration of the vertebrate animals of
these strata. In this vast natural museum, and in contributions from
other parts of the globe, he discovered the most extraordinary
creatures:--the Palæotherium,[41\18] which is intermediate between
the horse and the pig; the Anoplotherium, which stands nearest to
the rhinoceros and the tapir; the Megalonix and Megatherium, animals
of the sloth tribe, but of the size of the ox and the rhinoceros.
The Memoirs which contained these and many other discoveries, set
the naturalists to work in every part of Europe.

[Note 40\18:  _Annales du Muséum d'Hist. Nat._ tom. i. p. 308, and
the following volumes.]

[Note 41\18: Daubuisson, ii. 411.]

Another very curious class of animals was brought to light
principally by the geologists of England; animals of which the
bones, found in the _lias_ stratum, were at first supposed to be
those of crocodiles. But in 1816,[42\18] Sir Everard Home says, "In
truth, on a consideration of this skeleton, we cannot but be
inclined to believe, that among the animals destroyed by the
catastrophes of remote antiquity, there had {519} been some at least
that differ so entirely in their structure from any which now exist
as to make it impossible to arrange their fossil remains with any
known class of animals." The animal thus referred to, being clearly
intermediate between fishes and lizards, was named by Mr. König,
_Ichthyosaurus_; and its structure and constitution were more
precisely determined by Mr. Conybeare in 1821, when he had occasion
to compare with it another extinct animal of which he and Mr. de la
Beche had collected the remains. This animal, still more nearly
approaching the lizard tribe, was by Mr. Conybeare called
_Plesiosaurus_.[43\18] Of each of these two genera several species
were afterwards found.

[Note 42\18: _Phil. Trans._ 1816, p. 20.]

[Note 43\18: _Geol. Trans._ vol. v.]

Before this time, the differences of the races of animals and plants
belonging to the past and the present periods of the earth's
history, had become a leading subject of speculation among
geological naturalists. The science produced by this study of the
natural history of former states of the earth has been termed
_Palæontology_; and there is no branch of human knowledge more
fitted to stir men's wonder, or to excite them to the widest
physiological speculations. But in the present part of our history
this science requires our notice, only so far as it aims at the
restoration of the types of ancient animals, on clear and undoubted
principles of comparative anatomy. To show how extensive and how
conclusive is the science when thus directed, we need only refer to
Cuvier's _Ossemens Fossiles_;[44\18] a work of vast labor and
profound knowledge, which has opened wide the doors of this part of
geology. I do not here attempt even to mention the labors of the
many other eminent contributors to Palæontology; as Brocchi, Des
Hayes, Sowerby, Goldfuss, Agassiz, who have employed themselves on
animals, and Schlottheim, Brongniart, Hutton, Lindley, on plants.

[Note 44\18: The first edition appeared in 1812, consisting
principally of the Memoirs to which reference has already been made.]

[2nd Ed.] [Among the many valuable contributions to Palæontology in
more recent times, I may especially mention Mr. Owen's _Reports on
British Fossil Reptiles_, _on British Fossil Mammalia_, and _on the
Extinct Animals of Australia_, with descriptions of certain Fossils
indicative of large Marsupial Pachydermata: and M. Agassiz's _Report
on the Fossil Fishes of the Devonian System_, his _Synoptical Table
of British Fossil Fishes_, and his _Report on the Fishes of the
London Clay_. All these are contained in the volumes produced by the
British Association from 1839 to 1845. {520}

A new and most important instrument of palæontological investigation
has been put in the geologist's hand by Prof. Owen's discovery, that
the internal structure of teeth, as disclosed by the microscope, is
a means of determining the kind of the animal. He has carried into
every part of the animal kingdom an examination founded upon this
discovery, and has published the results of this in his
_Odontography_. As an example of the application of this character
of animals, I may mention that a tooth brought from Riga by Sir R.
Murchison was in this way ascertained by Mr. Owen to belong to a
fish of the genus _Dendrodus_. (_Geology of Russia_, i. 67.)]

When it had thus been established, that the strata of the earth are
characterized by innumerable remains of the organized beings which
formerly inhabited it, and that anatomical and physiological
considerations must be carefully and skilfully applied in order
rightly to interpret these characters, the geologist and the
palæontologist obviously had, brought before them, many very wide
and striking questions. Of these we may give some instances; but, in
the first place, we may add a few words concerning those eminent
philosophers to whom the science owed the basis on which succeeding
speculations were to be built.


_Sect._ 5.--_Intellectual Characters of the Founders of Systematic
Descriptive Geology._

IT would be in accordance with the course we have pursued in
treating of other subjects, that we should attempt to point out in
the founders of the science now under consideration, those
intellectual qualities and habits to which we ascribe their success.
The very recent date of the generalizations of geology, which has
hardly allowed us time to distinguish the calm expression of the
opinion of the wisest judges, might, in this instance, relieve us
from such a duty; but since our plan appears to suggest it, we will,
at least, endeavor to mark the characters of the founders of
geology, by a few of their prominent lines.

The three persons who must be looked upon as the main authors of
geological classification are, Werner, Smith, and Cuvier. These
three men were of very different mental constitution; and it will,
perhaps, not be difficult to compare them, in reference to those
qualities which we have all along represented as the main features
of the discoverer's genius, clearness of ideas, the possession of
numerous facts, and the power of bringing these two elements into
contact. {521}

In the German, considering him as a geologist, the ideal element
predominated. That Werner's powers of external discrimination were
extremely acute, we have seen in speaking of him as a mineralogist;
and his talent and tendency for classifying were, in his
mineralogical studies, fully fed by an abundant store of
observation; but when he came to apply this methodizing power to
geology, the love of system, so fostered, appears to have been too
strong for the collection of facts he had to deal with. As we have
already said, he promulgated, as representing the world, a scheme
collected from a province, and even too hastily gathered from that
narrow field. Yet his intense spirit of method in some measure
compensated for other deficiencies, and enabled him to give the
character of a science to what had been before a collection of
miscellaneous phenomena. The ardor of system-making produced a sort
of fusion, which, however superficial, served to bind together the
mass of incoherent and mixed materials, and thus to form, though by
strange and anomalous means, a structure of no small strength and
durability, like the ancient vitrified structures which we find in
some of our mountain regions.

Of a very different temper and character was William Smith. No
literary cultivation of his youth awoke in him the speculative love
of symmetry and system; but a singular clearness and precision of
the classifying power, which he possessed as a native talent, was
exercised and developed by exactly those geological facts among
which his philosophical task lay. Some of the advances which he
made, had, as we have seen, been at least entered upon by others who
preceded him: but of all this he was ignorant; and, perhaps, went on
more steadily and eagerly to work out his own ideas, from the
persuasion that they were entirely his own. At a later period of his
life, he himself published an account of the views which had
animated him in his earlier progress. In this account[45\18] he
dates his attempts to discriminate and connect strata from the year
1790, at which time he was twenty years old. In 1792, he "had
considered how he could best represent the order of
superposition--continuity of course--and general eastern declination
of the strata." Soon after, doubts which had arisen were removed by
the "discovery of a mode of identifying the strata by the organized
fossils respectively imbedded therein." And "thus stored with
ideas," as he expresses himself, he began to communicate them to his
friends. In all this, we see great vividness {522} of thought and
activity of mind, unfolding itself exactly in proportion to the
facts with which it had to deal. We are reminded of that cyclopean
architecture in which each stone, as it occurs, is, with wonderful
ingenuity, and with the least possible alteration of its form,
shaped so as to fit its place in a solid and lasting edifice.

[Note 45\18: _Phil. Mag._ 1833, vol. i. p. 38.]

Different yet again was the character (as a geological discoverer)
of the great naturalist of the beginning of the nineteenth century.
In that part of his labors of which we have now to speak, Cuvier's
dominant ideas were rather physiological than geological. In his
views of past physical changes, he did not seek to include any
ranges of facts which lay much beyond the narrow field of the Paris
basin. But his sagacity in applying his own great principle of the
Conditions of Existence, gave him a peculiar and unparalleled power
in interpreting the most imperfect fossil records of extinct
anatomy. In the constitution of his mind, all philosophical
endowments were so admirably developed and disciplined, that it was
difficult to say, whether more of his power was due to genius or to
culture. The talent of classifying which he exercised in geology,
was the result of the most complete knowledge and skill in zoology;
while his views concerning the revolutions which had taken place in
the organic and inorganic world, were in no small degree aided by an
extraordinary command of historical and other literature. His
guiding ideas had been formed, his facts had been studied, by the
assistance of all the sciences which could be made to bear upon
them. In his geological labors we seem to see some beautiful temple,
not only firm and fair in itself, but decorated with sculpture and
painting, and rich in all that art and labor, memory and
imagination, can contribute to its beauty.

[2nd Ed.] [Sir Charles Lyell (B. i. c. iv.) has quoted with approval
what I have elsewhere said, that the advancement of three of the
main divisions of geology in the beginning of the present century
was promoted principally by the three great nations of Europe,--the
German, the English, and the French:--Mineralogical Geology by the
German school of Werner:--Secondary Geology by Smith and his English
successors;--Tertiary Geology by Cuvier and his fellow-laborers in
France.] {523}




CHAPTER III.

SEQUEL TO THE FORMATION OF SYSTEMATIC DESCRIPTIVE GEOLOGY.


_Sect._ 1.--_Reception and Diffusion of Systematic Geology._

IF our nearness to the time of the discoveries to which we have just
referred, embarrasses us in speaking of their authors, it makes it
still more difficult to narrate the reception with which these
discoveries met. Yet here we may notice a few facts which may not be
without their interest.

The impression which Werner made upon his hearers was very strong;
and, as we have already said, disciples were gathered to his school
from every country, and then went forward into all parts of the
world, animated by the views which they had caught from him. We may
say of him, as has been so wisely said of a philosopher of a very
different kind,[46\18] "He owed his influence to various causes; at
the head of which may be placed that genius for system, which,
though it cramps the growth of knowledge, perhaps finally atones for
that mischief by the zeal and activity which it rouses among
followers and opponents, who discover truth by accident, when in
pursuit of weapons for their warfare." The list of Werner's pupils
for a considerable period included most of the principal geologists
of Europe; Freisleben, Mohs, Esmark, d'Andrada, Raumer, Engelhart,
Charpentier, Brocchi. Alexander von Humboldt and Leopold von Buch
went forth from his school to observe America and Siberia, the Isles
of the Atlantic, and the coast of Norway. Professor Jameson
established at Edinburgh a Wernerian Society; and his lecture-room
became a second centre of Wernerian doctrines, whence proceeded many
zealous geological observers; among these we may mention as one of
the most distinguished, M. Ami Boué, though, like several others, he
soon cast away the peculiar opinions of the Wernerian school. The
classifications of this school were, however, diffused over the
civilized world with {524} extraordinary success; and were looked
upon with great respect, till the study of organic fossils threw
them into the shade.

[Note 46\18: Mackintosh _on Hobbes_, Dissert. p. 177.]

Smith, on the other hand, long pursued his own thoughts without aid
and without sympathy. About 1799 he became acquainted with a few
gentlemen (Dr. Anderson, Mr. Richardson, Mr. Townsend, and Mr.
Davies), who had already given some attention to organic fossils,
and who were astonished to find his knowledge so much more exact and
extensive than their own. From this time he conceived the intention
of publishing his discoveries; but the want of literary leisure and
habits long prevented him. His knowledge was orally communicated
without reserve to many persons; and thus gradually and insensibly
became part of the public stock. When this diffusion of his views
had gone on for some time, his friends began to complain that the
author of them was deprived of his well-merited share of fame. His
delay in publication made it difficult to remedy this wrong; for
soon after he published his Geological Map of England, another
appeared, founded upon separate observations; and though, perhaps,
not quite independent of his, yet in many respects much more
detailed and correct. Thus, though his general ideas obtained
universal currency, he did not assume his due prominence as a
geologist. In 1818, a generous attempt was made to direct a proper
degree of public gratitude to him, in an article in the _Edinburgh
Review_, the production of Dr. Fitton, a distinguished English
geologist. And when the eminent philosopher, Wollaston, had
bequeathed to the Geological Society of London a fund from which a
gold medal was to be awarded to geological services, the first of
such medals was, in 1831, "given to Mr. William Smith, in
consideration of his being a great original discoverer in English
geology; and especially for his having been the first in this
country to discover and to teach the identification of strata, and
to determine their succession by means of their imbedded fossils."

Cuvier's discoveries, on the other hand, both from the high
philosophic fame of their author, and from their intrinsic
importance, arrested at once the attention of scientific Europe;
and, notwithstanding the undoubted priority of Smith's labors, for a
long time were looked upon as the starting-point of our knowledge of
organic fossils. And, in reality, although Cuvier's memoirs derived
the greatest part of their value from his zoological conclusions,
they reflected back no small portion of interest on the
classifications of strata which were involved in his inferences. And
the views which he presented gave to geology an attractive and
striking character, and a connexion with {525} large physiological
as well as physical principles, which added incomparably to its
dignity and charm.

In tracing the reception and diffusion of doctrines such as those of
Smith and Cuvier, we ought not to omit to notice more especially the
formation and history of the Geological Society of London, just
mentioned. It was established in 1807, with a view to multiply and
record observations, and patiently to await the result of some
future period; that is, its founders resolved to apply themselves to
Descriptive Geology, thinking the time not come for that theoretical
geology which had then long fired the controversial ardor of
Neptunists and Plutonists. The first volume of the Transactions of
this society was published in 1811. The greater part of the contents
of this volume[47\18] savor of the notions of the Wernerian school;
and there are papers on some of the districts in England most rich
in fossils, which Mr. Conybeare says, well exhibit the low state of
secondary geology at that period. But a paper by Mr. Parkinson
refers to the discoveries both of Smith and of Cuvier; and in the
next volume, Mr. Webster gives an account of the Isle of Wight,
following the admirable model of Cuvier and Brongniart's account of
the Paris basin. "If we compare this memoir of Mr. Webster with the
preceding one of Dr. Berger (also of the Isle of Wight), they at
once show themselves to belong to two very distinct eras of science;
and it is difficult to believe that the interval which elapsed
between their respective publication was only three or four
years."[48\18]

[Note 47\18: Conybeare, _Report. Brit. Assoc._ p. 372.]

[Note 48\18: Conybeare, _Report_, p. 372.]

Among the events belonging to the diffusion of sound geological
views in this country, we may notice the publication of a little
volume entitled, _The Geology of England and Wales_, by Mr.
Conybeare and Mr. Phillips, in 1821; an event far more important
than, from the modest form and character of the work, it might at
first sight appear. By describing in detail the geological structure
and circumstances of England (at least as far downwards as the
coal), it enabled a very wide class of readers to understand and
verify the classifications which geology had then very recently
established; while the extensive knowledge and philosophical spirit
of Mr. Conybeare rendered it, under the guise of a topographical
enumeration, in reality a profound and instructive scientific
treatise. The vast impulse which it gave to the study of sound
descriptive geology was felt and acknowledged in other countries, as
well as in Britain. {526}

Since that period, Descriptive Geology in England has constantly
advanced. The advance has been due mainly to the labors of the members
of the Geological Society; on whose merits as cultivators of their
science, none but those who are themselves masters of the subject,
have a right to dwell. Yet some parts of the scientific character of
these men may be appreciated by the general speculator; for they have
shown that there are no talents and no endowments which may not find
their fitting employment in this science. Besides that they have
united laborious research and comprehensive views, acuteness and
learning, zeal and knowledge; the philosophical eloquence with which
they have conducted their discussions has had a most beneficial
influence on the tone of their speculations; and their researches in
the field, which have carried them into every country and every class
of society, have given them that prompt and liberal spirit, and that
open and cordial bearing, which results from intercourse with the
world on a large and unfettered scale. It is not too much to say, that
in our time, Practical Geology has been one of the best schools of
philosophical and general culture of mind.


_Sect._ 2.--_Application of Systematic Geology. Geological Surveys
and Maps._

SUCH surveys as that which Conybeare and Phillips's book presented
with respect to England, were not only a means of disseminating the
knowledge implied in the classifications of such a work, but they
were also an essential part of the Application and Extension of the
principles established by the founders of Systematic Geology. As
soon as the truth of such a system was generally acknowledged, the
persuasion of the propriety of geological surveys and maps of each
country could not but impress itself on men's minds.

When the earlier writers, as Lister and Fontenelle, spoke of
mineralogical and fossilological maps, they could hardly be said to
know the meaning of the terms which they thus used. But when
subsequent classifications had shown how such a suggestion might be
carried into effect, and to what important consequences it might
lead, the task was undertaken in various countries in a vigorous and
consistent manner. In England, besides Smith's map, another, drawn
up by Mr. Greenough, was published by the Geological Society in
1819; and, being founded on very numerous observations of the author
and his friends, made with great labor and cost, was not only an
important {527} correction and confirmation of Smith's labors, but a
valuable storehouse and standard of what had then been done in
English geology. Leopold von Buch had constructed a geological map
of a large portion of Germany, about the same period; but, aware of
the difficulty of the task he had thus attempted, he still forbore
to publish it. At a later period, and as materials accumulated, more
detailed maps of parts of Germany were produced by Hoffmann and
others. The French government entrusted to a distinguished Professor
of the School of Mines (M. Brochant de Villiers), the task of
constructing a map of France on the model of Mr. Greenough's;
associating with him two younger persons, selected for their energy
and talents, MM. Beaumont and Dufrénoy. We shall have occasion
hereafter to speak of the execution of this survey. By various
persons, geological maps of almost every country and province of
Europe, and of many parts of Asia and America, have been published.
I need not enumerate these, but I may refer to the account given of
them by Mr. Conybeare, in the _Reports of the British Association
for_ 1832, p. 384. These various essays may be considered as
contributions, though hitherto undoubtedly very imperfect ones, to
that at which Descriptive Geology ought to aim, and which is
requisite as a foundation for sound theory;--a complete geological
survey of the whole earth. But we must say a few words respecting
the language in which such a survey must be written.

As we have already said, that condition which made such maps and the
accompanying descriptions possible, was that the strata and their
contents had previously undergone classification and arrangement at
the hands of the fathers of geology. Classification, in this as in
other cases, implied names which should give to the classes
distinctness and permanence; and when the series of strata belonging
to one country were referred to in the description of another, in
which they appeared, as was usually the case, under an aspect at
least somewhat different, the supposed identification required a
peculiar study of each case; and thus Geology had arrived at the
point, which we have before had to notice as one of the stages of
the progress of Classificatory Botany, at which a technical
_nomenclature_ and a well-understood _synonymy_ were essential parts
of the science.


_Sect._ 3.--_Geological Nomenclature._

BY Nomenclature we mean a _system_ of names; and hence we can {528}
not speak of a Geological Nomenclature till we come to Werner and
Smith. The earlier mineralogists had employed names, often
artificial and arbitrary, for special minerals, but no technical and
constant names for strata. The elements of Werner's names for the
members of his geological series were words in use among miners, as
_Gneiss_, _Grauwacke_, _Thonschiefer_, _Rothe todte liegende_,
_Zechstein_; or arbitrary names of the mineralogists, as Syenite,
Serpentine, Porphyry, Granite. But the more technical part of his
phraseology was taken from that which is the worst kind of name,
arbitrary numeration. Thus he had his _first_ sandstone formation,
_second_ sandstone, _third_ sandstone; _first_ flötz limestone,
_second_ flötz limestone, _third_ flötz limestone. Such names are,
beyond all others, liable to mistake in their application, and
likely to be expelled by the progress of knowledge; and accordingly,
though the Wernerian names for rocks mineralogically distinguished,
have still some currency, his sandstones and limestones, after
creating endless confusion while his authority had any sway, have
utterly disappeared from good geological works.

The nomenclature of Smith was founded upon English provincial terms
of very barbarous aspect, as _Cornbrash_, _Lias_, _Gault_, _Clunch
Clay_, _Coral Rag_. Yet these terms were widely diffused when his
classification was generally accepted; they kept their place,
precisely because they had no systematic signification; and many of
them are at present part of the geological language of the whole
civilized world.

Another kind of names which has been very prevalent among geologists
are those borrowed from places. Thus the Wernerians spoke of Alpine
Limestone and Jura Limestone; the English, of Kimmeridge Clay and
Oxford Clay, Purbeck Marble, and Portland Rock. These names,
referring to the stratum of a known locality as a type, were good,
as far as an identity with that type had been traced; but when this
had been incompletely done, they were liable to great ambiguity. If
the Alps or the Jura contain several formations of limestone, such
terms as we have noticed, borrowed from those mountains, cease to be
necessarily definite, and may give rise to much confusion.

Descriptive names, although they might be supposed to be the best,
have, in fact, rarely been fortunate. The reason of this is
obvious;--the mark which has been selected for description may
easily fail to be essential; and the obvious connexions of natural
facts may overleap the arbitrary definition. As we have already
stated in the history of botany, the establishment of descriptive
marks of real classes presupposes the important but difficult step,
of the discovery of such marks. {529} Hence those descriptive names
only have been really useful in geology which had been used without
any scrupulous regard to the appropriateness of the description. The
_Green Sand_ may be white, brown, or red; the _Mountain Limestone_
may occur only in valleys; the _Oolite_ may have no roe-like
structure; and yet these may be excellent geological names, if they
be applied to formations geologically identical with those which the
phrases originally designated. The signification may assist the
memory, but must not be allowed to subjugate the faculty of natural
classification.

The terms which have been formed by geologists in recent times have
been drawn from sources similar to those of the older ones, and will
have their fortune determined by the same conditions. Thus Mr. Lyell
has given to the divisions of the tertiary strata the appellations
_Pleiocene_, _Meiocene_, _Eocene_, accordingly as they contain a
_majority_ of recent species of shells, a _minority_ of such
species, or a small proportion of living species, which may be
looked upon as indicating the _dawn_ of the existing state of the
animate creation. But in this case, he wisely treats his
distinctions, not as definitions, but as the marks of natural
groups. "The plurality of species indicated by the name _pleiocene_
must not," he says,[49\18] "be understood to imply an absolute
majority of recent fossil shells in all cases, but a comparative
preponderance wherever the pleiocene are contrasted with strata of
the period immediately preceding."

[Note 49\18: _Geol._ iii. 392.]

Mr. Lyell might have added, that no precise percentage of recent
species, nor any numerical criterion whatever, can be allowed to
overbear the closer natural relations of strata, proved by evidence
of a superior kind, if such can be found. And this would be the
proper answer to the objection made by De la Beche to these names;
namely, that it may happen that the _meiocene_ rocks of one country
may be of the same date as the _pleiocene_ of another; the same
formation having in one place a majority, in another a minority, of
existing species. We are not to run into this incongruity, for we
are not so to apply the names. The formation which has been called
pleiocene, must continue to be so called, even where the majority of
recent species fails; and all rocks that agree with that in date,
without further reference to the numerical relations of their
fossils, must also share in the name.

To invent good names for these large divisions of the series of
strata is indeed extremely difficult. The term _Oolite_ is an
instance in which {530} a descriptive word has become permanent in a
case of this kind; and, in imitation of it, _Pœcilite_ (from
ποικίλος, various,**) has been proposed by Mr. Conybeare[50\18] as
a name for the group of strata inferior to the oolites, of which the
_Variegated_ Sandstone (Bunter Sandstein, Grès Bigarré,) is a
conspicuous member. For the series of formations which lies
immediately over the rocks in which no organic remains are found,
the term _Transition_ was long used, but with extreme ambiguity and
vagueness. When this series, or rather the upper part of it, was
well examined in South Wales, where it consists of many well-marked
members, and may be probably taken as a type for a large portion of
the rest of the world, it became necessary to give to the group thus
explored a name not necessarily leading to assumption or
controversy. Mr. Murchison selected the term _Silurian_, borrowed
from the former inhabitants of the country in which his types were
found; and this is a term excellent in many respects; but one which
will probably not quite supersede "Transition," because, in other
places, transition rocks occur which correspond to none of the
members of the Silurian region.

[Note 50\18: _Report_, p. 379.]

Though new names are inevitable accompaniments of new views of
classification, and though, therefore, the geological discoverer
must be allowed a right to coin them, this is a privilege which, for
the sake of his own credit, and the circulation of his tokens, he
must exercise with great temperance and judgment. M. Brongniart may
be taken as an example of the neglect of this caution. Acting upon
the principle, in itself a sound one, that inconveniences arise from
geological terms which have a mineralogical signification, he has
given an entirely new list of names of the members of the geological
series. Thus the primitive unstratified rocks are _terrains
agalysiens_; the transition semi-compact are _hemilysiens_; the
sedimentary strata are _yzemiens_; the diluvial deposits are
_clysmiens_; and these divisions are subdivided by designations
equally novel; thus of the "terrains yzemiens," members are--the
terrains _clastiques_, _tritoniens_, _protéïques_, _palæotheriens_,
_epilymniques_, _thalassiques_.[51\18] Such a nomenclature appears
to labor under great inconveniences, since the terms are descriptive
in their derivation, yet are not generally intelligible, and refer
to theoretical views yet have not the recommendation of systematic
connexion. {531}

[Note 51\18: Brongniart, _Tableau des Terrains_, 1829.]


_Sect._ 4.--_Geological Synonymy, or Determination of Geological
Equivalents._

IT will easily be supposed that with so many different sources of
names as we have mentioned, the same stratum may be called by
different designations; and thus a synonymy may be necessary for
geology; as it was for botany in the time of Bauhin, when the same
plants had been spoken of by so many different appellations in
different authors. But in reality, the synonymy of geology is a
still more important part of the subject than the analogy of botany
would lead us to suppose. For in plants, the species are really
fixed, and easily known when seen; and the ambiguity is only in the
imperfect communication or confused ideas of the observers. But in
geology, the identity of a stratum or formation in different places,
though not an arbitrary, may be a very doubtful matter, even to him
who has seen and examined. To assign its right character and place
to a stratum in a new country, is, in a great degree, to establish
the whole geological history of the country. To assume that the same
names may rightly be applied to the strata of different countries,
is to take for granted, not indeed the Wernerian dogma of universal
formations, but a considerable degree of generality and uniformity
in the known formations. And how far this generality and uniformity
prevail, observation alone can teach. The search for geological
synonyms in different countries brings before us two
questions;--first, _are_ there such synonyms? and only in the second
place, and as far as they occur, _what_ are they?

In fact, it is found that although formations which must be considered
as geologically identical (because otherwise no classification is
possible,) do extend over large regions, and pass from country to
country, their identity includes certain modifications; and the
determination of the identity and of the modifications are inseparably
involved with each other, and almost necessarily entangled with
theoretical considerations. And in two countries, in which we find
this modified coincidence, instead of saying that the strata are
identical, and that their designations are synonyms, we may, with more
propriety, consider them as two corresponding series; of which the
members of the one may be treated as the _Representatives_ or
_Equivalents_ of the members of the other.

This doctrine of Representatives or Equivalents supposes that the
geological phenomena in the two countries have been the results of
{532} similar series of events, which have, in some measure, coincided
in time and order; and thus, as we have said, refers us to a theory.
But yet, considered merely as a step in classification, the comparison
of the geological series of strata in different countries is, in the
highest degree, important and interesting. Indeed in the same manner
in which the separation of Classificatory from Chemical Mineralogy is
necessary for the completion of mineralogical science, the comparative
Classification of the strata of different countries according to their
resemblances and differences alone, is requisite as a basis for a
Theory of their causes. But, as will easily be imagined from its
nature, this part of descriptive geology deals with the most difficult
and the most elevated problems; and requires a rare union of laborious
observation with a comprehensive spirit of philosophical
classification.

In order to give instances of this process (for of the vast labor
and great talents which have been thus employed in England, France,
and Germany, it is only instances that we can give,) I may refer to
the geological survey of France, which was executed, as we have
already stated, by order of the government. In this undertaking it
was intended to obtain a knowledge of the whole mineral structure of
France; but no small portion of this knowledge was brought into
view, when a synonymy had been established between the Secondary
Rocks of France and the corresponding members of the English and
German series, which had been so well studied as to have become
classical points of standard reference. For the purpose of doing
this, the principal directors of the survey, MM. Brochant de
Villiers, De Beaumont, and Dufrénoy, came to England in 1822, and
following the steps of the best English geologists, in a few months
made themselves acquainted with the English series. They then
returned to France, and, starting from the chalk of Paris in various
directions, travelled on the lines which carried them over the edges
of the strata which emerge from beneath the chalk, identifying, as
they could, the strata with their foreign analogues. They thus
recognized almost all of the principal beds of the oolitic series of
England.[52\18] At the same time they found differences as well as
resemblances. Thus the Portland and Kimmeridge beds of France were
found to contain in abundance a certain shell, the _gryphæa
virgula_, which had not before been much remarked in those beds in
England. With regard to the synonyms in Germany, on the other hand,
a difference of opinion {538} arose between M. Elie de Beaumont and
M. Voltz,[53\18] the former considering the _Grès de Vosges_ as the
equivalent of the _Rothe todte liegende_, which occurs beneath the
Zechstein, while M. Voltz held that it was the lower portion of the
Red or _Variegated Sandstone_ which rests on the Zechstein.

[Note 52\18: De la Beche, _Manual_, 305.]

[Note 53\18: De la Beche, _Manual_, 381.]

In the same manner, from the first promulgation of the Wernerian
system, attempts were made to identify the English with the German
members of the geological alphabet; but it was long before this
alphabet was rightly read. Thus the English geologists who first
tried to apply the Wernerian series to this country, conceived the
Old and New Red Sandstone of England to be the same with the Old and
New Red Sandstone of Werner; whereas Werner's Old Red, the Rothe
todte liegende, is above the coal, while the English Old Red is
below it. This mistake led to a further erroneous identification of
our Mountain Limestone with Werner's First Flötz Limestone; and
caused an almost inextricable confusion, which, even at a recent
period, has perplexed the views of German geologists respecting this
country. Again, the Lias of England was, at first, supposed to be
the equivalent of the Muschelkalk of Germany. But the error of this
identification was brought into view by examinations and discussions
in which MM. Œyenhausen and Dechen took the lead; and at a later
period, Professor Sedgwick, by a laborious examination of the strata
of England, was enabled to show the true relation of this part of
the geology of the two countries. According to him, the New Red
Sandstone of England, considered as one great complex formation, may
be divided into seven members, composed of sandstones, limestones,
and marls; five of which represent respectively the _Rothe todte
liegende_; the _Kupfer schiefer_; the _Zechstein_, (with the
_Rauchwacké_, _Asche_, and _Stinkstein_ of the Thuringenwald;) the
_Bunter sandstein_; and the _Keuper_: while the _Muschelkalk_, which
lies between the two last members of the German list, has not yet
been discovered in our geological series. "Such a coincidence," he
observes,[54\18] "in the subdivisions of two distant mechanical
deposits, even upon the supposition of their being strictly
contemporaneous, is truly astonishing. It has not been assumed
hypothetically, but is the fair result of the facts which are
recorded in this paper."

[Note 54\18: _Geol. Trans._ Second Series, iii. 121.]

As an example in which the study of geological equivalents becomes
still more difficult, we may notice the attempts to refer the strata
of {534} the Alps to those of the north-west of Europe. The
dark-colored marbles and schists resembling mica slate[55\18] were,
during the prevalence of the Wernerian theory, referred, as was
natural, to the transition class. The striking physical characters
of this mountain region, and its long-standing celebrity as a
subject of mineralogical examination, made a complete subversion of
the received opinion respecting its place in the geological series,
an event of great importance in the history of the science. Yet this
was what occurred when Dr. Buckland, in 1820, threw his piercing
glance upon this district. He immediately pointed out that these
masses, by their fossils, approach to the Oolitic Series of this
country. From this view it followed, that the geological equivalents
of that series were to be found among rocks in which the
mineralogical characters were altogether different, and that the
loose limestones of England represent some of the highly-compact and
crystalline marbles of Italy and Greece. This view was confirmed by
subsequent investigations; and the correspondence was traced, not
only in the general body of the formations, but in the occurrence of
the Red Marl at its bottom, and the Green Sand and Chalk at its top.

[Note 55\18: De la Beche, _Manual_, 313.]

The talents and the knowledge which such tasks require are of no
ordinary kind; nor, even with a consummate acquaintance with the
well-ascertained formations, can the place of problematical strata
be decided without immense labor. Thus the examination and
delineation of hundreds of shells by the most skilful conchologists,
has been thought necessary in order to determine whether the
calcareous beds of Maestricht and of Gosau are or are not
intermediate, as to their organic contents, between the chalk and
the tertiary formations. And scarcely any point of geological
classification can be settled without a similar union of the
accomplished naturalist with the laborious geological collector.

It follows from the views already presented, of this part of geology,
that no attempt to apply to distant countries the names by which the
well-known European strata have been described, can be of any value,
if not accompanied by a corresponding attempt to show how far the
European series is really applicable. This must be borne in mind in
estimating the import of the geological accounts which have been given
of various parts of Asia, Africa, and America. For instance, when the
carboniferous group and the new red sandstone are stated to {535} be
found in India, we require to be assured that these formations are, in
some way, the equivalents of their synonyms in countries better
explored. Till this is done, the results of observation in such places
would be better conveyed by a nomenclature implying only those facts
of resemblance, difference, and order, which have been ascertained in
the country so described. We know that serious errors were incurred by
the attempts made to identify the Tertiary strata of other countries
with those first studied in the Paris basin. Fancied points of
resemblance, Mr. Lyell observes, were magnified into undue importance,
and essential differences in mineral character and organic contents
were slurred over.

[2nd Ed.] [The extension of geological surveys, the construction of
geological maps, and the determination of the geological equivalents
which replace each other in various countries, have been carried on
in continuation of the labors mentioned above, with enlarged
activity, range, and means. It is estimated that one-third of the
land of each hemisphere has been geologically explored; and that
thus Descriptive Geology has now been prosecuted so far, that it is
not likely that even the extension of it to the whole globe would
give any material novelty of aspect to Theoretical Geology. The
recent literature of the subject is so voluminous that it is
impossible for me to give any account of it here; very imperfectly
acquainted, as I am, even with the English portion, and still more,
with what has been produced in other countries.

While I admire the energetic and enlightened labors by which the
philosophers of France, Belgium, Germany, Italy, Russia, and
America, have promoted scientific geology, I may be allowed to
rejoice to see in the very phraseology of the subject, the evidence
that English geologists have not failed to contribute their share to
the latest advances in the science. The following order of strata
proceeding upwards is now, I think, recognized throughout Europe.
The _Silurian_; the _Devonian_ (Old Red Sandstone;) the
_Carboniferous_; the _Permian_, (Lower part of the new Red Sandstone
series;) the _Trias_, (Upper three members of the New Red Sandstone
series;) the _Lias_; the _Oolite_, (in which are reckoned by M.
D'Orbigny the Etages _Bathonien_, _Oxonien_, _Kimmeridgien_, and
_Portlandien_;) the _Neocomien_, (Lower Green Sand,) the Chalk; and
above these, Tertiary and Supra-Tertiary beds. Of these, the
Silurian, described by Sir R. Murchison from its types in South
Wales, has been traced by European Geologists through the Ardennes,
Servia, Turkey, the shores of the Gulf of Finland, the valley {536}
of the Mississippi, the west coast of North America, and the
mountains of South America. Again, the labors of Prof. Sedgwick and
Sir R. Murchison, in 1836, '7, and '8, aided by the sagacity of Mr.
Lonsdale, led to their placing certain rocks of Devon and Cornwall
as a formation intermediate between the Silurian and Carboniferous
Series; and the Devonian System thus established has been accepted
by geologists in general, and has been traced, not only in various
parts of Europe, but in Australia and Tasmania, and in the
neighborhood of the Alleganies.

Above the Carboniferous Series, Sir R. Murchison and his fellow
laborers, M. de Verneuil and Count Keyserling, have found in Russia
a well-developed series of rocks occupying the ancient kingdom of
Permia, which they have hence called the _Permian formation_; and
this term also has found general acceptance. The next group, the
Keuper, Muschelkalk, and Bunter Sandstein of Germany, has been
termed _Trias_ by the continental geologists. The _Neocomien_ is
called from Neuchatel, where it is largely developed. Below all
these rocks come, in England, the _Cambrian_ on which Prof. Sedgwick
has expended so many years of valuable labor. The comparison of the
Protozoic and Hypozoic rocks of different countries is probably
still incomplete.

The geologists of North America have made great progress in
decyphering and describing the structure of their own country; and
they have wisely gone, in a great measure, upon the plan which I
have commended at the end of the third Chapter;--they have compared
the rocks of their own country with each other, and given to the
different beds and formations names borrowed from their own
localities. This course will facilitate rather than impede the
redaction of their classification to its synonyms and equivalents in
the old world.

Of course it is not to be expected nor desired that books belonging
to Descriptive Geology shall exclude the other two branches of the
subject, Geological Dynamics and Physical Geology. On the contrary,
among the most valuable contributions to both these departments have
been speculations appended to descriptive works. And this is
naturally and rightly more and more the case as the description
embraces a wider field. The noble work _On the Geology of Russia and
the Urals_, by Sir Roderick Murchison and his companions, is a great
example of this, as of other merits in a geological book. The author
introduces into his pages the various portions of geological
dynamics of which I shall have to speak afterwards; and thus
endeavors to make out the {537} physical history of the region, the
boundaries of its raised sea bottoms, the shores of the great
continent on which the mammoths lived, the period when the gold ore
was formed, and when the watershed of the Ural chain was elevated.]




CHAPTER IV.

ATTEMPTS TO DISCOVER GENERAL LAWS IN GEOLOGY.


_Sect._ 1.--_General Geological Phenomena._

BESIDES thus noticing such features in the rocks of each country as
were necessary to the identification of the strata, geologists have
had many other phenomena of the earth's surface and materials
presented to their notice; and these they have, to a certain extent,
attempted to generalize, so as to obtain on this subject what we
have elsewhere termed the Laws of Phenomena, which are the best
materials for physical theory. Without dwelling long upon these, we
may briefly note some of the most obvious. Thus it has been observed
that mountain ranges often consist of a ridge of subjacent rock, on
which lie, on each side, strata sloping from the ridge. Such a ridge
is an _Anticlinal Line_, a _Mineralogical Axis_. The sloping strata
present their _Escarpements_, or steep edges, to this axis. Again,
in mining countries, the _Veins_ which contain the ore are usually a
system of _parallel_ and nearly vertical partitions in the rock; and
these are, in very many cases, intersected by another system of
veins parallel to each other and nearly _perpendicular_ to the
former. Rocky regions are often intersected by _Faults_, or fissures
interrupting the strata, in which the rock on one side the fissure
appears to have been at first continuous with that on the other, and
shoved aside or up or down after the fracture. Again, besides these
larger fractures, rocks have _Joints_,--separations, or tendencies
to separate in some directions rather than in others; and a _slaty
Cleavage_, in which the parallel subdivisions may be carried on, so
as to produce laminæ of indefinite thinness. As an example of those
laws of phenomena of which we have spoken, we may instance the
general law asserted by Prof. {538} Sedgwick (not, however, as free
from exception), that in one particular class of rocks the slaty
Cleavage _never_ coincides with the Direction of the strata.

The phenomena of metalliferous veins may be referred to, as another
large class of facts which demand the notice of the geologist. It
would be difficult to point out briefly any general laws which
prevail in such cases; but in order to show the curious and complex
nature of the facts, it may be sufficient to refer to the
description of the metallic veins of Cornwall by Mr. Carne;[56\18]
in which the author maintains that their various contents, and the
manner in which they cut across, and _stop_, or _shift_, each other,
leads naturally to the assumption of veins of no less than six or
eight different ages in one kind of rock.

[Note 56\18: _Transactions of the Geol. Soc. of Cornwall_, vol. ii.]

Again, as important characters belonging to the physical history of
the earth, and therefore to geology, we may notice all the general
laws which refer to its temperature;--both the laws of climate, as
determined by the _isothermal lines_, which Humboldt has drawn, by
the aid of very numerous observations made in all parts of the
world; and also those still more curious facts, of the increase of
temperature which takes place as we descend in the solid mass. The
latter circumstance, after being for a while rejected as a fable, or
explained away as an accident, is now generally acknowledged to be
the true state of things in many distant parts of the globe, and
probably in all.

Again, to turn to cases of another kind: some writers have
endeavored to state in a general manner laws according to which the
members of the geological series succeed each other; and to reduce
apparent anomalies to order of a wider kind. Among those who have
written with such views, we may notice Alexander von Humboldt,
always, and in all sciences, foremost in the race of generalization.
In his attempt to extend the doctrine of geological equivalents from
the rocks of Europe[57\18] to those of the Andes, he has marked by
appropriate terms the general modes of geological succession. "I
have insisted," he says[58\18] "principally upon the phenomena of
_alternation_, _oscillation_, and _local suppression_, and on those
presented by the _passages_ of formations from one to another, by
the effect of an _interior developement_."

[Note 57\18: _Gissement des Roches dans les deux Hemisphères_, 1823.]

[Note 58\18: Pref. p. vi.]

The phenomena of alternation to which M. de Humboldt here refers
are, in fact, very curious: as exhibiting a mode in which the
transitions from one formation to another may become gradual and
insensible, {539} instead of sudden and abrupt. Thus the coal
measures in the south of England are above the mountain limestone;
and the distinction of the formations is of the most marked kind.
But as we advance northward into the coal-field of Yorkshire and
Durham, the subjacent limestone begins to be subdivided by thick
masses of sandstone and carbonaceous strata, and passes into a
complex deposit, not distinguishable from the overlying coal
measures; and in this manner the transition from the limestone to
the coal is made by alternation. Thus, to use another expression of
M. de Humboldt's in ascending from the limestone, the coal, before
we quit the subjacent stratum, _preludes_ to its fuller exhibition
in the superior beds.

Again, as to another point: geologists have gone on up to the
present time endeavoring to discover general laws and facts, with
regard to the position of mountain and mineral masses upon the
surface of the earth. Thus M. Von Buch, in his physical description
of the Canaries, has given a masterly description of the lines of
volcanic action and volcanic products, all over the globe. And, more
recently, M. Elie de Beaumont has offered some generalizations of a
still wider kind. In this new doctrine, those mountain ranges, even
in distant parts of the world, which are of the same age, according
to the classifications already spoken of, are asserted to be
parallel[59\18] to each other, while those ranges which are of
different ages lie in different directions. This very wide and
striking proposition may be considered as being at present upon its
trial among the geologists of Europe.[60\18]

[Note 59\18: We may observe that the notion of parallelism, when
applied to lines drawn on _remote_ portions of a globular surface,
requires to be interpreted in so arbitrary a manner, that we can
hardly imagine it to express a physical law.]

[Note 60\18: Mr. Lyell, in the sixth edition of his _Principles_, B.
i. c. xii., has combated the hypothesis of M. Elie de Beaumont,
stated in the text. He has argued both against the catastrophic
character of the elevation of mountain chains, and the parallelism
of the contemporaneous ridges. It is evident that the former
doctrine may be true, though the latter be shown to be false.]

Among the organic phenomena, also, which have been the subject of
geological study, general laws of a very wide and comprehensive kind
have been suggested, and in a greater or less degree confirmed by
adequate assemblages of facts. Thus M. Adolphe Brongniart has not
only, in his _Fossil Flora_, represented and skilfully restored a
vast number of the plants of the ancient world; but he has also, in
the _Prodromus_ of the work, presented various important and
striking views of the general character of the vegetation of former
periods, as {540} insular or continental, tropical or temperate. And
M. Agassiz, by the examination of an incredible number of specimens
and collections of fossil fish, has been led to results which,
expressed in terms of his own ichthyological classification, form
remarkable general laws. Thus, according to him,[61\18] when we go
below the lias, we lose all traces of two of the four orders under
which he comprehends all known kinds of fish; namely, the
_Cycloïdean_ and the _Ctenoïdean_; while the other two orders, the
_Ganoïdean_ and _Placoïdean_, rare in our days, suddenly appear in
great numbers, together with large sauroid and carnivorous fishes.
Cuvier, in constructing his great work on ichthyology, transferred
to M. Agassiz the whole subject of fossil fishes, thus showing how
highly he esteemed his talents as a naturalist. And M. Agassiz has
shown himself worthy of his great predecessor in geological natural
history, not only by his acuteness and activity, but by the
comprehensive character of his zoological philosophy, and by the
courage with which he has addressed himself to the vast labors which
lie before him. In his _Report on the Fossil Fish discovered in
England_, published in 1835, he briefly sketches some of the large
questions which his researches have suggested; and then adds,[62\18]
"Such is the meagre outline of a history of the highest interest,
full of curious episodes, but most difficult to relate. To unfold
the details which it contains will be the business of my life."

[Note 61\18: Greenough, _Address to Geol. Soc._ 1835, p. 19.]

[Note 62\18: _Brit. Assoc. Report_, p. 72.]

[2nd Ed.] [In proceeding downwards through the series of formations
into which geologists have distributed the rocks of the earth, one
class of organic forms after another is found to disappear. In the
Tertiary Period we find all the classes of the present world:
Mammals, Birds, Reptiles, Fishes, Crustaceans, Mollusks, Zoophytes.
In the Secondary Period, from the Chalk down to the New Red
Sandstone, Mammals are not found, with the minute exception of the
marsupial _amphitherium_ and _phascolotherium_ in the Stonesfield
slate. In the Carboniferous and Devonian period we have no large
Reptiles, with, again, a minute amount of exception. In the lower
part of the Silurian rocks, Fishes vanish, and we have no animal
forms but Mollusks, Crustaceans and Zoophytes.

The Carboniferous, Devonian and Silurian formations, thus containing
the oldest forms of life, have been termed _palæozoic_. The
boundaries of the life-bearing series have not yet been determined;
but the series in which vertebrated animals do not appear has been
{541} provisionally termed _protozoic_, and the lower Silurian rocks
may probably be looked upon as its upper members. Below this,
geologists place a _hypozoic_ or _azoic_ series of rocks.

Geologists differ as to the question whether these changes in the
inhabitants of the globe were made by determinate steps or by
insensible gradations. M. Agassiz has been led to the conviction
that the organized population of the globe was renewed in the
interval of each principal member of its formations.[63\18] Mr.
Lyell, on the other hand, conceives that the change in the
collection of organized beings was gradual, and has proposed on this
subject an hypothesis which I shall hereafter consider.]

[Note 63\18: _Brit. Assoc. Report_ 1842, p. 83.]


_Sect._ 2.--_Transition to Geological Dynamics._

WHILE we have been giving this account of the objects with which
Descriptive Geology is occupied, it must have been felt how
difficult it is, in contemplating such facts, to confine ourselves
to description and classification. Conjectures and reasonings
respecting the causes of the phenomena force themselves upon us at
every step; and even influence our classification and nomenclature.
Our Descriptive Geology impels us to endeavor to construct a
Physical Geology. This close connexion of the two branches of the
subject by no means invalidates the necessity of distinguishing
them: as in Botany, although the formation of a Natural System
necessarily brings us to physiological relations, we still
distinguish Systematic from Physiological Botany.

Supposing, however, our Descriptive Geology to be completed, as far
as can be done without considering closely the causes by which the
strata have been produced, we have now to enter upon the other
province of the science, which treats of those causes, and of which
we have already spoken, as _Physical Geology_. But before we can
treat this department of speculation in a manner suitable to the
conditions of science, and to the analogy of other parts of our
knowledge, a certain intermediate and preparatory science must be
formed, of which we shall now consider the origin and progress.



{{542}}
GEOLOGICAL DYNAMICS.




CHAPTER V.

INORGANIC GEOLOGICAL DYNAMICS.


_Sect._ 1.--_Necessity and Object of a Science of Geological
Dynamics._

WHEN the structure and arrangement which men observed in the
materials of the earth instigated them to speculate concerning the
past changes and revolutions by which such results had been
produced, they at first supposed themselves sufficiently able to
judge what would be the effects of any of the obvious agents of
change, as water or volcanic fire. It did not at once occur to them
to suspect, that their common and extemporaneous judgment on such
points was far from sufficient for sound knowledge;--they did not
foresee that they must create a special science, whose object should
be to estimate the general laws and effects of assumed causes,
before they could pronounce whether such causes had actually
produced the particular facts which their survey of the earth had
disclosed to them.

Yet the analogy of the progress of knowledge on other subjects
points out very clearly the necessity of such a science. When
phenomenal astronomy had arrived at a high point of completeness, by
the labors of ages, and especially by the discovery of Kepler's
laws, astronomers were vehemently desirous of knowing the causes of
these motions; and sanguine men, such as Kepler, readily conjectured
that the motions were the effects of certain virtues and influences,
by which the heavenly bodies acted upon each other. But it did not
at first occur to him and his fellow-speculators, that they had not
ascertained what motions the influences of one body upon another
could produce: and that, therefore, they were not prepared to judge
whether such causes as they spoke of, did really regulate the
motions of the planets. Yet such was found to be the necessary
course of sound inference. Men needed a science of motion, in order
to arrive at a science of the {543} heavenly motions: they could not
advance in the study of the Mechanics of the heavens, till they had
learned the Mechanics of terrestrial bodies. And thus they were, in
such speculations, at a stand for nearly a century, from the time of
Kepler to the time of Newton, while the science of Mechanics was
formed by Galileo and his successors. Till that task was executed,
all the attempts to assign the causes of cosmical phenomena were
fanciful guesses and vague assertions; after that was done, they
became demonstrations. The science of _Dynamics_ enabled
philosophers to pass securely and completely from _Phenomenal
Astronomy_ to _Physical Astronomy_.

In like manner, in order that we may advance from Phenomenal Geology
to Physical Geology, we need a science of _Geological
Dynamics_;--that is, a science which shall investigate and determine
the laws and consequences of the known causes of changes such as
those which Geology considers:--and which shall do this, not in an
occasional, imperfect, and unconnected manner, but by systematic,
complete, and conclusive methods;--shall, in short, be a Science,
and not a promiscuous assemblage of desultory essays.

The necessity of such a study, as a distinct branch of geology, is
perhaps hardly yet formally recognized, although the researches
which belong to it have, of late years, assumed a much more
methodical and scientific character than they before possessed. Mr.
Lyell's work (_Principles of Geology_), in particular, has eminently
contributed to place Geological Dynamics in its proper prominent
position. Of the four books of his Treatise, the second and third
are upon this division of the subject; the second book treating of
aqueous and igneous causes of change, and the third, of changes in
the organic world.

There is no difficulty in separating this auxiliary geological
science from theoretical Geology itself, in which we apply our
principles to the explanation of the actual facts of the earth's
surface. The former, if perfected, would be a demonstrative science
dealing with general cases; the latter is an ætiological view having
reference to special facts; the one attempts to determine what
always must be under given conditions; the other is satisfied with
knowing what is and has been, and why it has been; the first study
has a strong resemblance to Mechanics, the other to philosophical
Archæology.

Since this portion of science is still so new, it is scarcely
possible to give any historical account of its progress, or any
complete survey of its shape and component parts. I can only attempt
a few notices, {544} which may enable us in some measure to judge to
what point this division of our subject is tending.

We may remark, in this as in former cases, that since we have here
to consider the formation and progress of a _science_, we must treat
as unimportant preludes to its history, the detached and casual
observations of the effects of causes of change which we find in
older writers. It is only when we come to systematic collections of
information, such as may afford the means of drawing general
conclusions; or to rigorous deductions from known laws of
nature;--that we can recognise the separate existence of geological
dynamics, as a path of scientific research.

The following may perhaps suffice, for the present, as a sketch of
the subjects of which this science treats:--the aqueous causes of
change, or those in which water adds to, takes from, or transfers,
the materials of the land:--the igneous causes; volcanoes, and,
closely connected with them, earthquakes, and the forces by which
they are produced;--the calculations which determine, on physical
principles, the effects of assumed mechanical causes acting upon
large portions of the crust of the earth;--the effect of the forces,
whatever they be, which produce the crystalline texture of rocks,
their fissile structure, and the separation of materials, of which
we see the results in metalliferous veins. Again, the estimation of
the results of changes of temperature in the earth, whether
operating by pressure, expansion, or in any other way;--the effects
of assumed changes in the superficial condition, extent, and
elevation, of terrestrial continents upon the climates of the
earth;--the effect of assumed cosmical changes upon the temperature
of this planet;--and researches of the same nature as these.

These researches are concerned with the causes of change in the
inorganic world; but the subject requires no less that we should
investigate the causes which may modify the forms and conditions of
organic things; and in the large sense in which we have to use the
phrase, we may include researches on such subjects also as parts of
Geological Dynamics; although, in truth, this department of
physiology has been cultivated, as it well deserves to be,
independently of its bearing upon geological theories. The great
problem which offers itself here, in reference to Geology, is, to
examine the value of any hypotheses by which it may be attempted to
explain the succession of different races of animals and plants in
different strata; and though it may be difficult, in this inquiry,
to arrive at any positive result, we {545} may at least be able to
show the improbability of some conjectures which have been
propounded.

I shall now give a very brief account of some of the attempts made
in these various departments of this province of our knowledge; and
in the present chapter, of Inorganic Changes.


_Sect._ 2.--_Aqueous Causes of Change._

THE controversies to which the various theories of geologists gave
rise, proceeding in various ways upon the effects of the existing
causes of change, led men to observe, with some attention and
perseverance, the actual operation of such causes. In this way, the
known effect of the Rhine, in filling up the Lake of Geneva at its
upper extremity, was referred to by De Luc, Kirwan, and others, in
their dispute with the Huttonians; and attempts were even made to
calculate how distant the period was, when this alluvial deposit
first began. Other modern observers have attended to similar facts
in the natural history of rivers and seas. But the subject may be
considered as having first assumed its proper form, when taken up by
Mr. Von Hoff; of whose _History of the Natural Changes of the
Earth's surface which are proved by Tradition_, the first part,
treating of aqueous changes, appeared in 1822. This work was
occasioned by a Prize Question of the Royal Society of Göttingen,
promulgated in 1818; in which these changes were proposed as the
subject of inquiry, with a special reference to geology. Although
Von Hoff does not attempt to establish any general inductions upon
the facts which his book contains, the collection of such a body of
facts gave almost a new aspect to the subject, by showing that
changes in the relative extent of land and water were going on at
every time, and almost at every place; and that mutability and
fluctuation in the form of the solid parts of the earth, which had
been supposed by most persons to be a rare exception to the common
course of events, was, in fact, the universal rule. But it was Mr.
Lyell's _Principles of Geology, being an attempt to explain the
former Changes of the Earth's Surface by the Causes now in action_
(of which the first volume was published in 1830), which disclosed
the full effect of such researches on geology; and which attempted
to present such assemblages of special facts, as examples of general
laws. Thus this work may, as we have said, be looked upon as the
beginning of Geological Dynamics, at least among us. Such
generalizations and applications as it contains give the most lively
{546} interest to a thousand observations respecting rivers and
floods, mountains and morasses, which otherwise appear without aim
or meaning; and thus this department of science cannot fail to be
constantly augmented by contributions from every side. At the same
time it is clear, that these contributions, voluminous as they must
become, must, from time to time, be resolved into laws of greater
and greater generality; and that thus alone the progress of this, as
of all other sciences, can be furthered.

I need not attempt any detailed enumeration of the modes of aqueous
action which are here to be considered. Some are destructive, as
when the rivers erode the channels in which they flow; or when the
waves, by their perpetual assault, shatter the shores, and carry the
ruins of them into the abyss of the ocean. Some operations of the
water, on the other hand, add to the land; as when _deltas_ are
formed at the mouths of rivers or when calcareous springs form
deposits of _travertin_. Even when bound in icy fetters, water is by
no mean deprived of its active power; the _glacier_ carries into the
valley masses of its native mountain, and often, becoming ice-bergs,
float with a lading of such materials far into the seas of the
temperate zone. It is indisputable that vast beds of worn down
fragments of the existing land are now forming into strata at the
bottom of the ocean; and that many other effects are constantly
produced by existing aqueous causes, which resemble some, at least,
of the facts which geology has to explain.

[2nd Ed.] [The effects of glaciers above mentioned are obvious; but
the mechanism of these bodies,--the mechanical cause of their
motions,--was an unsolved problem till within a very few years. That
they slide as rigid masses;--that they advance by the expansion of
their mass;--that they advance as a collection of rigid fragments;
were doctrines which were held by eminent physicists; though a very
slight attention to the subject shows these opinions to be
untenable. In Professor James Forbes's theory on the subject
(published in his _Travels through the Alps_, 1843,) we find a
solution of the problem, so simple, and yet so exact, as to produce
the most entire conviction. In this theory, the ice of a glacier is,
on a great scale, supposed to be a plastic or viscous mass, though
small portions of it are sensibly rigid. It advances down the slope
of the valley in which it lies as a plastic mass would do,
accommodating itself to the varying shape and size of its bed, and
showing by its crevasses its mixed character between fluid and
rigid. It shows this character still more curiously by a _ribboned_
{547} _structure_ on a small scale, which is common in the solid ice
of the glacier. The planes of these _ribbons_ are, for the most
part, at right angles to the crevasses, near the sides of the
glacier, while, near its central line, they _dip_ towards the upper
part of the glacier. This structure appears to arise from the
difference of velocities of contiguous moving filaments of the icy
mass, as the crevasses themselves arise from the tension of larger
portions. Mr. Forbes has, in successive publications, removed the
objections which have been urged against this theory. In the last of
them, a Memoir in the _Phil. Trans._, 1846, (_Illustrations of the
Viscous Theory of Glacier Motion_,) he very naturally expresses
astonishment at the opposition which has been made to the theory on
the ground of the rigidity of small pieces of ice. He has himself
shown that the ice of glaciers has a plastic flexibility, by marking
forty-five points in a transverse straight line upon the Mer de
Glace, and observing them for several days. The straight line in
that time not only became oblique to the side, but also became
visibly curved.

Both Mr. Forbes and other philosophers have made it in the highest
degree probable that glaciers have existed in many places in which
they now exist no longer, and have exercised great powers in
transporting large blocks of rock, furrowing and polishing the rocks
along which they slide, and leaving lines and masses of detritus or
_moraine_ which they had carried along with them or pushed before
them. It cannot be doubted that extinct glaciers have produced some
of the effects which the geologist has to endeavor to explain. But
this part of the machinery of nature has been worked by some
theorists into an exaggerated form, in which it cannot, as I
conceive, have any place in an account of Geological Dynamics which
aims at being permanent.

The great problem of the diffusion of drift and erratic blocks from
their parent rocks to great distances, has driven geologists to the
consideration of other hypothetical machinery by which the effects
may be accounted for: especially the great _northern drift_ and
_boulders_,--the rocks from the Scandinavian chain which cover the
north of Europe on a vast area, having a length of 2000 and breadth
of from 400 to 800 miles. The diffusion of these blocks has been
accounted for by supposing them to be imbedded in icebergs, detached
from the shore, and floated into oceanic spaces, where they have
grounded and been deposited by the melting of the ice. And this mode
of action may to some extent be safely admitted into geological
speculation. For it is a matter of fact, that our navigators in
arctic and antarctic regions have {548} repeatedly seen icebergs and
icefloes sailing along laden with such materials.

The above explanation of the phenomena of drift supposes the land on
which the travelled materials are found to have been the bottom of a
sea where they were deposited. But it does not, even granting the
conditions, account for some of the facts observed;--that the drift
and the boulders are deposited in "trainées" or streaks, which, in
direction, diverge from the parent rock;--and that the boulders are
of smaller and smaller size, as they are found more remote from that
centre. These phenomena rather suggest the notion of currents of
water as the cause of the distribution of the materials into their
present situations. And though the supposition that the whole area
occupied by drift and boulders was a sea-bottom when they were
scattered over it much reduces the amount of violence which it is
necessary to assume in order to distribute the loose masses, yet
still the work appears to be beyond the possible effect of ordinary
marine currents, or any movements which would be occasioned by a
slow and gradual rising of the centre of distribution.

It has been suggested that a _sudden_ rise of the centre of
distribution would cause a motion in the surrounding ocean sufficient
to produce such an effect: and in confirmation of this reference has
been made to Mr. Scott Russell's investigations with respect to waves,
already referred to. (Book VIII.) The wave in this case would be the
_wave of translation_, in which the motion of the water is as great at
the bottom as at the top; and it has hence been asserted that by
paroxysmal elevations of 100 or 200 feet, a current of 25 or 30 miles
an hour might be accounted for. But I think it has not been
sufficiently noted that at each point this "current" is transient: it
lasts only while the wave is passing over the point, and therefore it
would only either carry a single mass the whole way with its own
velocity, or move through a short distance a series of masses over
which it successively passed. It does not appear, therefore, that we
have here a complete account of the transport of a collection of
materials, in which each part is transferred through great
distances:--except, indeed, we were to suppose a numerous succession
of paroxysmal elevations. Such a _battery_ might, by successive
shocks, transmitting their force through the water, diffuse the
fragments of the central mass over any area, however wide.

The fact that the erratic blocks are found to rest on the lower
drift, is well explained by supposing the latter to have been spread
on the {549} sea bottom while rock-bearing ice-masses floated on the
surface till they deposited their lading.

Sir R. Murchison has pointed out another operation of ice in
producing mounds of rocky masses; namely, the effects of rivers and
lakes, in climates where, as in Russia, the waters carry rocky
fragments entangled in the winter ice, and leave them in heaps at
the highest level which the waters attain.

The extent to which the effects of glaciers, now vanished, are
apparent in many places, especially in Switzerland and in England,
and other phenomena of the like tendency, have led some of the most
eminent geologists to the conviction that, interior to the period of
our present temperature, there was a _Glacial Period_, at which the
temperature of Europe was lower than it now is.]

Although the study of the common operations of water may give the
geologist such an acquaintance with the laws of his subject as may
much aid his judgment respecting the extent to which such effects
may proceed, a long course of observation and thought must be
requisite before such operations can be analysed into their
fundamental principles, and become the subjects of calculation, or
of rigorous reasoning in any manner which is as precise and certain
as calculation. Various portions of Hydraulics have an important
bearing upon these subjects, including some researches which have
been pursued with no small labor by engineers and mathematicians; as
the effects of currents and waves, the laws of tides and of rivers,
and many similar problems. In truth, however, such subjects have not
hitherto been treated by mathematicians with much success; and
probably several generations must elapse before this portion of
geological dynamics can become an exact science.


_Sect._ 3.--_Igneous Causes of Change.--Motions of the Earth's
Surface._

THE effects of volcanoes have long been noted as important and
striking features in the physical history of our globe; and the
probability of their connexion with many geological phenomena, had
not escaped notice at an early period. But it was not till more
recent times, that the full import of these phenomena was
apprehended. The person who first looked at such operations with
that commanding general view which showed their extensive connexion
with physical geology, was Alexander von Humboldt, who explored the
volcanic phenomena {550} of the New World, from 1799 to 1804. He
remarked[64\18] the linear distribution of volcanic domes,
considering them as vents placed along the edge of vast fissures
communicating with reservoirs of igneous matter, and extending
across whole continents. He observed, also, the frequent sympathy of
volcanic and terremotive action in remote districts of the earth's
surface, thus showing how deeply seated must be the cause of these
convulsions. These views strongly excited and influenced the
speculations of geologists; and since then, phenomena of this kind
have been collected into a general view as parts of a
natural-historical science. Von Hoff, in the second volume of the
work already mentioned, was one of the first who did this; "At
least," he himself says,[65\18] (1824,) "it was not known to him
that any one before him had endeavored to combine so large a mass of
facts with the general ideas of the natural philosopher, so as to
form a whole." Other attempts were, however, soon made. In 1825, M.
von Ungern-Sternberg published his book _On the Nature and Origin of
Volcanoes_,[66\18] in which, he says, his object is, to give an
empirical representation of these phenomena. In the same year, Mr.
Poulett Scrope published a work in which he described the known
facts of volcanic action; not, however, confining himself to
description; his purpose being, as his title states, to consider
"the probable causes of their phenomena, the laws which determine
their march, the disposition of their products, and their connexion
with the present state and past history of the globe; leading to the
establishment of a new theory of the earth." And in 1826, Dr.
Daubeny, of Oxford, produced _A Description of Active_ and Extinct
_Volcanoes_, including in the latter phrase the volcanic rocks of
central France, of the Rhine, of northern and central Italy, and
many other countries. Indeed, the near connexion between the
volcanic effects now going on, and those by which the basaltic rocks
of Auvergne and many other places had been produced, was, by this
time, no longer doubted by any; and therefore the line which here
separates the study of existing causes from that of past effects may
seem to melt away. But yet it is manifest that the assumption of an
identity of scale and mechanism between volcanoes now active, and
the igneous catastrophes of which the products have {551} survived
great revolutions on the earth's surface, is hypothetical; and all
which depends on this assumption belongs to theoretical geology.

[Note 64\18: Humboldt, _Relation Historique_; and his other works.]

[Note 65\18: Vol. ii. Prop. 5.]

[Note 66\18: _Werden und Seyn des Vulkanischen Gebirges_. Carlsruhe,
1825.]

Confining ourselves, then, to volcanic effects, which have been
produced, certainly or probably, since the earth's surface assumed
its present form, we have still an ample exhibition of powerful
causes of change, in the streams of lava and other materials emitted
in eruptions; and still more in the earthquakes which, as men easily
satisfied themselves, are produced by the same causes as the
eruptions of volcanic fire.

Mr. Lyell's work was important in this as in other portions of this
subject. He extended the conceptions previously entertained of the
effects which such causes may produce, not only by showing how great
these operations are historically known to have been, and how
constantly they are going on, if we take into our survey the whole
surface of the earth; but still more, by urging the consequences
which would follow in a long course of time from the constant
repetition of operations in themselves of no extraordinary amount. A
lava-stream many miles long and wide, and several yards deep, a
subsidence or elevation of a portion of the earth's surface of a few
feet, are by no means extraordinary facts. Let these operations,
said Mr. Lyell, be repeated thousands of times; and we have results
of the same order with the changes which geology discloses.

The most mitigated earthquakes have, however, a character of
violence. But it has been thought by many philosophers that there is
evidence of a change of level of the land in cases where none of
these violent operations are going on. The most celebrated of these
cases is Sweden; the whole of the land from Gottenburg to the north
of the Gulf of Bothnia has been supposed in the act of rising,
slowly and insensibly, from the surrounding waters. The opinion of
such a change of level has long been the belief of the inhabitants;
and was maintained by Celsius in the beginning of the eighteenth
century. It has since been conceived to be confirmed by various
observations of marks cut on the face of the rock; beds of shells,
such as now live in the neighboring seas, raised to a considerable
height; and other indications. Some of these proofs appear doubtful;
but Mr. Lyell, after examining the facts upon the spot in 1834,
says, "In regard to the proposition that the land, in certain parts
of Sweden, is gradually rising, I have no hesitation in assenting to
it, after my visit to the districts above alluded to."[67\18] If
this conclusion be generally accepted by {552} geologists, we have
here a daily example of the operation of some powerful agent which
belongs to geological dynamics; and which, for the purposes of the
geological theorist, does the work of the earthquake upon a very
large scale, without assuming its terrors.

[Note 67\18: _Phil. Trans._ 1835, p. 32.]

[2nd Ed.] [Examples of changes of level of large districts occurring
at periods when the country has been agitated by earthquakes are
well ascertained, as the rising of the coast of Chili in 1822, and
the subsidence of the district of Cutch, in the delta of the Indus,
in 1819. (Lyell, B. II. c. xv.) But the cases of more slow and
tranquil movement seem also to be established. The gradual secular
rise of the shore of the Baltic, mentioned in the text, has been
confirmed by subsequent investigation. It appears that the rate of
elevation increases from Stockholm, where it is only a few inches in
a century, to the North Cape, where it is several feet. It appears
also that several other regions are in a like state of secular
change. The coast of Greenland is sinking. (Lyell, B. II. c. xviii.)
And the existence of "raised beaches" along various coasts is now
generally accepted among geologists. Such beaches, anciently forming
the margin of the sea, but now far above it, exist in many places;
for instance, along a great part of the Scotch coast; and among the
raised beaches of that country we ought probably, with Mr. Darwin,
to include the "parallel roads" of Glenroy, the subject, in former
days, of so much controversy among geologists and antiquaries.

Connected with the secular rise and fall of large portions of the
earth's surface, another agency which plays an important part in
Geological dynamics has been the subject of some bold yet singularly
persuasive speculations by Mr. Darwin. I speak of the formation of
Coral, and Coral Reefs. He says that the coral-building animal works
only at small and definite distances below the surface. How then are
we to account for the vast number of coral islands, rings, and
reefs, which are scattered over the Pacific and Indian Oceans! Can
we suppose that there are so many mountains, craters, and ridges,
all exactly within a few feet of the same height through this vast
portion of the globe's surface? This is incredible. How then are we
to explain the facts? Mr. Darwin replies, that if we suppose the
land to subside slowly beneath the sea, and at the same time suppose
the coralline zoophytes to go on building, so that their structure
constantly rises nearly to the surface of the water, we shall have
the facts explained. A submerged island will produce a ring; a long
coast, a barrier reef; and so on. Mr. Darwin also notes other
phenomena, as {553} elevated beds of coral, which, occurring in
other places, indicate a recent rising of the land; and on such
grounds as these he divides the surface of those parts of the ocean
into regions of elevation and of depression.

The labors of coralline zoophytes, as thus observed, form masses of
coral, such as are found fossilized in the strata of the earth. But
our knowledge of the laws of life which have probably affected the
distribution of marine remains in strata, has received other very
striking accessions by the labors of Prof. Edward Forbes in
observing the marine animals of the Ægean Sea. He found that, even
in their living state, the mollusks and zoophytes are already
distributed into strata. Dividing the depth into eight regions, from
2 to 230 fathoms, he found that each region had its peculiar
inhabitants, which disappeared speedily either in ascending or in
descending. The zero of animal life appeared to occur at about 300
fathoms. This curious result bears in various ways upon geology. Mr.
Forbes himself has given an example of the mode in which it may be
applied, by determining the depth at which the submarine eruption
took place which produced the volcanic isle of Neokaimeni in 1707.
By an examination of the fossils embedded in the pumice, he showed
that it came from the fourth region.[68\18]

[Note 68\18: _British Assoc. Reports_, 1843, p. 177.]

To the modes in which organized beings operate in producing the
materials of the earth, we must add those pointed out by the
extraordinary microscopic discoveries of Professor Ehrenberg. It
appears that whole beds of earthy matter consist of the cases of
certain infusoria, the remains of these creatures being accumulated
in numbers which it confounds our thoughts to contemplate.]

Speculations concerning the _causes_ of volcanoes and earthquakes,
and of the rising and sinking of land, are a highly important
portion of this science, at least as far as the calculation of the
possible results of definite causes is concerned. But the various
hypotheses which have been propounded on this subject can hardly be
considered as sufficiently matured for such calculation. A mass of
matter in a state of igneous fusion, extending to the centre of the
earth, even if we make such an hypothesis, requires some additional
cause to produce eruption. The supposition that this fire may be
produced by intense chemical action between combining elements,
requires further, not only some agency to bring together such
elements, but some reason why {554} they should be originally
separate. And if any other causes have been suggested, as
electricity or magnetism, this has been done so vaguely as to elude
all possibility of rigorous deduction from the hypothesis. The
doctrine of a Central Heat, however, has occupied so considerable a
place in theoretical geology, that it ought undoubtedly to form an
article in geological dynamics.


_Sect._ 4.--_The Doctrine of Central Heat._

THE early geological theorists who, like Leibnitz and Buffon,
assumed that the earth was originally a mass in a state of igneous
fusion, naturally went on to deduce from this hypothesis, that the
crust consolidated and cooled before the interior, and that there
might still remain a central heat, capable of producing many
important effects. But it is in more recent times that we have
measures of such effects, and calculations which we can compare with
measures. It was found, as we have said, that in descending below
the surface of the earth, the temperature of its materials
increased. Now it followed from Fourier's mathematical
investigations of the distribution of heat in the earth, that if
there be no primitive heat (_chaleur d'origine_), the temperature,
when we descend below the crust, will be constant in each vertical
line. Hence an observed increase of temperature in descending,
appeared to point out a central heat resulting from some cause now
no longer in action.

The doctrine of a central heat has usually been combined with the
supposition of a central igneous fluidity; for the heat in the
neighborhood of the centre must be very intense, according to any
law of its increase in descending which is consistent with known
principles. But to this central fluidity it has been objected that
such a fluid must be in constant circulation by the cooling of its
exterior. Mr. Daniell found this to be the case in all fused metals.
It has also been objected that there must be, in such a central
fluid, _tides_ produced by the moon and sun; but this inference
would require several additional suppositions and calculations to
give it a precise form.

Again, the supposition of a central heat of the earth, considered as
the effect of a more ancient state of its mass, appeared to indicate
that its cooling must still be going on. But if this were so, the
earth might contract, as most bodies do when they cool; and this
contraction might lead to mechanical results, as the shortening of
the day. Laplace satisfied himself, by reference to ancient
astronomical records, that no such {555} alteration in the length of
the day had taken place, even to the amount of one two-hundredth of
a second; and thus, there was here no confirmation of the hypothesis
of a primitive heat of the earth.

Though we find no evidence of the secular contraction of the earth
in the observations with which astronomy deals, there are some
geological facts which at first appear to point to the reality of a
refrigeration within geological periods; as the existence of the
remains of plants and shells of tropical climates, in the strata of
countries which are now near to or within the frigid zones. These
facts, however, have given rise to theories of the changes of
climate, which we must consider separately.

But we may notice, as connected with the doctrine of central heat,
the manner in which this hypothesis has been applied to explain
volcanic and geological phenomena. It does not enter into my plan,
to consider explanations in which this central heat is supposed to
give rise to an expansive force,[69\18] without any distinct
reference to known physical laws. But we may notice; as more likely
to become useful materials of the science now before us, such
speculations as those of Mr. Babbage; in which he combines the
doctrine of central heat with other physical laws;[70\18] as, that
solid rocks _expand_ by being heated, but that clay contracts; that
different rocks and strata _conduct_ heat differently; that the
earth _radiates_ heat differently, or at different parts of its
surface, according as it is covered with forests, with mountains,
with deserts, or with water. These principles, applied to large
masses, such as those which constitute the crust of the earth, might
give rise to changes as great as any which geology discloses. For
example: when the bed of a sea is covered by a thick deposit of new
matter worn from the shores, the strata below the bed, being
protected by a bad conductor of heat, will be heated, and, being
heated, maybe expanded; or, as Sir J. Herschel has observed, may
produce explosion by the conversion of their moisture into steam.
Such speculations, when founded on real data and sound calculations,
may hereafter be of material use in geology.

[Note 69\18: Scrope _On Volcanoes_, p. 192.]

[Note 70\18: _On the Temple of Serapis_, 1834. See also _Journal of
the Royal Inst._ vol.  ii., quoted in Conyb. and Ph. p. xv. Lyell,
B. ii. c. xix. p. 383, (4th ed.) on Expansion of Stone.]

The doctrine of central heat and fluidity has been rejected by some
eminent philosophers. Mr. Lyell's reasons for this rejection belong
{556} rather to Theoretical Geology; but I may here notice M.
**Poisson's opinion. He does not assent to the conclusion of Fourier,
that once the temperature increases in descending, there must be some
primitive central heat. On the contrary, he considers that such an
increase may arise from this;--that the earth, at some former period,
passed (by the motion of the solar system in the universe,) **through
a portion of space which was warmer than the space in which it now
revolves (by reason, it may be, of the heat of other stars to which it
was then nearer). He supposes that, since such a period, the surface
has cooled down by the influence of the surrounding circumstances;
while the interior, for a certain unknown depth, retains the trace of
the former elevation of temperature. But this assumption is not likely
to expel the belief is the terrestrial origin of the subterraneous
heat. For the supposition of such an inequality in the temperature of
the different regions in which the solar system is placed at different
times, is altogether arbitrary; and, if pushed to the amount to which
it must be carried, in order to account for the phenomenon, is highly
improbable.[71\18] The doctrine of central heat, on the other hand,
(which need not be conceived as implying the _universal_ fluidity of
the mass,) is not only naturally suggested by the subterraneous
increase of temperatures, but explains the spheroidal figure of the
earth; and falls in with almost any theory which can be devised, of
volcanoes, earthquakes, and great geological changes.

[Note 71\18: For this hypothesis would make it necessary to suppose
that the earth has, at some former period, derived from some other
star or stars more heat than she now derives from the sun. But this
would imply, as highly probable, that at some period some other star
or stars must have produced also a _mechanical_ effect upon the
solar system, greater than the effect of the sun. Now such a past
operation of forces, fitted to obliterate all order and symmetry, is
quite inconsistent with the simple, regular, and symmetrical
relation which the whole solar system, as far as Uranus, bears to
the present central body.]


_Sect._ 5.--_Problems respecting Elevations and Crystalline Forces._

OTHER problems respecting the forces by which great masses of the
earth's crust have been displaced, have also been solved by various
mathematicians. It has been maintained by Von Buch that there occur,
in various places, _craters of elevation_; that is, mountain-masses
resembling the craters of volcanoes, but really produced by an
expansive force from below, bursting an aperture through horizontal
strata, {557} and elevating them in a conical form. Against this
doctrine, as exemplified in the most noted instances, strong
arguments have been adduced by other geologists. Yet the protrusion
of fused rock by subterraneous forces upon a large scale is not
denied: and how far the examples of such operations may, in any
cases, be termed craters of elevation, must be considered as a
question not yet decided. On the supposition of the truth of Von
Buch's doctrine, M. de Beaumont has calculated the relations of
position, the fissures, &c., which would arise. And Mr.
Hopkins,[72\18] of Cambridge, has investigated in a much more
general manner, upon mechanical principles, the laws of the
elevations, fissures, faults, veins, and other phenomena which would
result from an elevatory force, acting simultaneously at every point
beneath extensive portions of the crust of the earth. An application
of mathematical reasoning to the illustration of the phenomena of
veins had before been made in Germany by Schmidt and
Zimmerman.[73\18] The conclusion which Mr. Hopkins has obtained,
respecting the two sets of fissures, at right angles to each other,
which would in general be produced by such forces as he supposes,
may suggest interesting points of examination respecting the
geological phenomena of fissured districts.

[Note 72\18: _Trans. Camb. Phil. Soc._ vol. vi. 1836.]

[Note 73\18:  _Phil. Mag._ July, 1836, p. 2.]

[2nd Ed.] [The theory of craters of elevation probably errs rather
by making the elevation of a point into a particular class of
volcanic agency, than by giving volcanic agency too great a power of
elevation.

A mature consideration of the subject will make us hesitate to
ascribe much value to the labors of those writers who have applied
mathematical reasoning to geological questions. Such reasoning, when
it is carried to the extent which requires symbolical processes, has
always been, I conceive, a source, not of knowledge, but of error,
and confusion; for in such applications the real questions are
slurred over in the hypothetical assumptions of the mathematician,
while the calculation misleads its followers by a false aspect of
demonstration. All symbolical reasonings concerning the fissures of
a semi-rigid mass produced by elevatory or other forces, appear to
me to have turned out valueless. At the same time it cannot be too
strongly borne in mind, that mathematical and mechanical habits of
thought are requisite to all clear thinking on such subjects.]

Other forces, still more secure in their nature and laws, have
played a very important part in the formation of the earth's crust.
I speak of the forces by which the crystalline, slaty, and jointed
structure of {558} mineral masses has been produced. These forces
are probably identical, on the one hand, with the cohesive forces
from which rocks derive their solidity and their physical
properties; while, on the other hand, they are closely connected
with the forces of chemical attraction. No attempts, of any lucid
and hopeful kind, have yet been made to bring such forces under
definite mechanical conceptions: and perhaps mineralogy, to which
science, as the point of junction of chemistry and crystallography,
such attempts would belong, is hardly yet ripe for such
speculations. But when we look at the universal prevalence of
crystalline forms and cleavages, at the extent of the phenomena of
slaty cleavage, and at the _segregation_ of special minerals into
veins and nodules, which has taken place in some unknown manner, we
cannot doubt that the forces of which we now speak have acted very
widely and energetically. Any elucidation of their nature would be
an important step in Geological Dynamics.

[2nd Ed.] [A point of Geological Dynamics of great importance is, the
change which rocks undergo in structure after they are deposited,
either by the action of subterraneous heat, or by the influence of
crystalline or other corpuscular forces. By such agencies, sedimentary
rocks may be converted into crystalline, the traces of organic fossils
may be obliterated, a slaty cleavage may be produced, and other like
effects. The possibility of such changes was urged by Dr. Hutton in
his Theory; and Sir James Hall's very instructive and striking
experiments were made for the purpose of illustrating this theory. In
these experiments, powdered chalk was, by the application of heat
under pressure, converted into crystalline calcspar. Afterwards Dr.
McCulloch's labors had an important influence in satisfying geologists
of the reality of corresponding changes in nature. Dr. McCulloch, by
his very lively and copious descriptions of volcanic regions, by his
representations of them, by his classification of igneous rocks, and
his comprehensive views of the phenomena which they exhibit, probably
was the means of converting many geologists from the Wernerian
opinions.

Rocks which have undergone changes since they were deposited are
termed by Mr. Lyell _metamorphic_. The great extent of metamorphic
rock changed by heat is now uncontested. The internal changes which
are produced by the crystalline forces of mountain masses have been
the subjects of important and comprehensive speculations by
Professor Sedgwick.] {559}


_Sect._ 6.--_Theories of Changes of Climate._

AS we have already stated, Geology offers to us strong evidence that
the climate of the ancient periods of the earth's history was hotter
than that which now exists in the same countries. This, and other
circumstances, have led geologists to the investigation of the
effects of any hypothetical causes of such changes of condition in
respect of heat.

The love of the contemplation of geometrical symmetry, as well as
other reasons, suggested the hypothesis that the earth's axis had
originally no obliquity, but was perpendicular to the equator. Such
a construction of the world had been thought of before the time of
Milton,[74\18] as what might be supposed to have existed when man
was expelled from Paradise; and Burnet, in his _Sacred Theory of the
Earth_ (1690), adopted this notion of the paradisiacal condition of
the globe:
                 The spring
  Perpetual smiled on earth with verdant flowers,
  Equal in days and nights.

[Note 74\18: Some said he bade his angels turn askance
             The poles of earth twice ten degrees and more
             From the sun's axle, &c.--_Paradise Lost_, x. 214.]

In modern times, too, some persons have been disposed to adopt this
hypothesis, because they have conceived that the present polar
distribution of light is inconsistent with the production of the
fossil plants which are found in those regions,[75\18] even if we
could, in some other way, account for the change of temperature. But
this alteration in the axes of a revolution could not take place
without a subversion of the equilibrium of the surface, such as does
not appear to have occurred; and the change has of late been
generally declared impossible by physical astronomers.

[Note 75\18: Lyell, i. 155. Lindley, _Fossil Flora_.]

The effects of other astronomical changes have been calculated by
Sir John Herschel. He has examined, for instance, the thermotical
consequences of the diminution of the eccentricity of the earth's
orbit, which has been going on for ages beyond the records of
history. He finds[76\18] that, on this account, the annual effect of
solar radiation would increase as we go back to remoter periods of
the past; but (probably at least) not in a degree sufficient to
account for the apparent past {560} changes of climate. He finds,
however, that though the effect of this change on the mean
temperature of the year may be small, the effect on the extreme
temperature of the seasons will be much more considerable; "so as to
produce alternately, in the same latitude of either hemisphere, a
perpetual spring, or the extreme vicissitudes of a burning summer
and a rigorous winter."[77\18]

[Note 76\18: _Geol. Trans._ vol. iii. p. 295.]

[Note 77\18: _Geol. Trans._ vol. iii. p. 298.]

Mr. Lyell has traced the consequences of another hypothesis on this
subject, which appears at first sight to promise no very striking
results, but which yet is found, upon examination, to involve
adequate causes of very great changes: I refer to the supposed
various distribution of land and water at different periods of the
earth's history. If the land were all gathered into the neighborhood
of the poles, it would become the seat of constant ice and snow, and
would thus very greatly reduce the temperature of the whole surface
of the globe. If, on the other hand, the polar regions were
principally water, while the tropics were occupied with a belt of
land, there would be no part of the earth's surface on which the
frost could fasten a firm hold, while the torrid zone would act like
a furnace to heat the whole. And, supposing a cycle of terrestrial
changes in which these conditions should succeed each other, the
winter and summer of this "great year" might differ much more than
the elevated temperature which we are led to ascribe to former
periods of the globe, can be judged to have differed from the
present state of things.

The ingenuity and plausibility of this theory cannot be doubted: and
perhaps its results may hereafter be found not quite out of the
reach of calculation. Some progress has already been made in
calculating the movement of heat into, through, and out of the
earth; but when we add to this the effects of the currents of the
ocean and the atmosphere, the problem, thus involving so many
thermotical and atmological laws, operating under complex
conditions, is undoubtedly one of extreme difficulty. Still, it is
something, in this as in all cases, to have the problem even stated;
and none of the elements of the solution appears to be of such a
nature that we need allow ourselves to yield to despair, respecting
the possibility of dealing with it in a useful manner, as our
knowledge becomes more complete and definite. {561}




CHAPTER VI.

PROGRESS OF THE GEOLOGICAL DYNAMICS OF ORGANIZED BEINGS.


_Sect._ 1.--_Objects of this Science._

PERHAPS in extending the term _Geological Dynamics_ to the causes of
changes in organized beings, I shall be thought to be employing a
forced and inconvenient phraseology. But it will be found that, in
order to treat geology in a truly scientific manner, we must bring
together all the classes of speculations concerning known causes of
change; and the Organic Dynamics of Geology, or of Geography, if the
reader prefers the word, appears not an inappropriate phrase for one
part of this body of researches.

As has already been said, the species of plants and animals which
are found embedded in the strata of the earth, are not only
different from those which now live in the same regions, but, for
the most part, different from any now existing on the face of the
earth. The remains which we discover imply a past state of things
different from that which now prevails; they imply also that the
whole organic creation has been renewed, and that this renewal has
taken place several times. Such extraordinary general facts have
naturally put in activity very bold speculations.

But it has already been said, we cannot speculate upon such facts in
the past history of the globe, without taking a large survey of its
present condition. Does the present animal and vegetable population
differ from the past, in the same way in which the products of one
region of the existing earth differ from those of another? Can the
creation and diffusion of the fossil species be explained in the
same manner as the creation and diffusion of the creatures among
which we live? And these questions lead us onwards another step, to
ask,--What _are_ the laws by which the plants and animals of
different parts of the earth differ? What was the manner in which
they were originally diffused?--Thus we have to include, as portions
of our subject, {562} the _Geography of Plants_, and _of Animals_,
and the _History of their change and diffusion_; intending by the
latter subject, of course, _palætiological_ history,--the
examination of the causes of what has occurred, and the inference of
past events, from what we know of causes.

It is unnecessary for me to give at any length a statement of the
problems which are included in these branches of science, or of the
progress which has been made in them; since Mr. Lyell, in his
_Principles of Geology_, has treated these subjects in a very able
manner, and in the same point of view in which I am thus led to
consider them. I will only briefly refer to some points, availing
myself of his labors and his ideas.


_Sect._ 2.--_Geography of Plants and Animals._

WITH regard both to plants and animals, it appears,[78\18] that
besides such differences in the products of different regions as we
may naturally suppose to be occasioned by climate and other external
causes; an examination of the whole organic population of the globe
leads us to consider the earth as divided into _provinces_, each
province being occupied by its own group of species, and these
groups not being mixed or interfused among each other to any great
extent. And thus, as the earth is occupied by various nations of
men, each appearing at first sight to be of a different stock, so
each other tribe of living things is scattered over the ground in a
similar manner, and distributed into its separate _nations_ in
distant countries. The places where species are thus peculiarly
found, are, in the case of plants, called their _stations_. Yet each
species in its own region loves and selects some peculiar conditions
of shade or exposure, soil or moisture: its place, defined by the
general description of such conditions, is called its _habitation_.

[Note 78\18: Lyell, _Principles_, B. iii. c. v.]

Not only each species thus placed in its own province, has its
position further fixed by its own habits, but more general groups
and assemblages are found to be determined in their situation by
more general conditions. Thus it is the character of the _flora_ of
a collection of islands, scattered through a wide ocean in a
tropical and humid climate, to contain an immense preponderance of
tree-ferns. In the same way, the situation and depth at which
certain genera of shells are found have been tabulated[79\18] by Mr.
Broderip. Such general inferences, if {563} they can be securely
made, are of extreme interest in their bearing on geological
speculations.

[Note 79\18: Greenough, _Add._ 1835, p. 20.]

The means by which plants and animals are now diffused from one
place to another, have been well described by Mr. Lyell.[80\18] And
he has considered also, with due attention, the manner in which they
become imbedded in mineral deposits of various kinds.[81\18] He has
thus followed the history of organized bodies, from the germ to the
tomb, and thence to the cabinet of the geologist.

[Note 80\18: Lyell, B. iii. c. v. vi. vii.]

[Note 81\18: B. iii. c. xiii. xiv. xv. xvi.]

But, besides the fortunes of individual plants and animals, there is
another class of questions, of great interest, but of great
difficulty;--the fortunes of each species. In what manner do species
which were not, begin to be? as geology teaches us that they many
times have done; and, as even our own reasonings convince us they must
have done, at least in the case of the species among which we live.

We here obviously place before us, as a subject of research, the
Creation of Living Things;--a subject shrouded in mystery, and not
to be approached without reverence. But though we may conceive,
that, on this subject, we are not to seek our belief from science
alone, we shall find, it is asserted, within the limits of allowable
and unavoidable speculation, many curious and important problems
which may well employ our physiological skill. For example, we may
ask:--how we are to recognize the species which were originally
created distinct?--whether the population of the earth at one
geological epoch could pass to the form which it has at a succeeding
period, by the agency of natural causes alone?--and if not, what
other account we can give of the succession which we find to have
taken place?

The most remarkable point in the attempts to answer these and the
like questions, is the controversy between the advocates and the
opponents of the doctrine of the _transmutation of species_. This
question is, even from its mere physiological import, one of great
interest; and the interest is much enhanced by our geological
researches, which again bring the question before us in a striking
form, and on a gigantic scale. We shall, therefore, briefly state
the point at issue.


_Sect._ 3.--_Question of the Transmutation of Species._

WE see that animals and plants may, by the influence of breeding,
and of external agents operating upon their constitution, be greatly
{564} modified, so as to give rise to varieties and races different
from what before existed. How different, for instance, is one kind
and breed of dog from another! The question, then, is, whether
organized beings can, by the mere working of natural causes, pass
from the type of one species to that of another? whether the wolf
may, by domestication, become the dog? whether the ourang-outang
may, by the power of external circumstances, be brought within the
circle of the human species? And the dilemma in which we are placed
is this;--that if species are not thus interchangeable, we must
suppose the fluctuations of which each species is capable, and which
are apparently indefinite, to be bounded by rigorous limits;
whereas, if we allow such a _transmutation of species_, we abandon
that belief in the adaptation of the structure of every creature to
its destined mode of being, which not only most persons would give
up with repugnance, but which, as we have seen, has constantly and
irresistibly impressed itself on the minds of the best naturalists,
as the true view of the order of the world.

But the study of Geology opens to us the spectacle of many groups of
species which have, in the course of the earth's history, succeeded
each other at vast intervals of time; one set of animals and plants
disappearing, as it would seem, from the face of our planet, and
others, which did not before exist, becoming the only occupants of
the globe. And the dilemma then presents itself to us anew:--either
we must accept the doctrine of the transmutation of species, and
must suppose that the organized species of one geological epoch were
transmuted into those of another by some long-continued agency of
natural causes; or else, we must believe in many successive acts of
creation and extinction of species, out of the common course of
nature; acts which, therefore, we may properly call miraculous.

This latter dilemma, however, is a question concerning the facts
which have happened in the history of the world; the deliberation
respecting it belongs to physical geology itself, and not to that
subsidiary science which we are now describing, and which is
concerned only with such causes as we know to be in constant and
orderly action.

The former question, of the limited or unlimited extent of the
modifications of animals and plants, has received full and careful
consideration from eminent physiologists; and in their opinions we
find, I think, an indisputable preponderance to that decision which
rejects the transmutation of species, and which accepts the former
side of the dilemma; namely, that the changes of which each species
is {565} susceptible, though difficult to define in words, are
limited in fact. It is extremely interesting and satisfactory thus
to receive an answer in which we can confide, to inquiries seemingly
so wide and bold as those which this subject involves. I refer to
Mr. Lyell, Dr. Prichard, Mr. Lawrence, and others, for the history
of the discussion, and for the grounds of the decision; and I shall
quote very briefly the main points and conclusions to which the
inquiry has led.[82\18]

[Note 82\18: Lyell, B. iii. c. iv.]

It may be considered, then, as determined by the over-balance of
physiological authority, that there is a capacity in all species to
accommodate themselves, to a certain extent, to a change of external
circumstances; this extent varying greatly according to the species.
There may thus arise changes of appearance or structure, and some of
these changes are transmissible to the offspring: but the mutations
thus superinduced are governed by constant laws, and confined within
certain limits. Indefinite divergence from the original type is not
possible; and the extreme limit of possible variation may usually be
reached in a brief period of time: in short, _species have a real
existence in nature_, and a transmutation from one to another does
not exist.

Thus, for example, Cuvier remarks, that notwithstanding all the
differences of size, appearance, and habits, which we find in the dogs
of various races and countries, and though we have (in the Egyptian
mummies) skeletons of this animal as it existed three thousand years
ago, the relation of the bones to each other remains essentially the
same; and, with all the varieties of their shape[83\18] and size,
there are characters which resist all the influences both of external
nature, of human intercourse, and of time.

[Note 83\18:  _Ossem. Foss._ Disc. Prél. p. 61.]


_Sect._ 4.--_Hypothesis of Progressive Tendencies._

WITHIN certain limits, however, as we have said, external
circumstances produce changes in the forms of organized beings. The
causes of change, and the laws and limits of their effects, as they
obtain in the existing state of the organic creation, are in the
highest degree interesting. And, as has been already intimated, the
knowledge thus obtained, has been applied with a view to explain the
origin of the existing population of the world, and the succession
of its past conditions. But those who have attempted such an
explanation, have found it necessary to assume certain additional
laws, in order to enable themselves to {566} deduce, from the tenet
of the transmutability of the species of organized beings, such a
state of things as we see about us, and such a succession of states
as is evidenced by geological researches. And here, again, we are
brought to questions of which we must seek the answers from the most
profound physiologists. Now referring, as before, to those which
appear to be the best authorities, it is found that these additional
positive laws are still more inadmissible than the primary
assumption of indefinite capacity of change. For example, in order
to account, on this hypothesis, for the seeming adaptation of the
endowments of animals to their wants, it is held that the endowments
are the result of the wants; that the swiftness of the antelope, the
claws and teeth of the lion, the trunk of the elephant, the long
neck of the giraffe have been produced by a certain plastic
character in the constitution of animals, operated upon, for a long
course of ages, by the attempts which these animals made to attain
objects which their previous organization did not place within their
reach. In this way, it is maintained that the most striking
attributes of animals, those which apparently imply most clearly the
providing skill of their Creator, have been brought forth by the
long-repeated efforts of the creatures to attain the object of their
desire; thus animals with the highest endowments have been gradually
developed from ancestral forms of the most limited organization;
thus fish, bird, and beast, have grown from _small gelatinous
bodies_, "petits corps gelatineux," possessing some obscure
principle of life, and the capacity of development; and thus man
himself with all his intellectual and moral, as well as physical
privileges, has been derived from some creature of the ape or baboon
tribe, urged by a constant tendency to improve, or at least to alter
his condition.

As we have said, in order to arrive even hypothetically at this
result, it is necessary to assume besides a mere capacity for
change, other positive and active principles, some of which we may
notice. Thus, we must have as the direct productions of nature on
this hypothesis, certain monads or rough draughts, the primary
_rudiments_ of plants and animals. We must have, in these, a
constant _tendency to progressive improvement_, to the attainment of
higher powers and faculties than they possess; which tendency is
again perpetually modified and controlled by the _force of external
circumstances_. And in order to account for the simultaneous
existence of animals in every stage of this imaginary progress, we
must suppose that nature is compelled to be _constantly_ producing
those elementary beings, from which all animals are successively
developed. {567}

I need not stay to point out how extremely arbitrary every part of
this scheme is; and how complex its machinery would be, even if it
did account for the facts. It may be sufficient to observe, as
others have done,[84\18] that the capacity of change, and of being
influenced by external circumstances, such as we really find it in
nature, and therefore such as in science we must represent it, is a
tendency, not to improve, but to deteriorate. When species are
modified by external causes, they usually degenerate, and do not
advance. And there is no instance of a species acquiring an entirely
new sense, faculty, or organ, in addition to, or in the place of,
what it had before.

[Note 84\18: Lyell, B. III. c. iv.]

Not only, then, is the doctrine of the transmutation of species in
itself disproved by the best physiological reasonings, but the
additional assumptions which are requisite, to enable its advocates
to apply it to the explanation of the geological and other phenomena
of the earth, are altogether gratuitous and fantastical.

Such is the judgment to which we are led by the examination of the
discussions which have taken place on this subject. Yet in certain
speculations, occasioned by the discovery of the _Sivatherium_, a
new fossil animal from the Sub-Himalaya mountains of India, M.
Geoffroy Saint-Hilaire speaks of the belief in the immutability of
species as a conviction which is fading away from men's minds. He
speaks too of the termination of the age of Cuvier, "la clôture du
siècle de Cuvier," and of the commencement of a better zoological
philosophy.[85\18] But though he expresses himself with great
animation, I do not perceive that he adduces, in support of his
peculiar opinions, any arguments in addition to those which he urged
during the lifetime of Cuvier. And the reader[86\18] may recollect
that the consideration of that controversy led us to very different
anticipations from his, respecting the probable future progress of
physiology. The discovery of the Sivatherium supplies no particle of
proof to the hypothesis, that the existing species of animals are
descended from extinct creatures which are specifically distinct:
and we cannot act more wisely than in listening to the advice of
that eminent naturalist, M. de Blainville.[87\18] "Against this
hypothesis, which, up to the present time, I regard as purely
gratuitous, and likely to turn geologists out of the sound and
excellent road in which they now are, I willingly raise my voice,
with the most absolute conviction of being in the right." {568}

[Note 85\18: _Compte Rendu de l'Acad. des Sc._ 1837, No. 3, p. 81.]

[Note 86\18: See B. XVII. c. vii.]

[Note 87\18: _Compte Rendu_, 1837, No. 5, p. 168.]

[2nd Ed.] [The hypothesis of the progressive developement of species
has been urged recently, in connexion with the physiological tenet
of Tiedemann and De Serres, noticed in B. XVII. c. vii. sect.
3;--namely, that the embryo of the higher forms of animals passes by
gradations through those forms which are permanent in inferior
animals. Assuming this tenet as exact, it has been maintained that
the higher animals which are found in the more recent strata may
have been produced by an ulterior development of the lower forms in
the embryo state; the circumstances being such as to favor such a
developement. But all the best physiologists agree in declaring that
such an extraordinary developement of the embryo is inconsistent
with physiological possibility. Even if the progression of the
embryo in time have a general correspondence with the order of
animal forms as more or less perfectly organized (which is true in
an extremely incomplete and inexact degree), this correspondence
must be considered, not as any indication of causality, but as one
of those marks of universal analogy and symmetry which are stamped
upon every part of the creation.

Mr. Lyell[88\18] notices this doctrine of Tiedemann and De Serres;
and observes, that though nature presents us with cases of animal
forms degraded by incomplete developement, she offers none of forms
exalted by extraordinary developement. Mr. Lyell's own hypothesis of
the introduction of new species upon the earth, not having any
physiological basis, hardly belongs to this chapter.]

[Note 88\18: _Principles_, B. III. c. iv.]


_Sect._ 5.--_Question of Creation as related to Science._

BUT since we reject the production of new species by means of
external influence, do we then, it may be asked, accept the other
side of the dilemma which we have stated; and admit a series of
creations of species, by some power beyond that which we trace in
the ordinary course of nature?

To this question, the history and analogy of science, I conceive,
teach us to reply as follows:--All palætiological sciences, all
speculations which attempt to ascend from the present to the remote
past, by the chain of causation, do also, by an inevitable
consequence, urge us to look for the beginning of the state of
things which we thus contemplate; but in none of these cases have
men been able, by the aid of science, to arrive at a beginning which
is homogeneous with the {569} known course of events. The first
origin of language, of civilization, of law and government, cannot
be clearly made out by reasoning and research; just as little, we
may expect, will a knowledge of the origin of the existing and
extinct species of plants and animals, be the result of
physiological and geological investigation.

But, though philosophers have never yet demonstrated, and perhaps
never will be able to demonstrate, what was that primitive state of
things in the social and material worlds, from which the progressive
state took its first departure; they can still, in all the lines of
research to which we have referred, go very far back;--determine many
of the remote circumstances of the past sequence of events;--ascend to
a point which, from our position at least, seems to be near the
origin;--and exclude many suppositions respecting the origin itself.
Whether, by the light of reason alone, men will ever be able to do
more than this, it is difficult to say. It is, I think, no irrational
opinion, even on grounds of philosophical analogy alone, that in all
those sciences which look back and seek a beginning of things, we may
be unable to arrive at a consistent and definite belief, without
having recourse to other grounds of truth, as well as to historical
research and scientific reasoning. When our thoughts would apprehend
steadily the creation of things, we find that we are obliged to summon
up other ideas than those which regulate the pursuit of scientific
truths;--to call in other powers than those to which we refer natural
events: it cannot, then, be considered as very surprizing, if, in this
part of our inquiry, we are compelled to look for other than the
ordinary evidence of science.

Geology, forming one of the palætiological class of sciences, which
trace back the history of the earth and its inhabitants on
philosophical grounds, is thus associated with a number of other
kinds of research, which are concerned about language, law, art, and
consequently about the internal faculties of man, his thoughts, his
social habits, his conception of right, his love of beauty. Geology
being thus brought into the atmosphere of moral and mental
speculations, it may be expected that her investigations of the
probable past will share an influence common to them; and that she
will not be allowed to point to an origin of her own, a merely
physical beginning of things; but that, as she approaches towards
such a goal, she will be led to see that it is the origin of many
trains of events, the point of convergence of many lines. It may be,
that instead of being allowed to travel up to this focus of being,
we are only able to estimate its place and nature, and {570} to form
of it such a judgment as this;--that it is not only the source of
mere vegetable and animal life, but also of rational and social
life, language and arts, law and order; in short, of all the
progressive tendencies by which the highest principles of the
intellectual and moral world have been and are developed, as well as
of the succession of organic forms, which we find scattered, dead or
living, over the earth.

This reflection concerning the natural scientific view of creation,
it will be observed, has not been sought for, from a wish to arrive
at such conclusions; but it has flowed spontaneously from the manner
in which we have had to introduce geology into our classification of
the sciences; and this classification was framed from an unbiassed
consideration of the general analogies and guiding ideas of the
various portions of our knowledge. Such remarks as we have made may
on this account be considered more worthy of attention.

But such a train of thought must be pursued with caution. Although
it may not be possible to arrive at a right conviction respecting
the origin of the world, without having recourse to other than
physical considerations, and to other than geological evidence: yet
extraneous considerations, and extraneous evidence, respecting the
nature of the beginning of things, must never be allowed to
influence our physics or our geology. Our geological dynamics, like
our astronomical dynamics, may be inadequate to carry us back to an
origin of that state of things, of which it explains the progress:
but this deficiency must be supplied, not by adding supernatural to
natural geological dynamics, but by accepting, in their proper
place, the views supplied by a portion of knowledge of a different
character and order. If we include in our Theology the speculations
to which we have recourse for this purpose, we must exclude from
them our Geology. The two sciences may conspire, not by having any
part in common: but because, though widely diverse in their lines,
both point to a mysterious and invisible origin of the world.

All that which claims our assent on those higher grounds of which
theology takes cognizance, must claim such assent as is consistent
with those grounds; that is, it must require belief in respect of
all that bears upon the highest relations of our being, those on
which depend our duties and our hopes. Doctrines of this kind may
and must be conveyed and maintained, by means of information
concerning the past history of man, and his social and material, as
well as moral and spiritual fortunes. He who believes that a
Providence has {571} ruled the affairs of mankind, will also believe
that a Providence has governed the material world. But any language
in which the narrative of this government of the material world can
be conveyed, must necessarily be very imperfect and inappropriate;
being expressed in terms of those ideas which have been selected by
men, in order to describe appearances and relations of created
things as they affect one another. In all cases, therefore, where we
have to attempt to interpret such a narrative, we must feel that we
are extremely liable to err; and most of all, when our
interpretation refers to those material objects and operations which
are most foreign to the main purpose of a history of providence. If
we have to consider a communication containing a view of such a
government of the world, imparted to us, as we may suppose, in order
to point out the right direction for our feelings of trust, and
reverence, and hope, towards the Governor of the world, we may
expect that we shall be in no danger of collecting from our
authority erroneous notions with regard to the power, and wisdom,
and goodness of His government; or with respect to our own place,
duties, and prospects, and the history of our race so far as our
duties and prospects are concerned. But that we shall rightly
understand the detail of all events in the history of man, or of the
skies, or of the earth, which are narrated for the purpose of thus
giving a right direction to our minds, is by no means equally
certain; and I do not think it would be too much to say, that an
immunity from perplexity and error, in such matters, is, on general
grounds, very improbable. It cannot then surprise us to find, that
parts of such narrations which seem to refer to occurrences like
those of which astronomers and geologists have attempted to
determine the laws, have given rise to many interpretations, all
inconsistent with one another, and most of them at variance with the
best established principles of astronomy and geology.

It may be urged, that all truths must be consistent with all other
truths, and that therefore the results of true geology or astronomy
cannot be irreconcileable with the statements of true theology. And
this universal consistency of truth with itself must be assented to;
but it by no means follows that we must be able to obtain a full
insight into the nature and manner of such a consistency. Such an
insight would only be possible if we could obtain a clear view of
that central body of truth, the source of the principles which
appear in the separate lines of speculation. To expect that we
should see clearly how the providential government of the world is
consistent with the unvarying laws {572} by which its motions and
developements are regulated, is to expect to understand thoroughly
the laws of motion, of developement, and of providence; it is to
expect that we may ascend from geology and astronomy to the creative
and legislative centre, from which proceeded earth and stars; and
then descend again into the moral and spiritual world, because its
source and centre are the same as those of the material creation. It
is to say that reason, whether finite or infinite, must be
consistent with itself; and that, therefore, the finite must be able
to comprehend the infinite, to travel from any one province of the
moral and material universe to any other, to trace their bearing,
and to connect their boundaries.

One of the advantages of the study of the history and nature of
science in which we are now engaged is, that it warns us of the
hopeless and presumptuous character of such attempts to understand
the government of the world by the aid of science, without throwing
any discredit upon the reality of our knowledge;--that while it
shows how solid and certain each science is, so long as it refers
its own facts to its own ideas, it confines each science within its
own limits, and condemns it as empty and helpless, when it
pronounces upon those subjects which are extraneous to it. The error
of persons who should seek a geological narrative in theological
records, would be rather in the search itself than in their
interpretation of what they might find; and in like manner the error
of those who would conclude against a supernatural beginning, or a
providential direction of the world, upon geological or
physiological reasonings, would be, that they had expected those
sciences alone to place the origin or the government of the world in
its proper light.

Though these observations apply generally to all the palætiological
sciences, they may be permitted here, because they have an especial
bearing upon some of the difficulties which have embarrassed the
progress of geological speculation; and though such difficulties
are, I trust, nearly gone by, it is important for us to see them in
their true bearing.

From what has been said, it follows that geology and astronomy are,
of themselves, incapable of giving us any distinct and satisfactory
account of the origin of the universe, or of its parts. We need not
wonder, then, at any particular instance of this incapacity; as, for
example, that of which we have been speaking, the impossibility of
accounting by any natural means for the production of all the
successive tribes of plants and animals which have peopled the world
in the {573} various stages of its progress, as geology teaches us.
That they were, like our own animal and vegetable contemporaries,
profoundly adapted to the condition in which they were placed, we
have ample reason to believe; but when we inquire whence they came
into this our world, geology is silent. The mystery of creation is
not within the range of her legitimate territory; she says nothing,
but she points upwards.


_Sect._ 6.--_The Hypothesis of the regular Creation and Extinction
of Species._

1. _Creation of Species._--We have already seen, how untenable, as a
physiological doctrine, is the principle of the transmutability and
progressive tendency of species; and therefore, when we come to
apply to theoretical geology the principles of the present chapter,
this portion of the subject will easily be disposed of. I hardly
know whether I can state that there is any other principle which has
been applied to the solution of the geological problem, and which,
therefore, as a general truth, ought to be considered here. Mr.
Lyell, indeed, has spoken[89\18] of an hypothesis that "the
successive creation of species may constitute a regular part of the
economy of nature:" but he has nowhere, I think, so described this
process as to make it appear in what department of science we are to
place the hypothesis. Are these new species created by the
production, at long intervals, of an offspring different in species
from the parents? Or are the species so created produced without
parents? Are they gradually evolved from some embryo substance? or
do they suddenly start from the ground, as in the creation of the
poet?
  . . . . . . . Perfect forms
  Limbed and full-grown: out of the ground up rose
  As from his lair, the wild beast where he wons
  In forest wild, in thicket, brake, or den; . . .
  The grassy clods now calved; now half appeared
  The tawny lion, pawing to get free
  His hinder parts; then springs as broke from bounds,
  And rampant shakes his brinded mane; &c. &c.
          _Paradise Lost_, B. vii.

[Note 89\18: B. III. c. xi. p. 234.]

Some selection of one of these forms of the hypothesis, rather than
the others, with evidence for the selection, is requisite to entitle
us to {574} place it among the known causes of change which in this
chapter we are considering. The bare conviction that a creation of
species has taken place, whether once or many times, so long as it
is unconnected with our organical sciences, is a tenet of Natural
Theology rather than of Physical Philosophy.

[2nd Ed.] [Mr. Lyell has explained his theory[90\18] by supposing
man to people a great desert, introducing into it living plants and
animals: and he has traced, in a very interesting manner, the
results of such a hypothesis on the distribution of vegetable and
animal species. But he supposes the agents who do this, before they
import species into particular localities, to study attentively the
climate and other physical conditions of each spot, and to use
various precautions. It is on account of the notion of design thus
introduced that I have, above, described this opinion as rather a
tenet of Natural Theology than of Physical Philosophy.

[Note 90\18: B. III. c. viii. p. 166.]

Mr. Edward Forbes has published some highly interesting speculations
on the distribution of existing species of animals and plants. It
appears that the manner in which animal and vegetable forms are now
diffused requires us to assume centres from which the diffusion took
place by no means limited by the present divisions of continents and
islands. The changes of land and water which have thus occurred
since the existing species were placed on the earth must have been
very extensive, and perhaps reach into the glacial period of which I
have spoken above.[91\18]

[Note 91\18: See, in _Memoirs of the Geological Survey of Great
Britain_, vol. i. p. 336, Professor Forbes's Memoir "On the
Connection between the Distribution of the existing Fauna and Flora
of the British Isles, and the Geological Changes which have affected
their area, especially during the epoch of the Northern Drift."]

According to Mr. Forbes's views, for which he has offered a great
body of very striking and converging reasons, the present vegetable
and animal population of the British Isles is to be accounted for by
the following series of events. The marine deposits of the
_meiocine_ formation were elevated into a great Atlantic continent,
yet separate from what is now America, and having its western shore
where now the great semi-circular belt of gulf-weed ranges from the
15th to the 45th parallel of latitude. This continent then became
stocked with life, and of its vegetable population, the flora of the
west of Ireland, which has many points in common with the flora of
Spain and the {575} Atlantic islands (the _Asturian_ flora), is the
record. The region between Spain and Ireland, and the rest of this
meiocene continent, was destroyed by some geological movement, but
there were left traces of the connexion which still remain.
Eastwards of the flora just mentioned, there is a flora common to
Devon and Cornwall, to the south-east part of Ireland, the Channel
Isles, and the adjacent provinces of France;--a flora passing to a
southern character; and having its course marked by the remains of a
great rocky barrier, the destruction of which probably took place
anterior to the formation of the narrower part of the channel.
Eastward from this _Devon_ or _Norman_ flora, again, we have the
_Kentish_ flora, which is an extension of the flora of North-western
France, insulated by the breach which formed the straits of Dover.
Then came the _Glacial period_, when the east of England and the
north of Europe were submerged, the northern drift was distributed,
and England was reduced to a chain of islands or ridges, formed by
the mountains of Wales, Cumberland, and Scotland, which were
connected with the land of Scandinavia. This was the period of
glaciers, of the dispersion of boulders, of the grooving and
scratching of rocks as they are now found. The climate being then
much colder than it now is, the flora, even down to the water's
edge, consisted of what are now Alpine plants; and this _Alpine_
flora is common to Scandinavia and to our mountain-summits. And
these plants kept their places, when, by the elevation of the land,
the whole of the present German Ocean became a continent connecting
Britain with central Europe. For the increased elevation of their
stations counterbalanced the diminished cold of the succeeding
period. Along the dry bed of the German Sea, thus elevated, the
principal part of the existing flora of England, the _Germanic_
flora, migrated. A large portion of our existing animal population
also came over through the same region; and along with those, came
hyenas, tigers, rhinoceros, aurochs, elk, wolves, beavers, which are
extinct in Britain, and other animals which are extinct altogether,
as the primigenian elephant or mammoth. But then, again, the German
Ocean and the Irish Channel were scooped out; and the climate again
changed. In our islands, so detached, many of the larger beasts
perished, and their bones were covered up in peat-mosses and caves,
where we find them. This distinguished naturalist has further shown
that the population of the sea lends itself to the same view. Mr.
Forbes says that the writings of Mr. Smith, of Jordan-hill, "On the
last Changes in the relative Levels of the Land and Sea in the
British Islands," published in the _Memoirs of the_ {576} _Wernerian
Society for_ 1837-8, must be esteemed the foundation of a critical
investigation of this subject in Britain.]

2. _Extinction of Species._--With regard to the extinction of
species Mr. Lyell has propounded a doctrine which is deserving of
great attention here. Brocchi, when he had satisfied himself, by
examination of the Sub-Apennines, that about half the species which
had lived at the period of their deposition, had since become
extinct, suggested as a possible cause for this occurrence, that the
vital energies of a species, like that of an individual, might
gradually decay in the progress of time and of generations, till at
last the prolific power might fail, and the species wither away.
Such a property would be conceivable as a physiological fact; for we
see something of the kind in fruit-trees propagated by cuttings:
after some time, the stock appears to wear out, and loses its
peculiar qualities. But we have no sufficient evidence that this is
the case in generations of creatures continued by the reproductive
powers. Mr. Lyell conceives, that, without admitting any inherent
constitutional tendency to deteriorate, the misfortunes to which
plants and animals are exposed by the change of the physical
circumstances of the earth, by the alteration of land and water, and
by the changes of climate, must very frequently occasion the loss of
several species. We have historical evidence of the extinction of
one conspicuous species, the Dodo, a bird of large size and singular
form, which inhabited the Isle of France when that island was first
discovered, and which now no longer exists. Several other species of
animals and plants seem to be in the course of vanishing from the
face of the earth, even under our own observation. And taking into
account the greater changes of the surface of the globe which
geology compels us to assume, we may imagine many or all the
existing species of living things to be extirpated. If, for
instance, that reduction of the climate of the earth which appears,
from geological evidence, to have taken place already, be supposed
to go on much further, the advancing snow and cold of the polar
regions may destroy the greater part of our plants and animals, and
drive the remainder, or those of them which possess the requisite
faculties of migration and accommodation, to seek an asylum near the
equator. And if we suppose the temperature of the earth to be still
further reduced, this zone of now-existing life, having no further
place of refuge, will perish, and the whole earth will be tenanted,
if at all, by a new creation. Other causes might produce the same
effect as a change of climate; and, without supposing such causes to
affect the whole globe, it is easy to {577} imagine circumstances
such as might entirely disturb the equilibrium which the powers of
diffusion of different species have produced;--might give to some
the opportunity of invading and conquering the domain of others; and
in the end, the means of entirely suppressing them, and establishing
themselves in their place.

That this extirpation of certain species, which, as we have seen,
happens in a few cases under common circumstances, might happen upon
a greater scale, if the range of external changes were to be much
enlarged, cannot be doubted. The extent, therefore, to which natural
causes may account for the extinction of species, will depend upon
the amount of change which we suppose in the physical conditions of
the earth. It must be a task of extreme difficulty to estimate the
effect upon the organic world, even if the physical circumstances
were given. To determine the physical condition to which a given
state of the earth would give rise, I have already noted as another
very difficult problem. Yet these two problems must be solved, in
order to enable us to judge of the sufficiency of any hypothesis of
the extinction of species; and in the mean time, for the mode in
which new species come into the places of those which are
extinguished, we have (as we have seen) no hypothesis which
physiology can, for a moment, sanction.


_Sect._ 7.--_The Imbedding of Organic Remains._

THERE is still one portion of the Dynamics of Geology, a branch of
great and manifest importance, which I have to notice, but upon
which I need only speak very briefly. The mode in which the spoils
of existing plants and animals are imbedded in the deposits now
forming, is a subject which has naturally attracted the attention of
geologists. During the controversy which took place in Italy
respecting the fossils of the Sub-Apennine hills, Vitaliano
Donati,[92\18] in 1750, undertook an examination of the Adriatic,
and found that deposits containing shells and corals, extremely
resembling the strata of the hills, were there in the act of
formation. But without dwelling on other observations of like kind,
I may state that Mr. Lyell has treated this subject, and all the
topics connected with it, in a very full and satisfactory manner. He
has explained,[93\18] by an excellent collection of illustrative
facts, how deposits of various substance and contents are formed;
how plants and animals become fossil in peat, in blown sand, in
volcanic matter, in {578} alluvial soil, in caves, and in the beds
of lakes and seas. This exposition is of the most instructive
character, as a means of obtaining right conclusions concerning the
causes of geological phenomena. Indeed, in many cases, the
similarity of past effects with operations now going on, is so
complete, that they may be considered as identical; and the
discussion of such cases belongs, at the same time, to Geological
Dynamics and to Physical Geology; just as the problem of the fall of
meteorolites may be considered as belonging alike to mechanics and
to physical astronomy. The growth of modern peat-mosses, for
example, fully explains the formation of the most ancient: objects
are buried in the same manner in the ejections of active and of
extinct volcanoes; within the limits of history, many estuaries have
been filled up; and in the deposits which have occupied these
places, are strata containing shells,[94\18] as in the older
formations.

[Note 92\18: Lyell, B. I. c. iii. p. 67. (4th ed.)]

[Note 93\18: B. III. c. xiii. xiv. xv. xvi. xvii.]

[Note 94\18: Lyell, B. III. c. xvii. p. 286. See also his Address to
the Geological Society in 1837, for an account of the Researches of
Mr. Stokes and of Professor Göppert, on the lapidification of
vegetables.]



{{579}}
PHYSICAL GEOLOGY.




CHAPTER VII.

PROGRESS OF PHYSICAL GEOLOGY.


_Sect._ 1.--_Object and Distinctions of Physical Geology._

BEING, in consequence of the steps which we have attempted to
describe, in possession of two sciences, one of which traces the
laws of action of known causes, and the other describes the
phenomena which the earth's surface presents, we are now prepared to
examine how far the attempts to refer the facts to their causes have
been successful: we are ready to enter upon the consideration of
Theoretical or _Physical_ Geology, as, by analogy with Physical
Astronomy, we may term this branch of speculation.

The distinction of this from other portions of our knowledge is
sufficiently evident. In former times, Geology was always associated
with Mineralogy, and sometimes confounded with it; but the mistake
of such an arrangement must be clear, from what has been said.
Geology is connected with Mineralogy, only so far as the latter
science classifies a large portion of the objects which Geology
employs as evidence of its statements. To confound the two is the
same error as it would be to treat philosophical history as
identical with the knowledge of medals. Geology procures evidence of
her conclusions wherever she can; from minerals or from seas; from
inorganic or from organic bodies; from the ground or from the skies.
The geologist's business is to learn the past history of the earth;
and he is no more limited to one or a few kinds of documents, as his
sources of information, than is the historian of man, in the
execution of a similar task.

Physical Geology, of which I now speak, may not be always easily
separable from Descriptive Geology: in fact, they have generally
been combined, for few have been content to describe, without
attempting in some measure to explain. Indeed, if they had done so,
it is {580} probable that their labors would have been far less
zealous, and their expositions far less impressive. We by no means
regret, therefore, the mixture of these two kinds of knowledge,
which has so often occurred; but still, it is our business to
separate them. The works of astronomers before the rise of sound
physical astronomy, were full of theories, but these were
advantageous, not prejudicial, to the progress of the science.

Geological theories have been abundant and various; but yet our
history of them must be brief. For our object is, as must be borne in
mind, to exhibit these, only so far as they are steps discoverably
tending to the _true_ theory of the earth: and in most of them we do
not trace this character. Or rather, the portions of the labors of
geologists which do merit this praise, belong to the two preceding
divisions of the subject, and have been treated of there.

The history of Physical Geology, considered as the advance towards a
science as real and stable as those which we have already treated of
(and this is the form in which we ought to trace it), hitherto
consists of few steps. We hardly know whether the progress is begun.
The history of Physical Astronomy almost commences with Newton, and
few persons will venture to assert that the Newton of Geology has
yet appeared.

Still, some examination of the attempts which have been made is
requisite, in order to explain and justify the view which the
analogy of scientific history leads us to take, of the state of the
subject. Though far from intending to give even a sketch of all past
geological speculations, I must notice some of the forms such
speculations have at different times assumed.


_Sect._ 2.--_Of Fanciful Geological Opinions._

REAL and permanent geological knowledge, like all other physical
knowledge, can be obtained only by inductions of classification and
law from many clearly seen phenomena. The labor of the most active,
the talent of the most intelligent, are requisite for such a
purpose. But far less than this is sufficient to put in busy
operation the inventive and capricious fancy. A few appearances
hastily seen, and arbitrarily interpreted, are enough to give rise
to a wondrous tale of the past, full of strange events and
supernatural agencies. The mythology and early poetry of nations
afford sufficient evidence of man's love of the wonderful, and of
his inventive powers, in early stages of intellectual development.
The scientific faculty, on the other hand, {581} and especially that
part of it which is requisite for the induction of laws from facts,
emerges slowly and with difficulty from the crowd of adverse
influences, even under the most favorable circumstances. We have
seen that in the ancient world, the Greeks alone showed themselves
to possess this talent; and what they thus attained to, amounted
only to a few sound doctrines in astronomy, and one or two extremely
imperfect truths in mechanics, optics, and music, which their
successors were unable to retain. No other nation, till we come to
the dawn of a better day in modern Europe, made any positive step at
all in sound physical speculation. Empty dreams or useless
exhibitions of ingenuity, formed the whole of their essays at such
knowledge.

It must, therefore, independently of positive evidence, be
considered as extremely improbable, that any of these nations
should, at an early period, have arrived, by observation and
induction, at wide general truths, such as the philosophers of
modern times have only satisfied themselves of by long and patient
labor and thought. If resemblances should be discovered between the
assertions of ancient writers and the discoveries of modern science,
the probability in all cases, the certainty in most, is that these
are accidental coincidences;--that the ancient opinion is no
anticipation of the modern discovery, but is one guess among many,
not a whit the more valuable because its expression agrees with a
truth. The author of the guess could not intend the truth, because
his mind was not prepared to comprehend it. Those of the ancients
who spoke of the _harmony_ which binds all things together, could
not mean the Newtonian gravitation, because they had never been led
to conceive an attractive force, governed by definite mathematical
laws in its quantity and operation.

In agreement with these views, we must, I conceive, estimate the
opinions which we find among the ancients, respecting the changes
which the earth's surface has undergone. These opinions, when they
are at all of a general kind, are arbitrary fictions of the fancy,
showing man's love of generality indeed, but indulging it without
that expense of labor and thought which alone can render it
legitimate.

We might, therefore, pass by all the traditions and speculations of
Oriental, Egyptian, and Greek cosmogony, as extraneous to our
subject. But since these have recently been spoken of, as
conclusions collected, however vaguely, from observed facts,[95\18]
we may make a remark or two upon them. {582}

[Note 95\18: Lyell, B. i. c. ii. p. 8. (4th ed.)]

The notion of a series of creations and destructions of worlds,
which appears in the sacred volume of the Hindoos, which formed part
of the traditionary lore of Egypt, and which was afterwards adopted
into the poetry and philosophy of Greece, must be considered as a
mythological, not a physical, doctrine. When this doctrine was dwelt
upon, men's thoughts were directed, not to the terrestrial facts
which it seemed to explain, but to the attributes of the deities
which it illustrated. The conception of a Supreme power, impelling
and guiding the progress of events, which is permanent among all
perpetual change, and regular among all seeming chance, was readily
entertained by contemplative and enthusiastic minds; and when
natural phenomena were referred to this doctrine, it was rather for
the purpose of fastening its impressiveness upon the senses, than in
the way of giving to it authority and support. Hence we perceive
that in the exposition of this doctrine, an attempt was always made
to fill and elevate the mind with the notions of marvellous events,
and of infinite times, in which vast cycles of order recurred. The
"great year," in which all celestial phenomena come round, offered
itself as capable of being calculated; and a similar great year was
readily assumed for terrestrial and human events. Hence there were
to be brought round by great cycles, not only deluges and
conflagrations which were to destroy and renovate the earth, but
also the series of historical occurrences. Not only the sea and land
were to recommence their alternations, but there was to be another
Argo, which should carry warriors on the first sea-foray,[96\18] and
another succession of heroic wars. Looking at the passages of
ancient authors which refer to terrestrial changes in this view, we
shall see that they are addressed almost entirely to the love of the
marvellous and the infinite, and cannot with propriety be taken as
indications of a spirit of physical philosophy. For example, if we
turn to the celebrated passage in Ovid,[97\18] where Pythagoras is
represented as asserting that land becomes sea, and sea land, and
many other changes which geologists have verified, we find that
these observations are associated with many fables, as being matter
of exactly the same kind;--the fountain of Ammon which was cold by
day and warm by night;[98\18]--the waters of Salmacis which
effeminate men;--the Clitorian spring which makes them loathe
wine;--the Simplegades islands which were once moveable;--the
Tritonian lake which covered men's bodies with feathers;--and many
similar marvels. And the general purport of {583} the whole is, to
countenance the doctrine of the metempsychosis, and the Pythagorean
injunction of not eating animal food. It is clear, I think, that
facts so introduced must be considered as having been contemplated
rather in the spirit of poetry than of science.

[Note 96\18: Virg. _Eclog._ 4.]

[Note 97\18: _Met._ Lib. xv.]

[Note 98\18: V. 309, &c.]

We must estimate in the same manner, the very remarkable passage
brought to light by M. Elie de Beaumont,[99\18] from the Arabian
writer, Kazwiri; in which we have a representation of the same spot
of ground, as being, at successive intervals of five hundred years,
a city, a sea, a desert, and again a city. This invention is
adduced, I conceive, rather to feed the appetite of wonder, than to
fix it upon any reality: as the title of his book, _The Marvels of
Nature_ obviously intimates.

[Note 99\18: _Ann. des Sc. Nat._ xxv. 380.]

The speculations of Aristotle, concerning the exchanges of land and
sea which take place in long periods, are not formed in exactly the
same spirit, but they are hardly more substantial; and seem to be
quite as arbitrary, since they are not confirmed by any examples and
proofs. After stating,[100\18] that the same spots of the earth are
not always land and always water, he gives the reason. "The
principle and cause of this is," he says, "that the inner parts of
the earth, like the bodies of plants and animals, have their ages of
vigor and of decline; but in plants and animals all the parts are in
vigor, and all grow old, at once: in the earth different parts
arrive at maturity at different times by the operation of cold and
heat: they grow and decay on account of the sun and the revolution
of the stars, and thus the parts of the earth acquire different
power, so that for a certain time they remain moist, and then become
dry and old: and then other places are revivified, and become
partially watery." We are, I conceive, doing no injustice to such
speculations by classing them among _fanciful_ geological opinions.

[Note 100\18: _Meteorol._ i. 14.]

We must also, I conceive, range in the same division another class
of writers of much more modern times;--I mean those who have trained
their geology by interpretations of Scripture. I have already
endeavored to show that such an attempt is a perversion of the
purpose of a divine communication, and cannot lead to any physical
truth. I do not here speak of geological speculations in which the
Mosaic account of the deluge has been referred to; for whatever
errors may have been committed on that subject, it would be as
absurd to disregard the most ancient historical record, in
attempting to trace back the history of the earth, as it would be,
gratuitously to reject any other {584} source of information. But
the interpretations of the account of the creation have gone further
beyond the limits of sound philosophy: and when we look at the
arbitrary and fantastical inventions by which a few phrases of the
writings of Moses have been moulded into complete systems, we cannot
doubt that these interpretations belong to the present Section.

I shall not attempt to criticize, nor even to enumerate, these
Scriptural Geologies,--_Sacred Theories of the Earth_, as Burnet
termed his. Ray, Woodward, Whiston, and many other persons to whom
science has considerable obligations, were involved, by the
speculative habits of their times, in these essays; and they have
been resumed by persons of considerable talent and some knowledge,
on various occasions up to the present day; but the more geology has
been studied on its own proper evidence, the more have geologists
seen the unprofitable character of such labors.

I proceed now to the next step in the progress of Theoretical
Geology.


_Sect._ 3.--_Of Premature Geological Theories._

WHILE we were giving our account of Descriptive Geology, the
attentive reader would perceive that we did, in fact, state several
steps in the advance towards general knowledge; but when, in those
cases, the theoretical aspect of such discoveries softened into an
appearance of mere classification, the occurrence was assigned to
the history of Descriptive rather than of Theoretical Geology. Of
such a kind was the establishment, by a long and vehement
controversy, of the fact, that the impressions in rocks are really
the traces of ancient living things; such, again, were the division
of rocks into Primitive, Secondary, Tertiary; the ascertainment of
the orderly succession of organic remains: the consequent fixation
of a standard series of formations and strata; the establishment of
the igneous nature of trap rocks; and the like. These are geological
truths which are assumed and implied in the very language which
geology uses; thus showing how in this, as in all other sciences,
the succeeding steps involve the preceding. But in the history of
geological theory, we have to consider the wider attempts to combine
the facts, and to assign them to their causes.

The close of the last century produced two antagonist theories of
this kind, which long maintained a fierce and doubtful
struggle;--that of Werner and that of Hutton: the one termed
_Neptunian_, from its {585} ascribing the phenomena of the earth's
surface mainly to aqueous agency; the other _Plutonian_ or
_Vulcanian_, because it employed the force of subterraneous fire as
its principal machinery. The circumstance which is most worthy of
notice in these remarkable essays is, the endeavor to give, by means
of such materials as the authors possessed, a complete and simple
account of all the facts of the earth's history. The Saxon
professor, proceeding on the examination of a small district in
Germany, maintained the existence of a chaotic fluid, from which a
series of universal formations had been precipitated, the position
of the strata being broken up by the falling in of subterraneous
cavities, in the intervals between these depositions. The Scotch
philosopher, who had observed in England and Scotland, thought
himself justified in declaring that the existing causes were
sufficient to spread new strata on the bottom of the ocean, and that
they are consolidated, elevated, and fractured by volcanic heat, so
as to give rise to new continents.

It will hardly be now denied that all that is to remain as permanent
science in each of these systems must be proved by the examination
of many cases and limited by many conditions and circumstances.
Theories so wide and simple, were consistent only with a
comparatively scanty collection of facts, and belong to the early
stage of geological knowledge. In the progress of the science, the
"theory" of each part of the earth must come out of the examination
of that part, combined with all that is well established, concerning
all the rest; and a general theory must result from the comparison
of all such partial theoretical views. Any attempt to snatch it
before its time must fail; and therefore we may venture at present
to designate general theories, like those of Hutton and Werner, as
_premature_.

This, indeed, is the sentiment of most of the good geologists of the
present day. The time for such general systems, and for the fierce
wars to which the opposition of such generalities gives rise, is
probably now past for ever; and geology will not again witness such
a controversy as that of the Wernerian and Huttonian schools.
  . . . . . . As when two black clouds
  With heaven's artillery fraught, come rattling on
  Over the Caspian: then stand front to front,
  Hovering a space, till winds the signal blow
  To join their dark encounter in mid-air.
  So frowned the mighty combatants, that hell
  Grew darker at their frown; so matched they stood:
  For never but once more was either like
  To meet so great a foe. {586}

The main points really affecting the progress of sound theoretical
geology, will find a place in one of the two next Sections.

[2nd Ed.] [I think I do no injustice to Dr. Hutton in describing his
theory of the earth as _premature_. Prof. Playfair's elegant work,
_Illustrations of the Huttonian Theory_ (1802,) so justly admired,
contains many doctrines which the more mature geology of modern
times rejects; such as the igneous origin of chalk-flints, siliceous
pudding stone, and the like; the universal formation of river-beds
by the rivers themselves; and other points. With regard to this
last-mentioned question, I think all who have read Deluc's
_Geologie_ (1810) will deem his refutation of Playfair complete.

But though Hutton's theory was premature, as well as Werner's, the
former had a far greater value as an important step on the road to
truth. Many of its boldest hypotheses and generalizations have
become a part of the general creed of geologists; and its
publication is perhaps the greatest event which has yet occurred in
the progress of Physical Geology.]




CHAPTER VIII.

THE TWO ANTAGONIST DOCTRINES OF GEOLOGY.


_Sect._ 1.--_Of the Doctrine of Geological Catastrophes._

THAT great changes, of a kind and intensity quite different from the
common course of events, and which may therefore properly be called
_catastrophes_, have taken place upon the earth's surface, was an
opinion which appeared to be forced upon men by obvious facts.
Rejecting, as a mere play of fancy, the notions of the destruction
of the earth by cataclysms or conflagrations, of which we have
already spoken, we find that the first really scientific examination
of the materials of the earth, that of the Sub-Apennine hills, led
men to draw this inference. Leonardo da Vinci, whom we have already
noticed for his early and strenuous assertion of the real marine
origin of fossil impressions of shells, also maintained that the
bottom of the sea had become the top of the mountain; yet his mode
of explaining this may perhaps be claimed by the modern advocates of
uniform causes as more allied to their {587} opinion, than to the
doctrine of catastrophes.[101\18] But Steno, in 1669, approached
nearer to this doctrine; for he asserted that Tuscany must have
changed its face at intervals, so as to acquire six different
configurations, by the successive breaking down of the older strata
into inclined positions, and the horizontal deposit of new ones upon
them. Strabo, indeed, at an earlier period had recourse to
earthquakes, to explain the occurrence of shells in mountains; and
Hooke published the same opinion later. But the Italian geologists
prosecuted their researches under the advantage of having, close at
hand, large collections of conspicuous and consistent phenomena.
Lazzaro Moro, in 1740, attempted to apply the theory of earthquakes
to the Italian strata; but both he and his expositor, Cirillo
Generelli, inclined rather to reduce the violence of these
operations within the ordinary course of nature,[102\18] and thus
leant to the doctrine of uniformity, of which we have afterwards to
speak. Moro was encouraged in this line of speculation by the
extraordinary occurrence, as it was deemed by most persons, of the
rise of a new volcanic island from a deep part of the Mediterranean,
near Santorino, in 1707.[103\18] But in other countries, as the
geological facts were studied, the doctrine of catastrophes appeared
to gain ground. Thus in England, where, through a large part of the
country, the coal-measures are extremely inclined and contorted, and
covered over by more horizontal fragmentary beds, the opinion that
some violent catastrophe had occurred to dislocate them, before the
superincumbent strata were deposited, was strongly held. It was
conceived that a period of violent and destructive action must have
succeeded to one of repose; and that, for a time, some unusual and
paroxysmal forces must have been employed in elevating and breaking
the pre-existing strata, and wearing their fragments into smooth
pebbles, before nature subsided into a new age of tranquillity and
vitality. In like manner Cuvier, from the alternations of
fresh-water and salt-water species in the strata of Paris, collected
the opinion of a series of great revolutions, in which "the thread
of induction was broken." Deluc and others, to whom we owe the first
steps in geological dynamics, attempted carefully to distinguish
between causes now in action, and those which have ceased to act; in
which latter class they reckoned the causes which have {588}
elevated the existing continents. This distinction was assented to
by many succeeding geologists. The forces which have raised into the
clouds the vast chains of the Pyrenees, the Alps, the Andes, must
have been, it was deemed, something very different from any agencies
now operating.

[Note 101\18: "Here is a part of the earth which has become more
light, and which rises, while the opposite part approaches nearer to
the centre, and what was the bottom of the sea is become the top of
the mountain."--Venturi's _Léonardo da Vinci_.]

[Note 102\18: Lyell, i. 3. p. 64. (4th ed.)]

[Note 103\18: Ib. p. 60.]

This opinion was further confirmed by the appearance of a complete
change in the forms of animal and vegetable life, in passing from
one formation to another. The species of which the remains occurred,
were entirely different, it was said, in two successive epochs: a
new creation appears to have intervened; and it was readily believed
that a transition, so entirely out of the common course of the
world, might be accompanied by paroxysms of mechanical energy. Such
views prevail extensively among geologists up to the present time:
for instance, in the comprehensive theoretical generalizations of
Elie de Beaumont and others, respecting mountain-chains, it is
supposed that, at certain vast intervals, systems of mountains,
which may be recognized by the parallelism of course of their
inclined beds, have been disturbed and elevated, lifting up with
them the aqueous strata which had been deposited among them in the
intervening periods of tranquillity, and which are recognized and
identified by means of their organic remains: and according to the
adherents of this hypothesis, these sudden elevations of
mountain-chains have been followed, again and again, by mighty
waves, desolating whole regions of the earth.

The peculiar bearing of such opinions upon the progress of physical
geology will be better understood by attending to the _doctrine of
uniformity_, which is opposed to them, and with the consideration of
which we shall close our survey of this science, the last branch of
our present task.


_Sect._ 2.--_Of the Doctrine of Geological Uniformity._

THE opinion that the history of the earth had involved a serious of
catastrophes, confirmed by the two great classes of facts, the
symptoms of mechanical violence on a very large scale, and of
complete changes in the living things by which the earth had been
tenanted, took strong hold of the geologists of England, France, and
Germany. Hutton, though he denied that there was evidence of a
beginning of the present state of things, and referred many
processes in the formation of strata to existing causes, did not
assert that the elevatory forces which raise continents from the
bottom of the ocean, were of the same order, {589} as well as of the
same kind, with the volcanoes and earthquakes which now shake the
surface. His doctrine of uniformity was founded rather on the
supposed analogy of other lines of speculation, than on the
examination of the amount of changes now going on. "The Author of
nature," it was said, "has not permitted in His works any symptom of
infancy or of old age, or any sign by which we may estimate either
their future or their past duration:" and the example of the
planetary system was referred to in illustration of this.[104\18]
And a general persuasion that the champions of this theory were not
disposed to accept the usual opinions on the subject of creation,
was allowed, perhaps very unjustly, to weigh strongly against them
in the public opinion.

[Note 104\18: Lyell, i. 4, p. 94.]

While the rest of Europe had a decided bias towards the doctrine of
geological catastrophes, the phenomena of Italy, which, as we have
seen, had already tended to soften the rigor of that doctrine, in the
progress of speculation from Steno to Generelli, were destined to
mitigate it still more, by converting to the belief of uniformity
transalpine geologists who had been bred up in the catastrophist
creed. This effect was, indeed, gradual. For a time the distinction of
the _recent_ and the _tertiary_ period was held to be marked and
strong. Brocchi asserted that a large portion of the Sub-Apennine
fossil shells belonged to a living species of the Mediterranean Sea:
but the geologists of the rest of Europe turned an incredulous ear to
this Italian tenet; and the persuasion of the distinction of the
tertiary and the recent period was deeply impressed on most geologists
by the memorable labors of Cuvier and Brongniart on the Paris basin.
Still, as other tertiary deposits were examined, it was found that
they could by no means be considered as contemporaneous, but that they
formed a chain of posts, advancing nearer and nearer to the recent
period. Above the strata of the basins of London and Paris,[105\18]
lie the newer strata of Touraine, of Bourdeaux, of the valley of the
Bormida and the Superga near Turin, and of the basin of Vienna,
explored by M. Constant Prevost. Newer and higher still than these,
are found the Sub-Apennine formations of Northern Italy, and probably
of the same period, the English "crag" of Norfolk and Suffolk. And
most of these marine formations are associated with volcanic products
and fresh-water deposits, so as to imply apparently a long train of
alternations of corresponding processes. It may easily be supposed
that, when the subject had assumed this form, the boundary of the
present and past condition of the earth {590} was in some measure
obscured. But it was not long before a very able attempt was made to
obliterate it altogether. In 1828, Mr. Lyell set out on a geological
tour through France and Italy.[106\18] He had already conceived the
idea of classing the tertiary groups by reference to the number of
recent species which were found in a fossil state. But as he passed
from the north to the south of Italy, he found, by communication with
the best fossil conchologists, Borelli at Turin, Guidotti at Parma,
Costa at Naples, that the number of extinct species decreased; so that
the last-mentioned naturalist, from an examination of the fossil
shells of Otranto and Calabria, and of the neighboring seas, was of
opinion that few of the tertiary shells were of extinct species. To
complete the series of proof, Mr. Lyell himself explored the strata of
Ischia, and found, 2000 feet above the level of the sea, shells, which
were all pronounced to be of species now inhabiting the Mediterranean;
and soon after, he made collections of a similar description on the
flanks of Etna, in the Val di Noto, and in other places.

[Note 105\18: Lyell, 1st ed. vol. iii. p. 61.]

[Note 106\18: 1st ed. vol. iii. Pref.]

The impression produced by these researches is described by
himself.[107\18] "In the course of my tour I had been frequently led
to reflect on the precept of Descartes, that a philosopher should
once in his life doubt everything he had been taught; but I still
retained so much faith in my early geological creed as to feel the
most lively surprize on visiting Sortino, Pentalica, Syracuse, and
other parts of the Val di Noto, at beholding a limestone of enormous
thickness, filled with recent shells, or sometimes with mere casts
of shells, resting on marl in which shells of Mediterranean species
were imbedded in a high state of preservation. All idea of
[necessarily] attaching a high antiquity to a regularly-stratified
limestone, in which the casts and impressions of shells alone were
visible, vanished at once from my mind. At the same time, I was
struck with the identity of the associated igneous rocks of the Val
di Noto with well-known varieties of 'trap' in Scotland and other
parts of Europe; varieties which I had also seen entering largely
into the structure of Etna.

[Note 107\18: Lyell, 1st ed. Pref. x.]

"I occasionally amused myself," Mr. Lyell adds, "with speculating on
the different rate of progress which geology might have made, had it
been first cultivated with success at Catania, where the phenomena
above alluded to, and the great elevation of the modern tertiary beds
in the Val di Noto, and the changes produced in the historical era by
the Calabrian earthquakes, would have been familiarly known." {591}

Before Mr. Lyell entered upon his journey, he had put into the hands
of the printer the first volume of his "Principles of Geology, being
an attempt to explain the former Changes of the Earth's Surface _by
reference to the Causes now in Operation_." And after viewing such
phenomena as we have spoken of, he, no doubt, judged that the
doctrine of catastrophes of a kind entirely different from the
existing course of events, would never have been generally received,
if geologists had at first formed their opinions upon the Sicilian
strata. The boundary separating the present from the anterior state
of things crumbled away; the difference of fossil and recent species
had disappeared, and, at the same time, the changes of position
which marine strata had undergone, although not inferior to those of
earlier geological periods, might be ascribed, it was thought, to
the same kind of earthquakes as those which still agitate that
region. Both the supposed proofs of catastrophic transition, the
organical and the mechanical changes, failed at the same time; the
one by the removal of the fact, the other by the exhibition of the
cause. The powers of earthquakes, even such as they now exist, were,
it was supposed, if allowed to operate for an illimitable time,
adequate to produce all the mechanical effects which the strata of
all ages display. And it was declared that all evidence of a
beginning of the present state of the earth, or of any material
alteration in the energy of the forces by which it has been modified
at various epochs, was entirely wanting.

Other circumstances in the progress of geology tended the same way.
Thus, in cases where there had appeared in one country a sudden and
violent transition from one stratum to the next, it was found, that
by tracing the formations into other countries, the chasm between
them was filled up by intermediate strata; so that the passage
became as gradual and gentle as any other step in the series. For
example, though the conglomerates, which in some parts of England
overlie the coal-measures, appear to have been produced by a
complete discontinuity in the series of changes; yet in the
coal-fields of Yorkshire, Durham, and Cumberland, the transition is
smoothed down in such a way that the two formations pass into each
other. A similar passage is observed in Central-Germany, and in
Thuringia is so complete, that the coal-measures have sometimes been
considered as subordinate to the _todtliegendes_.[108\18]

[Note 108\18: De la Beche, p. 414, _Manual_.]

Upon such evidence and such arguments, the doctrine of {592}
catastrophes was rejected with some contempt and ridicule; and it
was maintained, that the operation of the causes of geological
change may properly and philosophically be held to have been uniform
through all ages and periods. On this opinion, and the grounds on
which it he been urged, we shall make a few concluding remarks.

It must be granted at once, to the advocates of this geological
uniformity, that we are not arbitrarily to assume the existence of
catastrophes. The degree of uniformity and continuity with which
terremotive forces have acted, must be collected, not from any
gratuitous hypothesis, but from the facts of the case. We must
suppose the causes which have produced geological phenomena, to have
been as similar to existing causes, and as dissimilar, as the
effects teach us. We are to avoid all bias in favor of powers
deviating in kind and degree from those which act at present; a bias
which, Mr. Lyell asserts, has extensively prevailed among
geologists.

But when Mr. Lyell goes further, and considers it a merit in a
course of geological speculation that it _rejects_ any difference
between the intensity of existing and of past causes, we conceive
that he errs no less than those whom he censures. "An _earnest and
patient endeavor to reconcile_ the former indication of
change,"[109\18] with _any_ restricted class of causes,--a habit
which he enjoins,--is not, we may suggest, the temper in which
science ought to be pursued. The effects must themselves teach us
the nature and intensity of the causes which have operated; and we
are in danger of error, if we seek for slow and shun violent
agencies further than the facts naturally direct us, no less than if
we were parsimonious of time and prodigal of violence. _Time_,
inexhaustible and ever accumulating his efficacy, can undoubtedly do
much for the theorist in geology; but _Force_, whose limits we
cannot measure, and whose nature we cannot fathom, is also a power
never to be slighted: and to call in the one to protect us from the
other, is equally presumptuous, to whichever of the two our
superstition leans. To invoke Time, with ten thousand earthquakes,
to overturn and set on edge a mountain-chain, should the phenomena
indicate the change to have been sudden and not successive, would be
ill excused by pleading the obligation of first appealing to known
causes.[110\18] {593}

[Note 109\18: Lyell, B. iv. c. i. p. 328, 4th ed.]

[Note 110\18: [2nd Ed.] [I have, in the text, quoted the fourth
edition of Mr. Lyell's _Principles_, in which he recommends "an
earnest and patient endeavor to reconcile the former indications of
change with the evidence of gradual mutation now in progress." In
the sixth edition, in that which is, I presume, the corresponding
passage, although it is transferred from the fourth to the first
Book (B. i. c. xiii. p. 325) he recommends, instead, "an earnest and
patient inquiry how far geological appearances are reconcileable
with the effect of changes now in progress." But while Mr. Lyell has
thus softened the advocate's character in his language in this
passage, the transposition which I have noticed appears to me to
have an opposite tendency. For in the former edition, the causes now
in action were first described in the second and third Books, and
the great problem of Geology, stated in the first Book, was
attempted to be solved in the fourth. But by incorporating this
fourth Book with the first, and thus prefixing to the study of
existing causes arguments against the belief of their geological
insufficiency, there is an appearance as if the author wished his
reader to be prepared by a previous pleading against the doctrine of
catastrophes, before he went to the study of existing causes. The
Doctrines of Catastrophes and of Uniformity, and the other leading
questions of the Palætiological Sciences, are further discussed in
the _Philosophy of the Inductive Sciences_, Book x.]]

In truth, we know causes only by their effects; and in order to
learn the nature of the causes which modify the earth, we must study
them through all ages of their action, and not select arbitrarily
the period in which we live as the standard for all other epochs.
The forces which have produced the Alps and Andes are known to us by
experience, no less than the forces which have raised Etna to its
present height; for we learn their amount in both cases by their
results. Why, then, do we make a merit of using the latter case as a
measure for the former? Or how can we know the true scale of such
force, except by comprehending in our view all the facts which we
can bring together?

In reality when we speak of the _uniformity_ of nature, are we not
obliged to use the term in a very large sense, in order to make the
doctrine at all tenable? It includes catastrophes and convulsions of
a very extensive and intense kind; what is the limit to the violence
which we must allow to these changes? In order to enable ourselves
to represent geological causes as operating with uniform energy
through all time, we must measure our time by long cycles, in which
repose and violence alternate; how long may we extend this cycle of
change, the repetition of which we express by the word _uniformity_?

And why must we suppose that all our experience, geological as well
as historical, includes more than _one_ such cycle? Why must we
insist upon it, that man has been long enough an observer to obtain
the _average_ of forces which are changing through immeasurable
time? {594}

The analogy of other sciences has been referred to, as sanctioning
this attempt to refer the whole train of facts to known causes. To
have done this, it has been said, is the glory of Astronomy: she
seeks no hidden virtues, but explains all by the force of
gravitation, which we witness operating at every moment. But let us
ask, whether it would really have been a merit in the founders of
Physical Astronomy, to assume that the celestial revolutions
resulted from any selected class of known causes? When Newton first
attempted to explain the motions of the moon by the force of
gravity, and failed because the measures to which he referred were
erroneous, would it have been philosophical in him, to insist that
the difference which he found ought to be overlooked, since
otherwise we should be compelled to go to causes other than those
which we usually witness in action? Or was there any praise due to
those who assumed the celestial forces to be the same with gravity,
rather than to those who assimilated them with any other known
force, as magnetism, till the calculation of the laws and amount of
these forces, from the celestial phenomena, had clearly sanctioned
such an identification? We are not to select a conclusion now well
proved, to persuade ourselves that it would have been wise to assume
it anterior to proof, and to attempt to philosophize in the method
thus recommended.

Again, the analogy of Astronomy has been referred to, as confirming
the assumption of perpetual uniformity. The analysis of the heavenly
motions, it has been said, supplies no trace of a beginning, no
promise of an end. But here, also, this analogy is erroneously
applied. Astronomy, as the science of cyclical motions, has nothing
in common with Geology. But look at Astronomy where she has an
analogy with Geology; consider our knowledge of the heavens as a
palætiological science;--as the study of a past condition, from
which the present is derived by causes acting in time. Is there then
no evidence of a beginning, or of a progress? What is the import of
the Nebular Hypothesis? A luminous matter is condensing, solid
bodies are forming, are arranging themselves into systems of
cyclical motion; in short, we have exactly what we are told, on this
analogy, we ought not to have;--the beginning of a world. I will
not, to justify this argument, maintain the truth of the nebular
hypothesis; but if geologists wish to borrow maxims of
philosophizing from astronomy, such speculations as have led to that
hypothesis must be their model.

Or, let them look at any of the other provinces of palætiological
speculation; at the history of states, of civilization, of
languages. We {595} may assume some _resemblance_ or connexion
between the principles which determined the progress of government,
or of society, or of literature, in the earliest ages, and those
which now operate; but who has speculated successfully, assuming an
_identity_ of such causes? Where do we now find a language in the
process of formation, unfolding itself in inflexions, terminations,
changes of vowels by grammatical relations, such as characterize the
oldest known languages? Where do we see a nation, by its natural
faculties, inventing writing, or the arts of life, as we find them
in the most ancient civilized nations? We may assume hypothetically,
that man's faculties develop themselves in these ways; but we see no
such effects produced by these faculties, in our own time, and now
in progress, without the influence of foreigners.

Is it not clear, in all these cases, that history does not exhibit a
series of cycles, the aggregate of which may be represented as a
uniform state, without indication of origin or termination? Does it
not rather seem evident that, in reality, the whole course of the
world, from the earliest to the present times, is but one cycle, yet
unfinished;--offering, indeed, no clear evidence of the mode of its
beginning; but still less entitling us to consider it as a
repetition or series of repetitions of what had gone before?

Thus we find, in the analogy of the sciences, no confirmation of the
doctrine of uniformity, as it has been maintained in Geology. Yet we
discern, in this analogy, no ground for resigning our hope, that
future researches, both in Geology and in other palætiological
sciences, may throw much additional light on the question of the
uniform or catastrophic progress of things, and on the earliest
history of the earth and of man. But when we see how wide and
complex is the range of speculation to which our analogy has
referred us, we may well be disposed to pause in our review of
science;--to survey from our present position the ground that we
have passed over;--and thus to collect, so far as we may, guidance
and encouragement to enable us to advance in the track which lies
before us.

Before we quit the subject now under consideration, we may, however,
observe, that what the analogy of science really teaches us, as the
most promising means of promoting this science, is the strenuous
cultivation of the two subordinate sciences, Geological Knowledge of
Facts, and Geological Dynamics. These are the two provinces of
knowledge--corresponding to Phenomenal Astronomy, and Mathematical
Mechanics--which may lead on to the epoch of the Newton of {596}
geology. We may, indeed, readily believe that we have much to do in
both these departments. While so large a portion of the globe is
geologically unexplored;--while all the general views which are to
extend our classifications satisfactorily from one hemisphere to
another, from one zone to another, are still unformed; while the
organic fossils of the tropics are almost unknown, and their general
relation to the existing state of things has not even been
conjectured;--how can we expect to speculate rightly and securely,
respecting the history of the whole of our globe? And if Geological
Classification and Description are thus imperfect, the knowledge of
Geological Causes is still more so. As we have seen, the necessity
and the method of constructing a science of such causes, are only
just beginning to be perceived. Here, then, is the point where the
labors of geologists may be usefully applied; and not in premature
attempts to decide the widest and abstrusest questions which the
human mind can propose to itself.

It has been stated,[111\18] that when the Geological Society of
London was formed, their professed object was to multiply and record
observations, and patiently to await the result at some future time;
and their favorite maxim was, it is added, that the time was not yet
come for a General System of Geology. This was a wise and
philosophical temper, and a due appreciation of their position. And
even now, their task is not yet finished; their mission is not yet
accomplished. They have still much to do, in the way of collecting
Facts; and in entering upon the exact estimation of Causes, they
have only just thrown open the door of a vast Labyrinth, which it
may employ many generations to traverse, but which they must needs
explore, before they can penetrate to the Oracular Chamber of Truth.

[Note 111\18: Lyell, B. i. c. iv. p. 103.]

I REJOICE, on many accounts, to find myself arriving at the
termination of the task which I have attempted. One reason why I am
glad to close my history is, that in it I have been compelled,
especially in the latter part of my labors, to speak as a judge
respecting eminent philosophers whom I reverence as my Teachers in
those very sciences on which I have had to pronounce a
judgment;--if, indeed, even the appellation of Pupil be not too
presumptuous. But I doubt not that such men are as full of candor
and tolerance, as they are of knowledge and thought. And if they
deem, as I did, that such a history of {597} science ought to be
attempted, they will know that it was not only the historian's
privilege, but his duty, to estimate the import and amount of the
advances which he had to narrate; and if they judge, as I trust they
will, that the attempt has been made with full integrity of
intention and no want of labor, they will look upon the inevitable
imperfections of the execution of my work with indulgence and hope.

There is another source of satisfaction in arriving at this point of
my labors. If, after our long wandering through the region of
physical science, we were left with minds unsatisfied and unraised,
to ask, "Whether this be all?"--our employment might well be deemed
weary and idle. If it appeared that all the vast labor and intense
thought which has passed under our review had produced nothing but a
barren Knowledge of the external world, or a few Arts ministering
merely to our gratification; or if it seemed that the methods of
arriving at truth, so successfully applied in these cases, aid us
not when we come to the higher aims and prospects of our
being;--this History might well be estimated as no less melancholy
and unprofitable than those which narrate the wars of states and the
wiles of statesmen. But such, I trust, is not the impression which
our survey has tended to produce. At various points, the researches
which we have followed out, have offered to lead us from matter to
mind, from the external to the internal world; and it was not
because the thread of investigation snapped in our hands, but rather
because we were resolved to confine ourselves, for the present, to
the material sciences, that we did not proceed onwards to subjects
of a closer interest. It will appear, also, I trust, that the most
perfect method of obtaining speculative truth,--that of which I have
had to relate the result,--is by no means confined to the least
worthy subjects; but that the Methods of learning what is really
true, though they must assume different aspects in cases where a
mere contemplation of external objects is concerned, and where our
own internal world of thought, feeling, and will, supplies the
matter of our speculations, have yet a unity and harmony throughout
all the possible employments of our minds. To be able to trace such
connexions as this, is the proper sequel, and would be the high
reward, of the labor which has been bestowed on the present work.
And if a persuasion of the reality of such connexions, and a
preparation for studying them, have been conveyed to the reader's
mind while he has been accompanying me through our long survey, his
time may not have been employed on {598} these pages in vain.
However vague and hesitating and obscure may be such a persuasion,
it belongs, I doubt not, to the dawning of a better Philosophy,
which it may be my lot, perhaps, to develop more fully hereafter, if
permitted by that Superior Power to whom all sound philosophy
directs our thoughts.



{{599}}
ADDITIONS TO THE THIRD EDITION.




BOOK VIII.

ACOUSTICS.

CHAPTER III.

SOUND.


_The Velocity of Sound in Water._

THE Science of which the history is narrated in this Book has for
its objects, the minute Vibrations of the parts of bodies such as
those by which Sounds are produced, and the properties of Sounds.
The Vibrations of bodies are the result of a certain tension of
their structure which we term _Elasticity_. The Elasticity
determines the rate of Vibration: the rate of Vibration determines
the audible note: the Elasticity determines also the velocity with
which the vibration travels through the substance. These points of
the subject, Elasticity, Rate of Vibration, Velocity of Propagation,
Audible Note, are connected in each substance, and are different in
different substances.

In the history of this Science, considered as tending to a
satisfactory general theory, the Problems which have obviously
offered themselves were, to explain the properties of Sounds by the
relations of their constituent vibrations; and to explain the
existence of vibrations by the elasticity of the substances in which
they occurred: as in Optics, philosophers have explained the
phenomenon of light and colors by the Undulatory Theory, and are
still engaged in explaining the requisite modulations by means of
the elasticity of the Ether. But the _Undulatory Theory of Sound_
was seen to be true at an early period of the Science: and the
explanation, in a general way at least, of all kinds of such
undulations by means of the elasticity of the vibrating substances
has been performed by a series of mathematicians of whom I have
given an account in this Book. Hence the points of the subject
already mentioned (Elasticity, Vibrations and their Propagations,
{600} and Note), have a known material dependence, and each may be
employed in determining the other: for instance, the Note may be
employed in determining the velocity of sound and the elasticity of
the vibrating substance.

Chladni,[1\B] and the Webers,[2\B] had made valuable experimental
inquiries on such subjects. But more complete investigations of this
kind have been conducted with care and skill by M. Wertheim.[3\B]
For instance, he has determined the velocity with which sound
travels in water, by making an organ-pipe to sound by the passage of
water through it. This is a matter of some difficulty; for the
mouthpiece of an organ-pipe, if it be not properly and carefully
constructed, produces sounds of its own, which are not the genuine
musical note of the pipe. And though the note depends mainly upon
the length of the pipe, it depends also, in a small degree, on the
breadth of the pipe and the size of the mouthpiece.

[Note 1\B: _Traité d'Acoustique_, 1809.]

[Note 2\B: _Wellenlehre_, 1852.]

[Note 3\B: _Mémoires de Physique Mécanique_. Paris, 1848.]

If the pipe were a mere line, the time of a vibration would be the
time in which a vibration travels from one end of the pipe to the
other; and thus the note for a given length (which is determined by
the time of vibration), is connected with the velocity of vibration.
He thus found that the velocity of a vibration along the pipe in
sea-water is 1157 _mètres_ per second.

But M. Wertheim conceived that he had previously shown, by general
mathematical reasoning, that the velocity with which sound travels
in an unlimited expanse of any substance, is to the velocity with
which it travels along a pipe or linear strip of the same substance
as the square root of 3 to the square root of 2. Hence the velocity
of sound in sea-water would be 1454 _mètres_ a second. The velocity
of sound in air is 332 _mètres_.

M. Wertheim also employed the vibrations of rods of steel and other
metals in order to determine their _modulus of elasticity_--that is,
the quantity which determines for each substance, the extent to
which, in virtue of its elasticity, it is compressed and expanded by
given pressures or tensions. For this purpose he caused the rod to
vibrate near to a tuning-fork of given pitch, so that both the rod
and the tuning-fork by their vibrations traced undulating curves on
a revolving disk. The curves traced by the two could be compared so
as to give their relative rate, and thus to determine the elasticity
of the substance.



{{601}}
BOOK IX.

PHYSICAL OPTICS.


_Photography._

I HAVE, at the end of Chapter xi., stated that the theory of which I
have endeavored to sketch the history professes to explain only the
phenomena of radiant visible light; and that though we know that
light has other properties--for instance, that it produces chemical
effects--these are not contemplated as included within the domain of
the theory. The chemical effects of light cannot as yet be included
in exact and general truths, such as those which constitute the
undulatory theory of radiant visible light. But though the present
age has not yet attained to a _Science_ of the chemistry of Light,
it has been enriched with a most exquisite _Art_, which involves the
principles of such a science, and may hereafter be made the
instrument of bringing them into the view of the philosopher. I
speak of the Art of _Photography_, in which chemistry has discovered
the means of producing surfaces almost as sensitive to the
modifications of light as the most sensitive of organic textures,
the retina of the eye: and has given permanence to images which in
the eye are only momentary impressions. Hereafter, when the laws
shall have been theoretically established, which connect the
chemical constitution of bodies with the action of light upon them,
the prominent names in the Prelude to such an Epoch must be those
who by their insight, invention, and perseverance, discovered and
carried to their present marvellous perfection the processes of
photographic Art:--Niepce and Daguerre in France, and our own
accomplished countryman, Mr. Fox Talbot.


_Fluorescence._

As already remarked, it is not within the province of the undulatory
theory to explain the phenomena of the absorption of light which
take place in various ways when the light is transmitted through
various {602} mediums. I have, at the end of Chapter iii., given the
reasons which prevent my assenting to the assertion of a special
analysis of light by absorption. In the same manner, with regard to
other effects produced by media upon light, it is sufficient for the
defence of the theory that it should be consistent with the
possibility of the laws of phenomena which are observed, not that it
should explain those laws; for they belong, apparently, to another
province of philosophy.

Some of the optical properties of bodies which have recently
attracted notice appear to be of this kind. It was noticed by Sir
John Herschel,[4\B] that a certain liquid, sulphate of quinine,
which is under common circumstances colorless, exhibits in certain
aspects and under certain incidences of light, a beautiful celestial
blue color. It appeared that this color proceeded from the surface
on which the light first fell; and color thus produced Sir J.
Herschel called _epipolic_ colors, and spoke of the light as
_epipolized_. Sir David Brewster had previously noted effects of
color in transparent bodies which he ascribed to internal
dispersion:[5\B] and he conceived that the colors observed by Sir J.
Herschel were of the same class. Professor Stokes[6\B] of Cambridge
applied himself to the examination of these phenomena, and was led
to the conviction that they arise from a power which certain bodies
possess, of changing the color, and with it, the refrangibility of
the rays of light which fall upon them: and he traced this property
in various substances, into various remarkable consequences. As this
change of refrangibility always makes the rays _less_ refrangible,
it was proposed to call it a _degradation_ of the light; or again,
_dependent emission_, because the light is emitted in the manner of
self-luminous bodies, but only in dependence upon the active rays,
and so long as the body is under their influence. In this respect it
differs from _phosphorescence_, in which light is emitted without
such dependence. The phenomenon occurs in a conspicuous and
beautiful manner in certain kinds of fluor spar: and the term
_fluorescence_, suggested by Professor Stokes, has the advantage of
inserting no hypothesis, and will probably be found the most
generally acceptable.[7\B]

[Note 4\B: _Phil. Trans._ 1845.]

[Note 5\B: _Edinb. Trans._ 1833.]

[Note 6\B: _Phil. Trans._ 1852 and 1854.]

[Note 7\B: _Phil. Trans._ 1852.]

It may be remarked that Professor Stokes rejects altogether the
doctrine that light of definite refrangibility may still be
compound, and maybe analysed by absorption. He says, "I have not
overlooked the remarkable effect of absorbing media in causing
apparent changes {603} of color in a pure spectrum; but this I
believe to be a subjective phenomenon depending upon contrast."




CHAPTER XIII.

UNDULATORY THEORY.


_Direction of the Transverse Vibrations in Polarization._

IN the conclusion of Chapter xiii. I have stated that there is a
point in the undulatory theory which was regarded as left undecided
by Young and Fresnel, and on which the two different opinions have
been maintained by different mathematicians; namely, whether the
vibrations of polarized light are perpendicular to the plane of
polarization or in that plane. Professor Stokes of Cambridge has
attempted to solve this question in a manner which is,
theoretically, exceedingly ingenious, though it is difficult to make
the requisite experiments in a decisive manner. The method may be
briefly described.

If polarized light be _diffracted_ (see Chap. xi. sect. 2), each ray
will be bent from its position, but will still be polarized. The
original ray and the diffracted ray, thus forming a broken line, may
be supposed to be connected at the angle by a universal joint
(called a _Hooke's Joint_), such that when the original ray turns
about its axis, the diffracted ray also turns about its axis; as in
the case of the long handle of a telescope and the screw which is
turned by it. Now if the motion of the original ray round its axis
be uniform, the motion of the diffracted ray round its axis is not
uniform: and hence if, in a series of cases, the planes of
polarization of the original ray differ by equal angles, in the
diffracted ray the planes of polarization will differ by unequal
angles. Then if vibrations be perpendicular to the plane of
polarization, the planes of polarization in the diffracted rays will
be crowded together in the neighborhood of the plane in which the
diffraction takes place, and will be more rarely distributed in the
neighborhood of the plane perpendicular to this, in which is the
diffracting thread or groove.

On making the experiment, Prof. Stokes conceived that he found, in
his experiments, such a crowding of the planes of diffracted
polarization towards the plane of diffraction; and thus he held that
the {604} hypothesis that the transverse vibrations which constitute
polarization are perpendicularly transverse to the plane of
polarization was confirmed.[8\B]

[Note 8\B: _Camb. Trans._, vol. ix. part i. 1849.]

But Mr. Holtzmann,[9\B] who, assenting to the reasoning, has made
the experiment in a somewhat different manner, has obtained an
opposite result; so that the point may be regarded as still
doubtful.

[Note 9\B: _Phil. Mag._, Feb. 1857.]


_Final Disproof of the Emission Theory._

As I have stated in the History, we cannot properly say that there
ever was an Emission Theory of Light which was the _rival_ of the
Undulatory Theory: for while the undulatory theory provided
explanations of new classes of phenomena as fast as they arose, and
exhibited a _consilience_ of theories in these explanations, the
hypothesis of emitted particles required new machinery for every new
set of facts, and soon ceased to be capable even of expressing the
facts. The simple cases of the ordinary reflexion and refraction of
light were explained by Newton on the supposition that the
transmission of light is the motion of particles: and though his
explanation includes a somewhat harsh assumption (that a refracting
surface exercises an attractive force through a _fixed finite_
space), the authority of his great name gave it a sort of permanent
notoriety, and made it to be regarded as a standard point of
comparison between a supposed "Emission Theory" and the undulation
theory. And the way in which the theories were to be tested in this
case was obvious: in the Newtonian theory, the velocity of light is
increased by the refracting medium; in the undulatory theory, it is
diminished. On the former hypothesis the velocity of light in air
and in water is as 3 to 4; in the latter, as 4 to 3.

But the immense velocity of light made it appear impossible to
measure it, within the limits of any finite space which we can
occupy with refracting matter. The velocity of light is known from
astronomical phenomena;--from the eclipses of Jupiter's satellites,
by which it appears that light occupies 8 minutes in coming from the
sun to the earth; and from the aberration of light, by which its
velocity is shown to be 10,000 times the velocity of the earth in
its orbit. Is it, then, possible to make apparent so small a
difference as that between its passing through a few yards of air
and of water?

Mr. Wheatstone, in 1831, invented a machine by which this could
{605} be done. His object was to determine the velocity of the
electric shock. His apparatus consisted in a small mirror, turning
with great velocity about an axis which is in its own plane, like a
coin spinning on its edge. The velocity of spinning may be made so
great, that an object reflected shall change its place perceptibly
after an almost inconceivably small fraction of a second. The
application of this contrivance to measure the velocity of light,
was, at the suggestion of Arago, who had seen the times of the rival
theories of light, undertaken by younger men at Paris, his eyesight
not allowing him to prosecute such a task himself. It was necessary
that the mirrors should turn more than 1000 times in a second, in
order that the two images, produced, one by light coming through
air, and the other by light coming through an equal length of water,
should have places perceptibly different. The mechanical
difficulties of the experiment consisted in keeping up this great
velocity by the machinery without destroying the machinery, and in
transmitting the light without too much enfeebling it. These
difficulties were overcome in 1850, by M. Fizeau and M. Léon
Foucault separately: and the result was, that the velocity of light
was found to be less in water than in air. And thus the Newtonian
explanation of refraction, the last remnant of the Emission Theory,
was proved to be false.



{{606}}
BOOK X.

THERMOTICS.--ATMOLOGY.

CHAPTER III.

THE RELATION OF VAPOUR AND AIR.


_Sect._ 4.--_Force of Steam._

THE experiments on the elastic force of steam made by the French
Academy are fitted in an especial manner to decide the question
between rival formulæ, in consequence of the great amount of force
to which they extend; namely, 60 feet of mercury, or 24 atmospheres:
for formulæ which give results almost indistinguishable in the lower
part of the scale diverge widely at those elevated points. Mr.
Waterston[10\B] has reduced both these and other experiments to a
rule in the following manner:--He takes the zero of gaseous tension,
determined by other experimenters (Rudberg, Magnus, and Regnault,)
to be 461° below the zero of Fahrenheit, or 274° below the zero of
the centigrade scale: and temperatures reckoned from this zero he
calls "G temperatures." The square root of the G temperatures is the
element to which the elastic force is referred (for certain
theoretical reasons), and it is found that the density of steam is
as the _sixth power_ of this element. The agreement of this rule
with the special results is strikingly close. A like rule was found
by him to apply generally to many other gases in contact with their
liquids.

[Note 10\B: _Phil. Trans._ 1852.]

But M. Regnault has recently investigated the subject in the most
complete and ample manner, and has obtained results somewhat
different.[11\B] He is led to the conclusion that no formula
proceeding by {607} a power of the temperature can represent the
experiments. He also finds that the rule of Dalton (that as the
temperatures increase in arithmetical progression, the elastic force
increases in geometric progression) deviates from the observations,
especially at high temperatures. Dalton's rule would be expressed by
saying that the variable part of the elastic force is as _a^t_, where
_t_ is the temperature. This failing, M. Regnault makes trial of a
formula suggested by M. Biot, consisting of a sum of two terms, one of
which is as _a^t_, and the other is _b^t_: and in this way satisfies
the experiments very closely. But this can only be considered as a
formula of interpolation, and has no theoretical basis. M. Roche had
proposed a formula in which the force is as _a^z_, _z_ depending upon
the temperature by an equation[12\B] to which he had been led by
theoretical considerations. This agrees better with observation than
any other formula which includes only the same number of coefficients.

[Note 11\B: _Mém. de l'Institut_, vol. xxi. (1847). M. Regnault's
Memoir occupies 767 pages.]

[Note 12\B: The equation _z_ = _t_ ⁄ (1 + _mt_).]

Among the experimental thermotical laws referred to by M. Regnault
are, the Law of Watt,[13\B] that "the quantity of heat which is
required to convert a pint of water at a temperature of zero into
steam, is the same whatever be the pressure." Also, the Law of
Southern, that "the latent heat of vaporization, that is the heat
absorbed in the passage from the liquid to the gaseous consistence,
is constant for all purposes: and that we obtain the total heat in
adding to the constant latent heat the number which represents the
latent heat of steam." Southern found the latent heat of the steam
of water to be represented by about 950 degrees of Fahrenheit.[14\B]

[Note 13\B: See Robison's _Mechanical Philosophy_, vol. ii. p. 8.]

[Note 14\B: Ib. p. 160.]


_Sect._ 5.--_Temperature of the Atmosphere._

I MAY notice, as important additions to our knowledge on this
subject, the results of four balloon ascents made in 1852,[15\B] by
the Committee of the Meteorological Observatory established at Kew
by the British Association for the Advancement of Science. In these
ascents the observers mounted to more than 13,000, 18,000, and
19,000 feet, and in the last to 22,370; by which ascent the
temperature fell from 49 degrees to nearly 10 degrees below zero;
and the dew-point fell from 37° to 12°. Perhaps the most marked
result of these observations is the {608} following:--The temperature
of the air decreases uniformly as we ascend above the earth's
surface; but this decrease does not go on continuously. At a certain
elevation, varying on different days, the decrease is arrested: and
for a depth of two or three thousand feet of air, the temperature
decreases little, or even increases in ascending. Above this, the
diminution again takes place at nearly the same rate as in the lower
regions. This intermediate region of undecreasing temperature
extended in the various ascents, from about altitude 4000 to 6000
feet, 6500 to 10,000, 2000 to 4500, and 4000 to 8000. This
interruption in the decrease of temperature is accompanied by a
large and abrupt fall in the temperature of the dew-point, or by an
actual condensation of vapor. Thus, this region is the _region of
the clouds_, and the increase of heat appears to arise from the
latent heat liberated when aqueous vapor is formed into clouds.

[Note 15\B: _Phil. Trans._ 1853.]




CHAPTER IV.

THEORIES OF HEAT.


_The Dynamical Theory of Heat._

THAT the transmission of _radiant_ Heat takes place by means of the
vibrations of a medium, as the transmission of Sound certainly does,
and the transmission of Light most probably, is a theory which, as I
have endeavored to explain, has strong arguments and analogies in
its favor. But that Heat itself, in its essence and quantity, is
Motion is a hypothesis of quite another kind. This hypothesis has
been recently asserted and maintained with great ability. The
doctrine thus asserted is, that Motion may be converted into Heat,
and Heat into Motion; that Heat and Motion may produce each other,
as we see in the rarefaction and condensation of air, in
steam-engines, and the like: and that in all such cases the Motion
produced and the Heat expended exactly measure each other. The
foundation of this theory is conceived to have been laid by Mr.
Joule of Manchester, in 1844: and it has since been prosecuted by
him and by Professor Thomson of Glasgow, by experimental
investigations of various kinds. It is difficult to make these
experiments so as to be quite satisfactory; for it is {609}
difficult to measure _all_ the heat gained or lost in any of the
changes here contemplated. That friction, agitation of fluids,
condensation of gases, conversion of gases into fluids and liquids
into solids, produce heat, is undoubted: and that the quantity of
such heat may be measured by the mechanical force which produces it,
or which it produces, is a generalization which will very likely be
found a fertile source of new propositions, and probably of
important consequences.

As an example of the conclusions which Professor Thomson draws from
this doctrine of the mutual conversion of motion and heat, I may
mention his speculations concerning the cause which produces and
sustains the heat of the sun.[16\B] He conceives that the support of
the solar heat must be meteoric matter which is perpetually falling
towards the globe of the sun, and has its motion converted into
heat. He inclines to think that the meteors containing the stores of
energy for future Sun-light must be principally within the earth's
orbit; and that we actually see them there as the "Zodiacal Light,"
an illuminated shower, or rather tornado, of stones. The inner parts
of this tornado are always getting caught in the Sun's atmosphere,
and drawn to his mass by gravitation.

[Note 16\B: On the Mechanical Energies of the Solar System. _Edinb.
Trans._ vol. XXI. part i. (1854), p. 67.]



{{610}}
BOOK XI.

ELECTRICITY.


GENERAL REMARKS.


ELECTRICITY in the form in which it was originally
studied--Franklinic, frictional, or statical electricity--has been
so completely identified with electricity in its more comprehensive
form--Voltaic, chemical, or dynamical electricity--that any
additions we might have to make to the history of the earlier form
of the subject are included in the later science.

There are, however, several subjects which may still be regarded
rather as branches of Electricity than of the Cognate Sciences. Such
are, for instance, Atmospheric Electricity, with all that belongs to
Thunderstorms and Lightning Conductors. The observation of
Atmospheric Electricity has been prosecuted with great zeal at
various meteorological observatories; and especially at the
Observatory established by the British Association at Kew. The
Aurora Borealis, again, is plainly an electrical phenomenon; but
probably belonging rather to dynamical than to statical electricity.
For it strongly affects the magnetic needle, and its position has
reference to the direction of magnetism; but it has not been
observed to affect the electroscope. The general features of this
phenomenon have been described by M. de Humboldt, and more recently
by M. de Bravais; and theories of the mode of its production have
been propounded by MM. Biot, De la Rive, Kaemtz, and others.

Again, there are several fishes which have the power of giving an
electrical shock:--the torpedo, the gymnotus, and the silurus. The
agency of these creatures has been identified with electricity in
the most general sense. The peculiar energy of the animal has been
made to produce the effects which are produced by an electrical
discharge or a voltaic current:--not only to destroy life in small
animals, but to {611} deflect a magnet, to make a magnet, to
decompose water, and to produce a spark.


_Dr. Faraday's Views of Statical Electric Induction._

According to the theories of electricity of Æpinus and Coulomb,
which in this Book of our History are regarded as constituting a
main part of the progress of this portion of science, the particles
of the electric fluid or fluids exert forces, attractive and
repulsive, upon each other in straight lines at a distance, in the
same way in which, in the Newtonian theory of the universe, the
particles of matter are conceived as exerting attractive forces upon
each other. An electrized body presented a conducting body of any
form, determines a new arrangement of the electric fluids in the
conductor, attracting the like fluid to its own side, and repelling
the opposite fluid to the opposite side. This is Electrical
_Induction_. And as, by the theory, the attraction is greater at the
smaller distances, the distribution of the fluid upon the conductor
in virtue of this Induction will not be symmetrical, but will be
governed by laws which it will require a complex and difficult
calculation to determine--as we have seen was the case in the
investigations of Coulomb, Poisson, and others.

Instead of this action at a distance. Dr. Faraday has been led to
conceive Electrical Induction to be the result of an action taking
place between the electrized body and the conductor through lines of
contiguous particles in the mass of the intermediate body, which he
calls the _Dielectric_. And the irregularities of the distribution
of the electricity in these cases of Induction, and indeed the
existence of an action in points protected from direct action by the
protuberant sides of the conductor, are the causes, I conceive,
which lead him to the conclusion that Induction takes place in
_curved lines_[17\B] of such contiguous particles.

[Note 17\B: _Researches_, 1165, &c.]

With reference to this, I may remark that, as I have said, the
distribution of electricity on a conductor in the presence of an
electrized body is so complex a mathematical problem that I do not
conceive any merely popular way of regarding the result can entitle
us to say, that the distribution which we find cannot be explained
by the Coulombian theory, and must force us upon the assumption of
an action in curved lines:--which is, indeed, itself a theory, and
so vague a one {612} that it requires to be made much more precise
before we can say what consequences it does or does not lead to.
Professor W. Thomson has arrived at a mathematical proof that the
effect of induction on the view of Coulomb and of Faraday must,
under certain conditions, be necessarily and universally the same.

With regard to the influence of different _Dielectrics_ upon
Induction, the inquiry appears to be of the highest importance; and
may certainly necessitate some addition to the theory.



{{613}}
BOOK XII.

MAGNETISM.


_Recent Progress of Terrestrial Magnetism._

IN Chapter II., I have noticed the history of Terrestrial Magnetism;
Hansteen's map published in 1819; the discovery of "magnetic storms"
about 1825; the chain of associated magnetic observations, suggested
by M. de Humboldt, and promoted by the British Association and the
Royal Society; the demand for the continuation of these till 1848;
the magnetic observations made in several voyages; the magnetic
surveys of various countries. And I have spoken also of Gauss's
theory of Terrestrial Magnetism, and his directions and requirements
concerning the observations to be made. I may add a few words with
regard to the more recent progress of the subject.

The magnetic observations made over large portions of the Earth's
surface by various persons, and on the Ocean by British officers,
have been transmitted to Woolwich, where they have been employed by
General Sabine in constructing magnetic maps of the Earth for the
year 1840.[18\B] Following the course of inquiry described in the
part of the history referred to, these maps exhibit the declination,
inclination, and intensity of the magnetic force at every point of
the earth's surface. The curves which mark equal amounts of each of
these three elements (the _lines of equal declination_,
_inclination_, and _force_:--the _isogonal_, the _isoclinal_, and
the _isodynamic_ lines,) are, in their general form, complex and
irregular; and it has been made a matter of question (the facts
being agreed upon) whether it be more proper to say that they
indicate four poles, as Halley and as Hansteen said, or only two
poles, as Gauss asserts. The matter appears to become more clear if
we draw magnetic _meridians_; that is, lines obtained by following
the directions, or pointings, of the magnetic needle to the north or
to {614} the south, till we arrive at the points of convergence of
all their directions; for there are only two such poles, one in the
Arctic and one in the Antarctic region. But in consequence of the
irregularity of the magnetic constitution of the earth, if we follow
the inclination of the magnetic force round the earth on any
parallel of latitude, we find that it has two _maxima_ and two
_minima_, as if there were four magnetic poles. The isodynamic map
is a new presentation of the facts of this subject; the first having
been constructed by Colonel Sabine in 1837.

[Note 18\B: These maps are published in Mr. Keith Johnstone's
_Physical Atlas_.]

I have stated also that the magnetic elements at each place are to
be observed in such a manner as to bring into view both their
_periodical_, their _secular_, and their _irregular_ or _occasional_
changes. The observations made at Toronto in Canada, and at Hobart
Town in Van Diemen's Land, two stations at equal distances from the
two poles of the earth, and also at St Helena, a station within the
tropics, have been discussed by General Sabine with great care, and
with an amount of labor approaching to that employed upon reductions
of astronomical observations. And the results have been curious and
unexpected.

The declination was first examined.[19\B] This magnetical element is,
as we have already seen (p. 232), liable both to a diurnal and to an
annual inequality; and also to irregular perturbations which have been
termed magnetic storms. Now it was found that all these inequalities
went on increasing gradually and steadily from 1843 to 1848, so as to
become, at the end of that time, above twice as large as they were at
the beginning of it. A new periodical change in all these elements
appeared to be clearly established by this examination. M. Lamont, of
Munich, had already remarked indications of a decennial period in the
diurnal variation of the declination of the needle. The duration of
the period from minimum to maximum being about five years, and
therefore the whole period about ten years. The same conclusion was
found to follow still more decidedly from the observations of the dip
and intensity.

[Note 19\B: _Phil. Trans._ 1852 and 1856.]

This period of ten years had no familiar meaning in astronomy; and
if none such had been found for it, its occurrence as a magnetic
period must have been regarded, as General Sabine says,[20\B] in the
light of a fragmentary fact. But it happened about this time that
the scientific world was made aware of the existence of a like
period in a {615} phenomenon which no one would have guessed to be
connected with terrestrial magnetism, namely, the spots in the Sun.
M. Schwabe, of Dessau, had observed the Sun's disk with immense
perseverance for 24 years:--often examining it more than 300 days in
the year; and had found that the spots had, as to their quantity and
frequency, a periodical character. The years of maximum are 1828,
1838, 1848, in which there were respectively 225,[21\B] 282, 330
groups of spots. The minimum years, 1833, 1843, had only 33 and 34
such groups. This curious fact[22\B] was first made public by M. de
Humboldt, in the third volume of his _Kosmos_ (1850). The
coincidence of the periods and epochs of these two classes of facts
was pointed out by General Sabine in a Memoir presented to the Royal
Society in March, 1852.

[Note 20\B: _Phil. Trans._ 1856, p. 382.]

[Note 21\B: In 1837 there were 333.]

[Note 22\B: The observations up to 1844 were published in
Poggendorf's _Annalen_.]

Of course it was natural to suppose, even before this discovery,
that the diurnal and annual inequalities of the magnetic element at
each place depend upon the action of the sun, in some way or other.

Dr. Faraday had endeavored to point out how the effect of the solar
heat upon the atmosphere would, according to the known relations of
heat and magnetism, explain many of the phenomena. But this new
feature of the phenomena, their quinquennial increase and decrease,
makes us doubt whether such an explanation can really be the true one.

Of the _secular_ changes in the magnetic elements, not much more is
known than was known some years ago. These changes go on, but their
laws are imperfectly known, and their causes not even conjectured.
M. Hansteen, in a recent memoir,[23\B] says that the decrease of the
inclination goes on progressively diminishing. With us this rate of
decrease appears to be at present nearly uniform. We cannot help
conjecturing that the sun, which has so plain a connexion with the
diurnal, annual, and occasional movements of the needle, must also
have some connexion with its secular movements.

[Note 23\B: See K. Johnstone's _Physical Atlas_.]

In 1840 the observations made at various places had to a great
extent enabled Gauss, in connexion with W. Weber, to apply his
Theory to the actual condition of the Earth;[24\B]  and he
calculated the Declination, Inclination, and Intensity at above 100
places, and found {616} the agreement, as he says, far beyond his
hopes. They show, he says, that the Theory comes near to the Truth.

[Note 24\B: _Atlas des Erdmagnetismus nach den Elementen der Theorie
Entworfen_. See Preface.]


_Correction of Ship's Compasses._

The magnetic needle had become of importance when it was found that
it always pointed to the North. Since that time the history of
magnetism has had its events reflected in the history of navigation.
The change of the declination arising from a change of place
terrified the companions of Columbus. The determination of the laws
of this change was the object of the voyage of Halley; and has been
pursued with the utmost energy in the Arctic and Antarctic regions
by navigators up to the present time. Probably the dependence of the
magnetic declination upon place is now known well enough for the
purposes of navigation. But a new source of difficulty has in the
meantime come into view; the effect of the iron in the ship upon the
Compass. And this has gone on increasing as guns, cables, stays,
knees, have been made of iron; then steam-engines with funnels,
wheels, and screws, have been added; and finally the whole ship has
been made of iron. How can the compass be trusted in such cases?

I have already said in the history that Mr. Barlow proposed to
correct the error of the compass by placing near to the compass an
iron plate, which from its proximity to the compass might
counterbalance magnetically the whole effect of the ship's iron upon
the compass. This correction was not effectual, because the magnetic
forces of the plate and of the ship do not change their direction
and value according to the same law, with the change of position. I
have further stated that Mr. Airy devised other means of correcting
the error. I may add a few words on the subject; for the subject has
been further examined by Mr. Airy[25\B] and by others.

[Note 25\B: _Phil. Trans._ 1856.]

It appears, by mathematical reasoning, that the magnetic effect of
the iron in a ship may be regarded as producing two kinds of
deviation which are added together;--a "polar-magnet deviation,"
which changes from positive to negative as the direction of the
ship's keel, in a horizontal revolution, passes from semicircle to
semicircle; and a "quadrantal deviation," which changes from
positive to negative as the keel turns from quadrant to quadrant.
The latter deviation may be remedied completely by a mass of
unmagnetized iron placed on a level {617} with the compass, either
in the athwartship line or in the fore-and-aft line, according to
circumstances. "The polar-magnet-deviation" may be corrected at _any
given place_ by a magnet or magnets, but the magnets thus applied at
one place will not always correct the deviation in another magnetic
latitude. For it appears that this deviation arises partly from a
magnetism inherent in the materials of the ship, not changing with
the change of magnetic position, and partly from the effect of
terrestrial magnetism upon the ship's iron. But the errors arising
from both sources may be remedied by adjusting, at a new locality,
the positions of the corrective magnets.

The inherent magnetism of the ship, of which I have spoken, may be
much affected by the position in which the ship was built; and may
change from time to time; for instance, by the effect of the
battering of the waves, and other causes. Hence it is called by Mr.
Airy "sub-permanent magnetism."

Another method of correcting the errors of a ship's compass has been
proposed, and is used to some extent; namely, by _swinging_ the ship
round (in harbor) to all points of azimuth, and thus constructing a
_Table of Compass Errors_ for that particular ship. But to this
method it is objected that the Table loses its value in a new
magnetic latitude much more than the correction by magnets does;
besides the inconveniences of steering a ship by a Table.



{{618}}
BOOK XIII.

VOLTAIC ELECTRICITY.

CHAPTER VII.

MAGNETO-ELECTRIC INDUCTION.


FARADAY'S discovery that, in combinations like those in which a
voltaic current was known to produce motion, motion would produce a
voltaic current, naturally excited great attention among the
scientific men of Europe. The general nature of his discovery was
communicated by letter[26\B] to M. Hachette at Paris, in December,
1831; and experiments having the like results were forthwith made by
MM. Becquerel and Ampère at Paris, and MM. Nobili and Antinori at
Florence.

[Note 26\B: _Ann. de Chimie_, vol. xlviii. (1831), p. 402.]

It was natural also that in a case in which the relations of space
which determine the results are so complicated, different
philosophers should look at them in different ways. There had been,
from the first discovery by Oersted of the effect of a voltaic
current upon a magnet, two rival methods of regarding the facts.
Electric and magnetic lines exert an effort to place themselves
transverse to each other (see chapter iv. of this Book), and (as I
have already said) two ways offered themselves of simplifying this
general truth:--to suppose an electric current made up of transverse
magnetic lines; or to suppose magnetic lines made up of transverse
electric currents. On either of these assumptions, the result was
expressed by saying that _like_ currents or lines (electric or
magnetic) tend to place themselves parallel; which is a law more
generally intelligible than the law of transverse position. Faraday
had adopted the former view; had taken the lines of magnetic force
for the fundamental lines of his system, and defined the direction
of the magneto-electric current of induction by the relation {619}
of the motion to these lines. Ampère, on the other hand, supposed
the magnet to be made up of transverse electric currents (chap.
vi.); and had deduced all the facts of electro-dynamical action,
with great felicity, from this conception. The question naturally
arose, in what manner, on this view, were the new facts of
magneto-electric induction by motion to be explained, or even
expressed?

Various philosophers attempted to answer this question. Perhaps the
form in which the answer has obtained most general acceptance is
that in which it was put by Lenz, who discoursed on the subject to
the Academy of St. Petersburg in 1833.[27\B] His general rule is to
this effect: when a wire moves in the neighborhood of an electric
current or a magnet, a current takes place in it, such as, existing
independently, would have produced a motion opposite to the actual
motion. Thus two parallel _forward_ currents move towards each
other:--hence if a current move towards a parallel wire, it produces
in it a _backward_ current. A moveable wire conducting a current
_downwards_ will move round the north pole of a magnet in the
direction N., W., S., E.:--hence if, when the wire have in it no
current, we move it in the direction N., W., S., E., we produce in
the wire an _upward_ current. And thus, as M. de la Rive
remarks,[28\B] in cases in which the mutual action of two currents
produces a limited motion, as attraction or repulsion, or a
deviation right or left, the corresponding magneto-electric
induction produces an instantaneous current only; but when the
electrodynamic action produces a continued motion, the corresponding
motion produces, by induction, a continued current.

[Note 27\B: _Acad. Petrop._ Nov. 29, 1833. _Pogg. Ann._ vol. xxxi.
p. 483.]

[Note 28\B: _Traité de l'Electricité_, vol. i. p. 441 (1854).]

Looking at this mode of stating the law, it is impossible not to
regard this effect as a sort of reaction; and accordingly, this view
was at once taken of it. Professor Ritchie said, in 1833, "The law
is founded on the universal principle that action and reaction are
equal." Thus, if voltaic electricity induce magnetism under certain
arrangements, magnetism will, by similar arrangements, react on a
conductor and induce voltaic electricity.[29\B]

[Note 29\B: On the Reduction of Mr. Faraday's discoveries in
Magneto-electric Induction to a General Law. _Trans._ of R. S. in
_Phil. Mag._ N.S. vol. iii. 37, and vol. iv. p. 11. In the second
edition of this history I used the like expressions.]

There are still other ways of looking at this matter. I have
elsewhere pointed out that where polar properties co-exist, they are
{620} generally found to be connected,[30\B] and have illustrated
this law in the case of electrical, magnetical, and chemical
polarities. If we regard motion backwards and forwards, to the right
and the left, and the like, as _polar_ relations, we see that
magneto-electric induction gives us a new manifestation of connected
polarities.

[Note 30\B: _Phil. Ind. Sc._ B. v. c. ii.]


_Diamagnetic Polarity_.

But the manifestation of co-existent polarities which are brought into
view in this most curious department of nature is not yet exhausted by
those which we have described. I have already spoken (chap. **vii.) of
Dr. Faraday's discovery that there are diamagnetic as well as magnetic
bodies; bodies which are repelled by the pole of a magnet, as well as
bodies which are attracted. Here is a new opposition of properties.
What is the exact definition of this opposition in connexion with
other polarities? To this, at present, different philosophers give
different answers. Some say that diamagnetism is completely the
opposite of ordinary magnetism, or, as Dr. Faraday has termed it for
the sake of distinction, of _paramagnetism_. They say that as a north
pole of a magnet gives to the neighboring extremity of a piece of soft
iron a south pole, so it gives to the neighboring extremity of a piece
of bismuth a north pole, and that the bismuth becomes for a time an
inverted magnet; and hence, arranges itself across the line of
magnetised force, instead of along it. Dr. Faraday himself at first
adopted this view;[31\B] but he now conceives that the bismuth is not
made polar, but is simply repelled by the magnet; and that the
transverse position which it assumes, arises merely from its elongated
form, each end trying to recede as far as possible from the repulsive
pole of the magnet.

[Note 31\B: Faraday's _Researches_, Art. 2429, 2430.]

Several philosophers of great eminence, however, who have examined
the subject with great care, adhere to Dr. Faraday's first view of
the nature of Diamagnetism--as W. Weber,[32\B] Plücker, and Mr.
Tyndall among ourselves. If we translate this view into the language
of Ampère's theory, it comes to this:--that as currents are induced
in iron and magnetics parallel to those existing in the inducing
magnet or battery wire; so in bismuth, heavy glass, and other
diamagnetic bodies, the currents induced are in the contrary {621}
directions:--these hypothetical currents being in non-conducting
diamagnetic, as in magnetic bodies, not in the mass, but round the
particles of the matter.

[Note 32\B: Poggendorf's _Ann. Jou._ 1848.]


_Magneto-optic Effects and Magnecrystallic Polarity._

Not even yet have we terminated the enumeration of the co-existent
polarities which in this province of nature have been brought into
view. Light has polar properties; the very term _polarization_ is
the record of the discovery of these. The forces which determine the
crystalline forms of bodies are of a polar nature: crystalline
forms, when complete, may be defined as those forms which have a
certain degree of symmetry in reference to opposite poles. Now has
this optical and crystalline polarity any relation to the electrical
polarity of which we have been speaking?

However much we might be disposed beforehand to conjecture that
there is some relation between these two groups of polar properties,
yet in this as in the other parts of this history of discoveries
respecting polarities, no conjecture hits the nature of the
relation, such as experiment showed it to be. In November, 1846,
Faraday announced the discovery of what he then called "the action
of magnets on light." But this action was manifested, not on light
directly, but on light passing through certain kinds of glass.[33\B]
When this glass, subjected to the action of the powerful magnets
which he used, transmitted a ray of light parallel to the line of
magnetic force, an effect was produced upon the light. But of what
nature was this effect? When light was ordinary light, no change in
its condition was discoverable. But if the light were light
polarized in any plane, the plane of polarization was turned round
through a certain angle while the ray passed through the glass:--a
greater angle, in proportion as the magnetic force was greater, and
the thickness of the glass greater.

[Note 33\B: Silicated borate of lead. See _Researches_, § 2151, &c.
Also flint glass, rock salt, water (2215).]

A power in some respects of this kind, namely, a power to rotate the
plane of polarization of a ray passing through them, is possessed by
some bodies in their natural state; for instance, quartz crystals,
and oil of turpentine. But yet, as Dr. Faraday remarks,[34\B] there
is a great difference in the two cases. When polarized rays pass
through oil of turpentine, in whatever direction they pass, they all
of them have their {622} plane of polarization rotated in the same
direction; that is, all to the right or all to the left; but when a
ray passes through the heavy glass, the power of rotation exists
only in a plane perpendicular to the magnetic line, and its
direction as right or left-handed is reversed by reversing the
magnetic polarity.

[Note 34\B: _Researches_, Art. 2231.]

In this case, we have optical properties, which do not depend on
crystalline form, affected by the magnetic force. But it has also been
found that crystalline form, which is so fertile a source of optical
properties, affords indications of magnetic forces. In 1847, M.
Plücker,[35\B] of the University of Bonn, using a powerful magnetic
apparatus, similar to Faraday's, found that crystals in general are
magnetic, in this sense, that the axes of crystalline form tend to
assume a certain position with reference to the magnetic lines of
force. The possession of one optic axis or of two is one of the broad
distinctions of the different crystalline forms: and using this
distinction, M. Plücker found that a crystal having a single optic
axis tends to place itself with this axis transverse to the magnetic
line of force, as if its optic axis were repelled by each magnetic
pole; and crystals with two axes act as if each of these axes were
repelled by the magnetic poles. This force is independent of the
magnetic or diamagnetic character of the crystal; and is a directive,
more properly than an attractive or repulsive force.

[Note 35\B: Taylor's _Scientific Memoirs_, vol. v.]

Soon afterwards (in 1848) Faraday also discovered[36\B] an effect of
magnetism depending on crystalline form, which at first sight appeared
to be different from the effects observed by M. Plücker. He found that
a crystal of bismuth, of which the form is nearly a cube, but more
truly a rhombohedron with one diagonal a little longer than the
others, tends to place itself with this diagonal in the direction of
the lines of magnetic force. At first he conceived[37\B] the
properties thus detected to be different from those observed by M.
Plücker; since in this case the force of a crystalline axis is axial,
whereas in those, it was equatorial. But a further consideration of
the subject, led him[38\B] to a conviction that these forces must be
fundamentally identical: for it was easy to conceive a combination of
bismuth crystals which would behave in the magnetic field as a crystal
of calcspar does; or a combination of calcspar crystals which would
behave as a crystal of bismuth does.

[Note 36\B: _Researches_, Art. 2454, &c.]

[Note 37\B: Art. 2469.]

[Note 38\B: Art 2593, 2601.]

And thus we have fresh examples to show that the Connexion of
coexistent Polarities is a thought deeply seated in the minds of the
{623} profoundest and most sagacious philosophers, and perpetually
verified and illustrated, by unforeseen discoveries in unguessed
forms, through the labors of the most skilful experimenters.


_Magneto-electric Machines._

The discovery that a voltaic wire moved in presence of a magnet, has
a current generated in it, was employed as the ground of the
construction of machines to produce electrical effects. In Saxton's
machine two coils of wire including a core of soft iron revolved
opposite to the ends of a horseshoe magnet, and thus, as the two
coils came opposite to the N. and S. and to the S. and N. poles of
the magnet, currents were generated alternately in the wires in
opposite directions. But by arranging the connexions of the ends of
the wires, the successive currents might be made to pass in
corresponding directions. The alternations or successions of
currents in such machines are governed by a contrivance which
alternately interrupts and permits the action; this contrivance has
been called a _rheotome_. Clarke gave a new form to a machine of the
same nature as Saxton's. But the like effect may be produced by
using an electro-magnet instead of a common magnet. When this is
done, a current is produced which by induction produces a current in
another wire, and the action is alternately excited and interrupted.
When the inducing current is interrupted, a momentary current _in an
opposite direction_ is produced in the induced wire; and when this
current stops, it produces in the inducing wire a current _in the
original direction_, which may be adjusted so as to reinforce the
resumed action of the original current. This was pointed out by M.
De la Rive in 1843.[39\B] Machines have been constructed on such
principles by him and others. Of such machines the most powerful
hitherto known is that constructed by M. Ruhmkorff. The effects of
this instrument are exceedingly energetic.

[Note 39\B: _Traité de l'Elect._ i. 391.]


_Applications of Electrodynamic Discoveries._

The great series of discoveries of which I have had to speak have
been applied in many important ways to the uses of life. The
_Electric Telegraph_ is one of the most remarkable of these. By
wires extended to the most distant places, the electric current is
transmitted {624} thither in an imperceptible time; and by means of
well-devised systems of operation, is made to convey from man to man
words, which are now most emphatically "winged words." In the most
civilised states such wires now form a net-work across the land,
which is familiar to our thoughts as the highway is to our feet; and
wide seas have such pathways of human thought buried deep in their
waves from shore to shore. Again, by using the chemical effects of
electrodynamic action, of which we shall have to speak in the next
Book, a new means has been obtained of copying, with an exactness
unattainable before, any forms which art or nature has produced, and
of covering them with a surface of metal. The _Electrotype Process_
is now one of the great powers which manufacturing art employs.

But these discoveries have also been employed in explaining natural
phenomena, the causes of which had before been altogether
inscrutable. This is the case with regard to the diurnal variation
of the magnetic needle; a fact  which as to its existence is
universal in all places, and which yet is so curiously diverse in
its course at different places. Dr. Faraday has shown that some of
the most remarkable of these diversities, and probably all, seem to
be accounted for by the different magnetic effects of air at
different temperatures: although, as I have already said, **(Book
xii.) the discovery of a decennial period in the diurnal changes of
magnetic declination shows that any explanation of those changes
which refers them to causes existing in the atmosphere must be very
incomplete.[40\B]

[Note 40\B: _Researches_, Art. 2892.]



{{625}}
BOOK XIV.

CHEMISTRY.

CHAPTER IX.

THE ELECTRO-CHEMICAL THEORY.


AMONG the consequences of the Electro-chemical Theory, must be
ranged the various improvements which have been made in the voltaic
battery. Daniel introduced between the two metals a partition
permeable by chemical action, but such as to allow of two different
acid solutions being in contact with the two metals. Mr. Grove's
battery, in which the partition is of porous porcelain, and the
metals are platinum and amalgamated zinc, is one of the most
powerful hitherto known. Another has been constructed by Dr. Callan,
in which the negative or conducting plate is a cylinder of cast
iron, and the positive element a cylinder of amalgamated zinc placed
in a porous cell. This also has great energy.


_The Number of Elementary Substances._

There have not been, I believe, any well-established additions to
the list of the simple substances recognized by chemists. Indeed the
tendency at present appears to be rather to deny the separate
elementary character of some already announced as such substances.
Pelopium and Niobium were, as I have said, two of the new metals.
But Naumann, in his _Elemente der Mineralogie_ (4th ed. 1855), says,
in a foot note (page 25): "_Pelopium_ is happily again got rid of;
for Pelopic Acid and Niobic Acid possess the same Radical.
_Donarium_ had a still shorter existence."

In the same way, when Hermann imagined that he had discovered a new
simple metallic substance in the mineral Samarskite from Miask, the
discovery was disproved by H. Rose (_Pogg. Ann._ B. 73, s. 449). {626}

In general the insulation of the new simple substances, the metallic
bases of the earths, and the like,--their separation from their
combinations, and the exhibition of them in a metallic form--has been
a difficult chemical process, and has rarely been executed on any
considerable scale. But in the case of _Aluminium_, the basis of the
earth Alumina, the process of its extraction has recently been so much
facilitated, that the metal can be produced in abundance. This being
the case, it will probably soon be applied to special economical uses,
for which it is fitted by possessing special properties.



{{626}}
BOOK XV.

MINERALOGY.


BY the kindness of W. H. Miller, Esq., Professor of Mineralogy in
the University of Cambridge, I am able to add to this part the
following notices of books and memoirs.

1. _Crystallography._

_Elemente der Krystallographie, nebst einer tabellarischen
Uebersicht der Mineralien nach der Krystallformen_, von Gustav Rose.
2. Auflage. Berlin, 1838. The crystallographic method here adopted
is, for the most part, that of Weiss. The method of this work has
been followed in

_A System of Crystallography, with its Applications to Mineralogy_.
By John Joseph Griffin. Glasgow, 1841. Mr. Griffin has, however,
modified the notation of Rose. He has constructed a series of models
of crystalline forms.

Frankenheim's _System der Krystalle_. 1842. This work adopts nearly
the Mohsian systems of crystallization. It contains Tables of the
chemical constitution, inclinations of the axis, and magnitude of
the axes of all the crystals of which a description was to be found,
including those formed in the laboratory, as well as those usually
called minerals; 713 in all.

Fr. Aug. Quenstedt, _Methode der Krystallographie_, 1840, employs a
fanciful method of representing a crystal by projecting upon one
face of the crystal all the other faces. This invention appears to
be more curious than useful.

Dr. Karl Naumann, who is spoken of in Chap. ix. of this Book, as the
author of the best of the Mixed Systems of Classification, published
also _Grundriss der Krystallographie_, Leipzig, 1826. In this and
other works he modifies the notation of Mohs in a very advantageous
manner. {628}

Professor Dana, in his _System of Mineralogy_, New Haven (U.S.),
1837, follows Naumann for the most part, both in crystallography and
in mineral classification. In the latter part of the subject, he has
made the attempt, which in all cases is a source of confusion and of
failure, to introduce a whole system of new names of the members of
his classification.

The geometry of crystallography has been investigated in a very
original manner by M. Bravais, in papers published in the Journal of
the Ecole Polytechnique, entitled _Mémoires sur les Systèmes formés
par des Points_. 1850. _Etudes Crystallographiques_. 1851.

Hermann Kopp (_Einleitung in die Krystallographie_, Braunschweig.
1849) has given the description and measurement of the angles of a
large number of laboratory crystals.

Rammelsberg (_Krystallographische Chemie_, Berlin, 1855) has
collected an account of the systems, simple forms and angles of all
the laboratory crystals of which he could obtain descriptions.

Schabus of Vienna (_Bestimmung der Krystallgestalten **in Chemischen
Laboratorien erzeugten Producte_, Wien, 1855; a successful Prize
Essay) has given a description, accompanied by measurements, of 90
crystalline species from his own observations.

To these attempts made in other countries to simplify and improve
crystallography, I may add a remarkable Essay very recently made
here by Mr. Brooke, and suggested to him by his exact and familiar
knowledge of Mineralogy. It is to this effect. All the crystalline
forms of any given mineral species are derived from the _primitive
form_ of that species; and the degree of symmetry, and the
_parameters_, of this form determine the angles of all derivative
forms. But how is this primitive form selected and its parameters
determined? The selection of the kind of the primitive form depends
upon the _degree of symmetry_ which appears in all the derivative
forms; according to which they belong to the _rhombohedral_,
_prismatic_, _square pyramidal_, or some other _system_: and this
determination is commonly clear. But the parameters, or the angles,
of the primitive form, are commonly determined by the _cleavage_ of
the mineral. Is this a sufficient and necessary ground of such
determination? May not a simplification be effected, in some cases,
by taking some other parameters? by taking a primitive form which
belongs to the proper system, but which has some other angles than
those given by cleavage? Mr. Brooke has tried whether, for instance,
crystals of the rhombohedral system may not be referred with
advantage to primitive rhombohedrons which have, in all {629} the
species, nearly the same angles. The advantage to be obtained by
such a change would be the simplification of the laws of derivation
in the derivative forms: and therefore we have to ask, whether the
indices of derivation are smaller numbers in this way or with the
hitherto accepted fundamental angles. It appears to me, from the
examples given, that the advantage of simplicity in the indices is
on the side of the old system: but whether this be so or not, it was
a great benefit to crystallography to have the two methods compared.
Mr. Brooke's Essay is a Memoir presented to the Royal Society in 1856.


2. _Optical Properties of Minerals._

The _Handbuch der Optik_, von F. W. G. Radicke, Berlin, 1839,
contains a chapter on the optical properties of crystals. The
author's chief authority is Sir D. Brewster, as might be expected.

M. Haidinger has devoted much attention to experiments on the
_pleochroism_ of minerals. He has invented an instrument which makes
the dichroism of minerals more evident by exhibiting the two colors
side by side.

The pleochroism of minerals, and especially the remarkable clouds
that in the cases of Iolite, Andalusite, Augite, Epidote, and
Axinite, border the positions of either optical axis, have been most
successfully imitated by M. de Senarmont by means of artificial
crystallizations. (_Ann. de Chim._ 3 _Ser._ xli. p. 319.)

M. Pasteur has found that Racemic Acid consists of two different
acids, having the same density and composition. The salts of these
acids, with bases of Ammonia and of Potassa, are hemihedral, the
hemihedral faces which occur in the one being wanting in the other.
The acids of these different crystals have circular polarization of
opposite kinds. (_Ann. de Chim._ 3 _Ser._ xxviii. 56, 99.) This
discovery was marked by the assignation of the Rumford Medal to M.
Pasteur in 1856.

M. Marbach has discovered that crystals of chlorate of soda, which
apparently belongs to the cubic or tessular system, exhibit hemihedral
faces of a peculiar character; and that the crystals have circular
polarization of opposite kinds in accordance with the differences of
the plagihedral faces. (_Poggendorf's Annalen_, xci. 482.)

M. Seybolt of Vienna has found a means of detecting plagihedral
faces in quartz crystals which do not reveal them externally.
(_Akad. d. Wissenschaft zu Wien_, B. xv. s. 59.) {630}


3. _Classification of Minerals._

In the _Philosophy of the Inductive Sciences_, B. VIII. C. iii., I
have treated of the Application of the Natural-history Method of
Classification to Mineralogy, and have spoken of the Systems of this
kind which have been proposed. I have there especially discussed the
system proposed in the treatise of M. Necker, _Le Règne Minéral
ramené aux Méthodes d'Histoire Naturelle_ (Paris, 1835). More
recently have been published M. Beudant's _Cours élémentaire
d'Histoire Naturelle, Minéralogie_ (Paris, 1841); and M. A.
Dufresnoy's _Traité de Minéralogie_ (Paris, 1845). Both these works
are so far governed by mere chemical views that they lapse into the
inconveniences and defects which are avoided in the best systems of
German mineralogists.

The last mineral system of Berzelius has been developed by M.
Rammelsberg (Nürnberg, 1847). It is in principle such as we have
described it in the history.

M. **Nordenskiöld's system (3rd Ed. 1849,) has been criticised by G.
Rose, who observes that it removes the defects of the system of
Berzelius only in part. He himself proposes what he calls a
"Krystallo-Chemisches System," in which the crystalline form
determines the genus and the chemical composition the species. His
classes are--
1. Simple Substances.
2. Combinations of Sulphur, Selenium, Titanium, Arsenic, Antimony.
3. Chlorides, Fluorides, Bromides, Iodides.
4. Combinations with Oxygen.

We have already said that for us, all chemical compounds are
_minerals_, in so far that they are included in our classifications.
The propriety of this mode of dealing with the subject is confirmed
by our finding that there is really no tenable distinction between
native minerals and the products of the laboratory. A great number
of eminent chemists have been employed in producing, by artificial
means, crystals which had before been known only as native products.



{{631}}
BOOK XVI.

CLASSIFICATORY SCIENCES.

BOTANY.


FOR the purpose of giving to my reader some indication of the
present tendency of Botanical Science, I conceive that I cannot do
better than direct his attention to the reflections, procedure, and
reasonings which have been suggested by the most recent extensions
of man's knowledge of the vegetable world. And as a specimen of
these, I may take the labors of Dr. Joseph Hooker, on the Flora of
the Antarctic Regions,[41\B] and especially of New Zealand. Dr.
Hooker was the Botanist to an expedition commanded by Sir James
Ross, sent out mainly for the purpose of investigating the phenomena
of Terrestrial Magnetism near the South Pole; but directed also to
the improvement of Natural History. The extension of botanical
descriptions and classifications to a large mass of new objects
necessarily suggests wider views of the value of classes (genera,
species, &c.,) and the conclusions to be drawn from their constancy
or inconstancy. A few of Dr. Hooker's remarks may show the nature of
the views taken under such circumstances.

[Note 41\B: _The Botany of the Antarctic Voyage of H. M. Discovery
Ships Erebus and Terror, in the years_ 1839-40. Published 1847.
_Flora Novæ Zelandiæ_. 1853.]

I may notice, in the first place, (since this work is intended for
general rather than for scientific readers,) Dr. Hooker's testimony
to the value of a technical descriptive language for a
classificatory science--a Terminology, as it is called. He says, "It
is impossible to write Botanical descriptions which a person
ignorant of Botany can understand, although it is supposed by many
unacquainted with science that this can and should be done." And
hence, he says, the state of botanical science demands Latin
descriptions of the plants; and this is a lesson which he especially
urges upon the Colonists who study the indigenous plants. {632}

Dr. Hooker's remarks on the limits of species, their dispersion and
variation, are striking and instructive. He is of opinion that
species vary more, and are more widely diffused, than is usually
supposed. Hence he conceives that the number of species has been
needlessly and erroneously multiplied, by distinguishing the
specimens which occur in different places, and vary in unessential
features. He says that though, according to the lowest estimate of
compilers, 100,000 is the commonly received number of known plants,
he thinks that half that number is much nearer the truth. "This," he
says, "may be well conceived, when it is notorious that nineteen
species have been made of the Common Potatoe, and many more of
_Solanum nigrum_ alone. _Pteris aquilina_ has given rise to numerous
book species; _Vernonia cinerea_ of India to fifteen at least. . . .
. . . Many more plants are common to most countries than is
supposed; I have found 60 New Zealand flowering plants and 9 Ferns
to be European ones, besides inhabiting numerous intermediate
countries. . . . . . So long ago as 1814, Mr. Brown drew attention
to the importance of such considerations, and gave a list of 150
European plants common to Australia."

As an example of the extent to which unessential differences may go,
he says (p. xvii.,) "The few remaining native Cedars of Lebanon may
be abnormal states of the tree which was once spread over the whole
of the Lebanon; for there are now growing in England varieties of it
which have no existence in a wild state. Some of them closely
resemble the Cedars of Atlas and of the Himalayas (_Deodar_;) and
the absence of any valid botanical differences tends to prove that
all, though generally supposed to be different species, are one."

Still the great majority of the species of plants in those Southern
regions are peculiar. "There are upwards of 100 genera, subgenera,
or other well marked groups of plants, entirely or nearly confined
to New Zealand, Australia, and extra-tropical South America. They
are represented by one or more species in two or more of those
countries, and thus effect a botanical relationship or affinity
between them all which every botanist appreciates."

In reference to the History of Botany, I have received corrections
and remarks from Dr. Hooker, with which I am allowed to enrich my
pages.

"P. 359. Note ^3. ~= Note 3\16~ _Nelumbium speciosum_, the Lotus of
India. The _Nelumbium_ does not float, but raises both leaf and flower
several feet above the water: the _Nymphæa Lotus_ has floating leaves.
Both enter largely into the symbolism of the Hindoos, and are often
confounded. {633}

"P. 362. Note ^5. ~= Note 13\16~ For _Arachnis_ read _Arachis_. The
_Arachidna_ of Theophrastus cannot, however, be the _Arachis_ or
ground-nut.

"Pp. 388 and 394. For _Harlecamp_ read _Hartecamp_.

"P. 394. For _Kerlen_ read _Kalm_.

"P. 394. For _Asbech_ read _Osbeck_.

"P. 386. _John Ray_. Ray was further the author of the present
Natural System in its most comprehensive sense. He first divided
plants into Flowerless and Flowering; and the latter into
Monocotyledonous and Dicotyledonous:--'Floriferas dividemus in
DICOTYLEDONES, quarum semina sata binis foliis, seminalibus dictis,
quæ cotyledonorum usum præstant, e terra exeunt, vel in binos saltem
lobos dividuntur, quamvis eos supra terram foliorum specie non
efferant; et MONOCOTYLEDONES, quæ nec folia bina seminalia efferunt
nec lobos binos condunt. Hæc divisio ad arbores etiam extendi
potest; siquidem Palmæ et congeneres hoc respectu eodem modo a
reliquis arboribus differunt quo Monocotyledones a reliquis herbis.'

"P. 408. _Endogenous and Exogenous Growth._ The exact course of the
wood fibres which traverse the stems of both Monocotyledonous and
Dicotyledonous plants has been only lately discovered. In the
Monocotyledons, those fibres are collected in bundles, which follow
a very peculiar course:--from the base of each leaf they may be
followed downwards and inwards, towards the axis of the trunk, when
they form an arch with the convexity to the centre; and curving
outwards again reach the circumference, where they are lost amongst
the previously deposited fibres. The intrusion of the bases of these
bundles amongst those already deposited, causes the circumference of
the stem to be harder than the centre; and as all these arcs have a
short course (their chords being nearly equal), the trunk does not
increase in girth, and grows at the apex only. The wood-bundles are
here definite. In the Dicotyledonous trunks, the layers of wood run
in parallel courses from the base to the top of the trunk, each
externally to that last formed, and the trunk increases both in
height and girth; the wood-bundles are here indefinite.

"With regard to the Cotyledons, though it is often difficult to
distinguish a Monocotyledonous Embryo from a Dicotyledonous, they
may always be discriminated when germinating. The Cotyledons, when
two or more, and primordial leaves (when no Cotyledons are visible)
of a Monocotyledon, are alternate; those of a Dicotyledon are
opposite.

"A further physiological distinction between Monocotyledons and
{634} Dicotyledons is observed in germination, when the
Dicotyledonous radicle elongates and forms the root of the young
plant; the Monocotyledonous radicle does not elongate, but pushes
out rootlets from itself at once. Hence the not very good terms,
_exorhizal_ for Dicotyledonous, and _endorhizal_ for
Monocotyledonous.

"The highest physiological generalization in the vegetable kingdom
is between _Phænogama_ and _Cryptogama_. In the former,
fertilization is effected by a pollen-tube touching the nucleus of
an ovule; in Cryptogams, the same process is effected by the contact
of a sperm-cell, usually ciliated (_antherozoid_), upon another kind
of cell called a germ-cell. In Phænogams, further, the organs of
fructification are all modified leaves; those of Cryptogams are not
homologous." (J. D. H.)


ZOOLOGY.

I have exemplified the considerations which govern zoological
classification by quoting the reflexions which Cuvier gives us, as
having led him to his own classification of Fishes. Since the
varieties of Quadrupeds, or _Mammals_ (omitting whales, &c.), are
more familiar to the common reader than those of Fishes, I may
notice some of the steps in their classification; the more so as
some curious questions have recently arisen thereupon.

Linnæus first divides Mammals into two groups, as they have Claws,
or Hoofs (_unguiculata_, _ungulata_.) But he then again divides them
into six orders (omitting whales, &c.), according to their number of
_incisor_, _laniary_, and _molar_ teeth; namely:--
_Primates_. (Man, Monkey, &c.)
_Bruta_. (Rhinoceros, Elephant, &c.)
_Feræ_. (Dog, Cat, Bear, Mole, &c.)
_Glires_. (Mouse, Squirrel, Hare, &c.)
_Pecora_. (Camel, Giraffe, Stag, Goat, Sheep, Ox, &c.)
_Belluæ_. (Horse, Hippopotamus, Tapir, Sow, &c.)

In the place of these, Cuvier, as I have stated in the _Philosophy_
(_On the Language of Sciences_, Aphorism xvi.), introduced the
following orders: _Bimanes_, _Quadrumanes_, _Carnassiers_,
_Rongeurs_, _Edentés_, _Pachyderms_, _Ruminans_. Of these, the
_Carnassiers_ correspond to the _Feræ_ of Linnæus; the _Rongeurs_ to
his _Glires_; the _Edentés_ are a new order, taking the Sloths,
Ant-eaters, &c., from the _Bruta_ of Linnæus, the Megatherium from
extinct animals, and the Ornithorhynchus, &c., from the new animals
of Australia; the _Ruminans_ agree with the {635} _Pecora_; the
_Pachyderms_ include some of the _Bruta_ and the _Belluæ_,
comprehending also extinct animals, as _Anoplotherium_ and
_Palæotherium_.

But the two orders of Hoofed Animals, the Pachyderms and the
Ruminants, form a group which is held by Mr. Owen to admit of a
better separation, on the ground of a character already pointed out
by Cuvier; namely, as to whether they are _two-toed_ or
_three-toed_. According to this view, the Horse is connected with
the Tapir, the Palæotherium, and the Rhinoceros, not only by his
teeth, but by his feet, for he has really three digits. And Cuvier
notices that in the two-toed or even-toed Pachyderms, the astragalus
bone has its face divided into two equal parts by a ridge; while in
the uneven-toed pachyderms it has a narrow cuboid face. Mr. Owen has
adopted this division of Pachyderms and Ruminants, giving the names
_artiodactyla_ and _perissodactyla_ to the two groups; the former
including the Ox, Hog, Peccary, Hippopotamus, &c.; the latter
comprehending the Horse, Tapir, Rhinoceros, Hyrax, &c. And thus the
Ruminants take their place as a subordinate group of the great
natural even-toed Division of the Hoofed Section of Mammals; and the
Horse is widely separated from them, inasmuch as he belongs to the
odd-toed division.[42\B]

[Note 42\B: Owen, _Odontography_.]

As we have seen, these modern classifications are so constructed as
to include extinct as well as living species of animals; and indeed
the species which have been discovered in a fossil state have tended
to fill up the gaps in the series of zoological forms which had
marred the systems of modern zoologists. This has been the case with
the division of which we are speaking.

Mr. Owen had established two genera of extinct Herbivorous Animals,
on the strength of fossil remains brought from South
America:--_Toxodon_, and _Nesodon_. In a recent communication to the
Royal Society[43\B] he has considered the bearing of these genera
upon the divisions of odd-toed and even-toed animals. He had already
been led to the opinion that the three sections, _Proboscidea_,
_Perissodactyla_, and _Artiodactyla_, formed a natural division of
Ungulata; and he is now led to think that this division implies
another group, "a distinct division of the _Ungulata_, of equal
value, if not with the _Perissodactyla_ and _Artiodactyla_ at least
with the _Proboscidea_. This group he proposes to call _Toxodonta_.

[Note 43\B: _Phil. Trans._, 1853.]



{{636}}
BOOK XVII.

PHYSIOLOGY AND COMPARATIVE ANATOMY.

VEGETABLE MORPHOLOGY.


_Morphology in Linnæus._

I HAVE stated that Linnæus had some views on this subject. Dr.
Hooker conceives these views to be more complete and correct than is
generally allowed, though unhappily clothed in metaphorical language
and mixed with speculative matter. By his permission I insert some
remarks which I have received from him.

The fundamental passage on this subject is in the _Systema Naturæ_;
in the Introduction to which work the following passage occurs:--

"Prolepsis (Anticipation) exhibits the mystery of the metamorphosis
of plants, by which the herb, which is the _larva_ or imperfect
condition, is changed into the declared fructification: for the
plant is capable of producing either a leafy herb or a
fructification. . . . . .

"When a tree produces a flower, nature anticipates the produce of
five years where these come out all at once; forming of the
bud-leaves of the next year _bracts_; of those of the following
year, the _calyx_; of the following, the _corolla_; of the next, the
_stamina_; of the subsequent, the _pistils_, filled with the
granulated marrow of the seed, the terminus of the life of a
vegetable."

Dr. Hooker says, "I derive my idea of his having a better knowledge
of the subject than most Botanists admit, not only from the
Prolepsis, but from his paper called _Reformatio Botanices_ (_Amœn.
Acad._ vol. vi.); a remarkable work, in respect of his candor in
speaking of his predecessors' labors, and the sagacity he shows in
indicating researches to be undertaken or completed. Amongst the
latter is V. 'Prolepsis plantarum, ulterius extendenda per earum
metamorphoses.' The last word occurs rarely in his _Prolepsis_; but
when it does it seems to me that he uses it as indicating a normal
change and not an accidental one. {637}

"In the _Prolepsis_ the speculative matter, which Linnæus himself
carefully distinguishes as such, must be separated from the rest,
and this may I think be done in most of the sections. He starts with
explaining clearly and well the origin and position of buds, and
their constant presence, whether developed or not, in the axil of
the leaf: adding abundance of acute observations and experiments to
prove his statements. The leaf he declares to be the first effort of
the plant in spring: he proceeds to show, successively, that bracts,
calyx, corolla, stamens, and pistil are each of them metamorphosed
leaves, in every case giving MANY EXAMPLES, both from monsters and
from characters presented by those organs in their normal condition.

"The (to me) obscure and critical part of the _Prolepsis_ was that
relating to the change of the style of _Carduus_ into two leaves. Mr.
Brown has explained this. He says it was a puzzle to him, till he went
to Upsala and consulted Fries and Wahlenberg, who informed him that
such monstrous _Cardui_ grew in the neighborhood, and procured him
some. Considering how minute and masked the organs of _Compositæ_ are,
it shows no little skill in Linnæus, and a very clear view of the
whole matter, to have traced the metamorphosis of all their floral
organs into leaves, except their stamens, of which he says, 'Sexti
anni folia e staminibus me non in compositis vidisse fateor, sed
illorum loco folia pistillacea, quæ in compositis aut plenis sunt
frequentissima.' I must say that nothing could well be clearer to my
mind than the full and accurate appreciation which Linnæus shows of
the whole series of phenomena, and their _rationale_. He over and over
again asserts that these organs are leaves, every one of them,--I do
not understand him to say that the prolepsis is an accidental change
of leaves into bracts, of bracts into calyx, and so forth. Even were
the language more obscure, much might be inferred from the wide range
and accuracy of the observations he details so scientifically. It is
inconceivable that a man should have traced the sequence of the
phenomena under so many varied aspects, and shown such skill,
knowledge, ingenuity, and accuracy in his methods of observing and
describing, and yet missed the _rationale_ of the whole. Eliminate the
speculative parts and there is not a single error of observation or
judgment; whilst his history of the developement of buds, leaves, and
floral organs, and of various other obscure matters of equal interest
and importance, are of a very high order of merit, are, in fact, for
the time profound.

"There is nothing in all this that detracts from the merit of
Goethe's {638} re-discovery. With Goethe it was, I think, a
deductive process,--with Linnæus an inductive. Analyse Linnæus's
observations and method, and I think it will prove a good example of
inductive reasoning.

"P. 473. Perhaps Professor Auguste St Hilaire of Montpellier should
share with De Candolle the honor of contributing largely to
establish the metamorphic doctrine;--their labors were
cotemporaneous.

"P. **474. Linnæus pointed out that the pappus was calyx: 'Et
_pappum_ gigni ex quarti anni foliis, in jam nominatis
Carduis.'--_Prol. Plant._ 338." (_J. D. H._)




CHAPTER VII.

ANIMAL MORPHOLOGY.


THE subject of Animal Morphology has recently been expanded into a
form strikingly comprehensive and systematic by Mr. Owen; and
supplied by him with a copious and carefully-chosen language; which
in his hands facilitates vastly the comparison and appreciation of
the previous labors of physiologists, and opens the way to new
truths and philosophical generalizations. Though the steps which
have been made had been prepared by previous anatomists, I will
borrow my view of them mainly from him; with the less scruple,
inasmuch as he has brought into full view the labors of his
predecessors.

I have stated in the History that the skeletons of all vertebrate
animals are conceived to be reducible to a single Type, and the
skull reducible to a series of vertebræ. But inasmuch as this
reduction includes not only a detailed correspondence of the bones
of man with those of beasts, but also with those of birds, fishes,
and reptiles, it may easily be conceived that the similarities and
connexions are of a various and often remote kind. The views of such
relations, held by previous Comparative Anatomists, have led to the
designations of the bones of animals which have been employed in
anatomical descriptions; and these designations having been framed
and adopted by anatomists looking at the subject from different
sides, and having different views of analogies and relations, have
been very various and unstable; besides being often of cumbrous
length and inconvenient form.

The corresponding parts in different animals are called _homologues_,
{639} a term first applied to anatomy by the philosophers of Germany;
and this term Mr. Owen adopts, to the exclusion of terms more loosely
denoting identity or similarity. And the Homology of the various bones
of vertebrates having been in a great degree determined by the labors
of previous anatomists, Mr. Owen has proposed names for each of the
bones: the condition of such names being, that the homologues in all
vertebrates shall be called by the same name, and that these names
shall be founded upon the terms and phrases in which the great
anatomists of the 16th, 17th, and 18th centuries expressed the results
of their researches respecting the human skeleton. These names, thus
selected, so far as concerned the bones of the Head of Fishes, one of
the most difficult cases of this Special Homology, he published in a
Table,[44\B] in which they were compared, in parallel columns, with
the names or phrases used for the like purpose by Cuvier, Agassiz,
Geoffroy, Hallman, Sœmmering, Meckel, and Wagner. As an example of the
considerations by which this selection of names was determined, I may
quote what he says with regard to one of these bones of the skull.

[Note 44\B: _Lectures on Vertebrates_. 1846, p. 158. And _On the
Archetype and Homologies of the Vertebrate Skeleton_. 1848, p. 172.]

"With regard to the 'squamosal' (_squamosum_. Lat. pars squamosa
ossis temporis.--Sœmmering), it might be asked why the term
'temporal' might not be retained for this bone. I reply, because
that term has long been, and is now universally, understood in human
anatomy to signify a peculiarly anthropotomical coalesced congeries
of bones, which includes the 'squamosal' together with the
'petrosal,' the 'tympanic,' the 'mastoid,' and the 'stylohyal.' It
seems preferable, therefore, to restrict the signification of the
term 'temporal' to the whole (in Man) of which the 'squamosal' is a
part. To this part Cuvier has unfortunately applied the term
'temporal' in one class, and 'jugal' in another; and he has also
transferred the term 'temporal' to a third equally distinct bone in
fishes; while to increase the confusion M. Agassiz has shifted the
name to a fourth different bone in the skull of fishes. Whatever,
therefore, may be the value assigned to the arguments which will be
presently set forth, as to the special homologies of the 'pars
squamosa ossis temporis,' I have felt compelled to express the
conclusion by a definite term, and in the present instance, have
selected that which recalls the best accepted anthropomorphical
designation of the part; although 'squamosal' must be understood and
applied in an arbitrary sense; and not as descriptive of a
scale-like {640} form; which in reference to the bone so called, is
rather its exceptional than normal figure in the vertebrate series."

The principles which Mr. Owen here adopts in the selection of names
for the parts of the skeleton are wise and temperate. They agree
with the aphorisms concerning the language of science which I
published in the _Philosophy of the Inductive Sciences_; and Mr.
Owen does me the great honor of quoting with approval some of those
Aphorisms. I may perhaps take the liberty of remarking that the
system of terms which he has constructed, may, according to our
principles, be called rather a _Terminology_ **than a
_Nomenclature_: that is, they are analogous more nearly to the
_terms_ by which botanists describe the parts and organs of plants,
than to the _names_ by which they denote genera and species. As we
have seen in the History, plants as well as animals are subject to
morphological laws; and the names which are given to organs in
consequence of those laws are a part of the Terminology of the
science. Nor is this distinction between Terminology and
Nomenclature without its use; for the rules of prudence and
propriety in the selection of words in the two cases are different.
The Nomenclature of genera and species may be arbitrary and casual,
as is the case to a great extent in Botany and in Zoology,
especially of fossil remains; names being given, for instance,
simply as marks of honor to individuals. But in a Terminology, such
a mode of derivation is not admissible: some significant analogy or
idea must be adopted, at least as the origin of the name, though not
necessarily true in all its applications, as we have seen in the
case of the "squamosal" just quoted. This difference in the rules
respecting two classes of scientific words is stated in the
_Aphorisms_ xiii. and xiv. _concerning the Language of Science_.

Such a Terminology of the bones of the skeletons of all vertebrates
as Mr. Owen has thus propounded, cannot be otherwise than an immense
acquisition to science, and a means of ascending from what we know
already to wider truths and new morphological doctrines.

With regard to one of these doctrines, the resolution of the human
head into vertebræ, Mr. Owen now regards it as a great truth, and
replies to the objections of Cuvier and M. Agassiz, in detail.[45\B]
He gives a Table in which the Bones of the Head are resolved into
four vertebræ, which he terms the Occipital, Parietal, Frontal, and
Nasal Vertebra, respectively. These four vertebræ agree in general
with what Oken called the Ear-vertebra, the Jaw-vertebra, the
Eye-vertebra, and {641} the Nose-vertebra, in his work _On the
Signification of the Bones of the Skull_, published in 1807: and in
various degrees, with similar views promulgated by Spix (1815),
Bojanus (1818), Geoffroy (1824), Carus **(1828). And I believe that
these views, bold and fanciful as they at first appeared, have now
been accepted by most of the principal physiologists of our time.

[Note 45\B: _Archetype and Homologies of the Vertebrate Skeleton_.
1848, p. 141.]

But another aspect of this generalization has been propounded among
physiologists; and has, like the others, been extended,
systematized, and provided with a convenient language by Mr. Owen.
Since animal skeletons are thus made up of vertebræ and their parts
are to be understood as developements of the parts of vertebræ,
Geoffroy (1822), Carus (1828), Müller (1834), Cuvier (1836), had
employed certain terms while speaking of such developements; Mr.
Owen in the _Geological Transactions_ in 1838, while discussing the
osteology of certain fossil Saurians, used terms of this kind, which
are more systematic than those of his predecessors, and to which he
has given currency by the quantity of valuable knowledge and thought
which he has embodied in them.

According to his Terminology,[46\B] a vertebra, in its typical
completeness, consists of a central part or _centrum_; at the back
of this, two plates (the _neural apophyses_) and a third outward
projecting piece (the _neural spine_), which three, with the
centrum, form a canal for the spinal marrow; at the front of the
centrum two other plates (the _hæmal apophyses_) and a projecting
piece, forming a canal for a vascular trunk. Further lateral
elements (_pleuro-apophyses_) and other projections, are in a
certain sense dependent on these principal bones; besides which the
vertebra may support _diverging appendages_. These parts of the
vertebra are fixed together, so that a vertebra is by some
anatomists described as a single bone; but the parts now mentioned
are usually developed from distinct and independent centres, and are
therefore called by Mr. Owen "autogenous" elements.

[Note 46\B: _Archetype and Homologies of the Vertebrate Skeleton_.
1848, p. 81.]

The _General_ Homology of the vertebral skeleton is the reference of
all the parts of a skeleton to their true types in a series of
vertebræ: and thus, as _special_ homology refers all the parts of
skeletons to a given type of skeleton, say that of Man, _general_
homology refers all the parts of every skeleton, say that of Man, to
the parts of a series of Vertebræ. And thus as Oken propounded his
views of the Head as a resolution of the Problem of _the
Signification of the Bones of the Head_, {642} so have we in like
manner, for the purposes of General Homology, to solve the Problem
of _the Signification of Limbs_. The whole of the animal being a
string of vertebræ, what are arms and legs, hands and paws, claws
and fingers, wings and fins, and the like? This inquiry Mr. Owen has
pursued as a necessary part of his inquiries. In giving a public
lecture upon the subject in 1849,[47\B] he conceived that the phrase
which I have just employed would not be clearly apprehended by an
English Audience, and entitled his Discourse "On the _Nature_ of
Limbs:" and in this discourse he explained the modifications by
which the various kinds of limbs are derived from their rudiments in
an archetypal skeleton, that is, a mere series of vertebræ without
head, arms, legs, wings, or fins.

[Note 47\B: _On the Nature of Limbs_, a discourse delivered at a
Meeting of the Royal Institution, 1849.]


_Final Causes_

It has been mentioned in the History that in the discussions which
took place concerning the Unity of Plan of animal structure, this
principle was in some measure put in opposition to the principle of
Final Causes: Morphology was opposed to Teleology. It is natural to
ask whether the recent study of Morphology has affected this
antithesis.

If there be advocates of Final Causes in Physiology who would push
their doctrines so far as to assert that every feature and every
relation in the structure of animals have a purpose discoverable by
man, such reasoners are liable to be perpetually thwarted and
embarrassed by the progress of anatomical knowledge; for this
progress often shows that an arrangement which had been explained
and admired with reference to some purpose, exists also in cases
where the purpose disappears; and again, that what had been noted as
a special teleological arrangement is the result of a general
morphological law. Thus to take an example given by Mr. Owen: that
the ossification of the head originates in several centres, and thus
in its early stages admits of compression, has been pointed out as a
provision to facilitate the birth of viviparous animals; but our
view of this provision is disturbed, when we find that the same mode
of the formation of the bony framework takes place in animals which
are born from an egg. And the number of points from which
ossification begins, depends in a wider sense on the general
homology of the animal frame, according to which each part is
composed of a certain number of autogenous vertebral elements. In
this {643} way, the admission of a new view as to Unity of Plan will
almost necessarily displace or modify some of the old views
respecting Final Causes.

But though the view of Final Causes is displaced, it is not
obliterated; and especially if the advocate of Purpose is also ready
to admit visible correspondences which have not a discoverable
object, as well as contrivances which have. And in truth, how is it
possible for the student of anatomy to shut his eyes to either of
these two evident aspects of nature? The arm and hand of man are
made for taking and holding, the wing of the sparrow is made for
flying; and each is adapted to its end with subtle and manifest
contrivance. There is plainly Design. But the arm of man and the
wing of the sparrow correspond to each other in the most exact
manner, bone for bone. Where is the Use or the Purpose of this
correspondence? If it be said that there may be a purpose though we
do not see it, that is granted. But Final Causes _for us_ are
contrivances of which _we see_ the end; and nothing is added to the
evidence of Design by the perception of a unity of plan which in no
way tends to promote the design.

It may be said that the design appears in the modification of the
plan in special ways for special purposes;--that the vertebral plan
of an animal being given, the fore limbs are modified in Man and in
Sparrow, as the nature and life of each require. And this is truly
said; and is indeed the truth which we are endeavoring to bring into
view:--that there are in such speculations, two elements; one given,
the other to be worked out from our examination of the case; the
_datum_ and the _problem_; the homology and the teleology.

Mr. Owen, who has done so much for the former of these portions of
our knowledge, has also been constantly at the same time
contributing to the other. While he has been aiding our advances
towards the Unity of Nature, he has been ever alive to the
perception of an Intelligence which pervades Nature. While his
morphological doctrines have moved the point of view from which he
sees Design, they have never obscured his view of it, but, on the
contrary, have led him to present it to his readers in new and
striking aspects. Thus he has pointed out the final purposes in the
different centres of ossification of the long bones of the limbs of
mammals, and shown how and why they differ in this respect from
reptiles (_Archetype_, p. 104). And in this way he has been able to
point out the insufficiency of the rule laid down both by Geoffroy
St. Hilaire and Cuvier, for ascertaining the true number of bones in
each species. {644}

Final Causes, or Evidences of Design, appear, as we have said, not
merely as contrivances for evident purposes, but as modifications of
a given general Plan for special given ends. If the general Plan be
discovered after the contrivance has been noticed, the discovery may
at first seem to obscure our perception of Purpose; but it will soon
be found that it merely transfers us to a higher point of view. The
adaptation of the Means to the End remains, though the Means are
parts of a more general scheme than we were aware of. No
generalization of the Means can or ought permanently to shake our
conviction of the End; because we must needs suppose that the
Intelligence which contemplates the End is an intelligence which can
see at a glance along a vista of Means, however long and complex.
And on the other hand, no special contrivance, however clear be its
arrangement, can be unconnected with the general correspondences and
harmonies by which all parts of nature are pervaded and bound
together. And thus no luminous teleological point can be
extinguished by homology; nor, on the other hand, can it be detached
from the general expanse of homological light.

The reference to Final Causes is sometimes spoken of as
unphilosophical, in consequence of Francis Bacon's comparison of
Final Causes in Physics to Vestal Virgins devoted to God, and
barren. I have repeatedly shown that, in Physiology, almost all the
great discoveries which have been made, have been made by the
assumption of a purpose in animal structures. With reference to
Bacon's simile, I have elsewhere said that if he had had occasion to
develope its bearings, full of latent meaning as his similes so
often are, he would probably have said that to those Final Causes
barrenness was no reproach, seeing they ought to be not the Mothers
but the Daughters of our Natural Sciences; and that they were
barren, not by imperfection of their nature, but in order that they
might be kept pure and undefiled, and so fit ministers in the temple
of God. I might add that in Physiology, if they are not Mothers,
they are admirable Nurses; skilful and sagacious in perceiving the
signs of pregnancy, and helpful in bringing the Infant Truth into
the light of day.

There is another aspect of the doctrine of the Archetypal Unity of
Composition of Animals, by which it points to an Intelligence from
which the frame of nature proceeds; namely this:--that the Archetype
of the Animal Structure being of the nature of an _Idea_, implies a
mind in which this Idea existed; and that thus Homology itself
points the way to the Divine Mind. But while we acknowledge the full
{645} value of this view of theological bearing of physiology, we
may venture to say that it is a view quite different from that which
is described by speaking of "Final Causes," and one much more
difficult to present in a lucid manner to ordinary minds.



{{646}}
BOOK XVIII.

GEOLOGY.


WITH regard to Geology, as a Palætiological Science, I do not know
that any new light of an important kind has been thrown upon the
general doctrines of the science. Surveys and examinations of
special phenomena and special districts have been carried on with
activity and intelligence; and the animals of which the remains
people the strata, have been reconstructed by the skill and
knowledge of zoologists:--of such reconstructions we have, for
instance, a fine assemblage in the publications of the
Palæontological Society. But the great questions of the manner of
the creation and succession of animal and vegetable species upon the
earth remain, I think, at the point at which they were when I
published the last edition of the History.

I may notice the views propounded by some chemists of certain
bearings of Mineralogy upon Geology. As we have, in mineral masses,
organic remains of former organized beings, so have we crystalline
remains of former crystals; namely, what are commonly called
_pseudomorphoses_--the shape of one crystal in the substance of
another. M. G. Bischoff[48\B] considers the study of pseudomorphs as
important in geology, and as frequently the only means of tracing
processes which have taken place and are still going on in the
mineral kingdom.

[Note 48\B: _Chemical and Physical Geology_.]

I may notice also Professor Breithaupt's researches on the order of
succession of different minerals, by observing the mode in which
they occur and the order in which different crystals have been
deposited, promise to be of great use in following out the
geological changes which the crust of the globe has undergone. (_Die
Paragenesis der Mineralien_. Freiberg. 1849.)

In conjunction with these may be taken M. de Senarmont's experiments
on the formation of minerals in veins; and besides Bischoff's {647}
_Chemical Geology_, Sartorius von Walterhausen's Observations on the
occurrence of minerals in Amygdaloid.

As a recent example of speculations concerning Botanical
Palætiology, I may give Dr. Hooker's views of the probable history
of the Flora of the Pacific.

In speculating upon this question, Dr. Hooker is led to the
discussion of geological doctrines concerning the former continuity
of tracts of land which are now separate, the elevation of low lands
into mountain ranges in the course of ages, and the like. We have
already seen, in the speculations of the late lamented Edward
Forbes, (see Book xviii. chap. vi. of this History,) an example of a
hypothesis propounded to account for the existing Flora of England:
a hypothesis, namely, of a former Connexion of the West of the
British Isles with Portugal, of the Alps of Scotland with those of
Scandinavia, and of the plains of East Anglia with those of Holland.
In like manner Dr. Hooker says (p. xxi.) that he was led to
speculate on the possibility of the plants of the Southern Ocean
being the remains of a Flora that had once spread over a larger and
more continuous tract of land than now exists in the ocean; and that
the peculiar Antarctic genera and species may be the vestiges of a
Flora characterized by the predominance of plants which are now
scattered throughout the Southern islands. He conceives this
hypothesis to be greatly supported by the observations and
reasonings of Mr. Darwin, tending to show that such risings and
sinkings are in active progress over large portions of the
continents and islands of the Southern hemisphere: and by the
speculations of Sir C. Lyell respecting the influence of climate on
the migrations of plants and animals, and the influence of
geological changes upon climate.

In Zoology I may notice (following Mr. Owen)[49\B] recent
discoveries of the remains of the animals which come nearest to man
in their structure. At the time of Cuvier's death, in 1832, no
evidence had been obtained of fossil Quadrumana; and he supposed
that these, as well as Bimana, were of very recent introduction.
Soon after, in the oldest (eocene) tertiary deposits of Suffolk,
remains were found proving the existence of a monkey of the genus
Macacus. In the Himalayan tertiaries were found petrified bones of a
Semnopithecus; in Brazil, remains of an extinct platyrhine monkey of
great size; and lastly, in the middle tertiary series of the South
of France, was discovered a fragment of the jaw of the long-armed
ape (_Hylobates_). But no fossil human {648} remains have been
discovered in the regularly deposited layers of any divisions (not
even the pleiocene) of the tertiary series; and thus we have evidence
that the placing of man on the earth was the last and peculiar act
of Creation.

[Note 49\B: _Brit. Asso._ 1854, p. 112.]


THE END.




Transcriber's Notes

Whewell's book was originally published in 3 volumes in London in
1837. A second edition appeared in 1847, and a third in 1857. A
2-volume version of the 3rd edition was published in New York in 1858,
reprinted 1875. This Project Gutenberg text, combining both volumes
in sequence, was derived from the 1875 version, relying upon resources
kindly provided by the Internet Archive.

Three items have been added to the Contents of the First Volume;
they are marked off by ~ ~, as are any other additions to the text.

Printed page numbers have been transcribed in { }; pages without a
printed number have been indicated by {{ }}. Where words were
hyphenated across pages, the number has been placed before the word.

Fractions have been transcribed as numerator/denominator, occasionally
using parentheses to disambiguate. The original sometimes has
numerator over a line with denominator below, at other times numerator
hyphen denominator. Superscripted characters are marked by a ^ before
the character.

Footnotes in the original text were numbered by chapter; here they
have been numbered by Book (the number of which is given after a \,
for the two appendices to the 3rd edition A has been used for volume
1, B for volume 2). They are placed after the paragraph in which
they occur, and are transcribed [Note m\n: ...]. Footnote anchors
are transcribed [m\n]. All other square brackets are in the original
text.

One difficult item is the use of numbers within a ring as names of
asteroids; here the numbers are in ( ).

Corrections to the text have been marked with **. They are listed
below, and were usually confirmed by reference to English printings
of the text. Inconsistencies, especially with respect to accents and
formatting, are numerous and have in general not been adjusted, though
Greek quotations have been checked against other versions where
available. Nor have Whewell's unbalanced quotation marks been
modernised. The English versions have been used to restore Whewell's
"gesperrt" emphases in some Greek passages.

Location               1875 Text                        Correction
Vol. 1
p. 25                Cruikshanks                      Cruickshank
p. 30                         19                               65
p. 30                          :                                ;
p. 33 (thrice)               184                              182
p. 36                        184                              182
p. 71               Arisotelians                    Aristotelians
p. 75                                                           "
p. 79                 σερματικοὶ                      σπερματικοὶ
p. 101                         "
note 1\2                       6                                7
p. 175                ecliptical                       elliptical
note 1\4                     iv.                              vi.
note 75\4                  Summæ                            Summa
note 10\5                   iii.                              iv.
p. 271 (twice)           Mastlin                          Mæstlin
p. 282                  _Dialogo                        "_Dialogo
p. 284                     semil                            semel
p. 287                  endeaver                         endeavor
note 7\6                      1.                               i.
note 8\6         Dial. i. p. 40.                          p. 141.
note 9\6          _Speculutionum                   _Speculationum
p. 325                  Gualtier                          Gualter
p. 341 and 342          Marsenne                         Mersenne
p. 374                                                         of
p. 377          prependicularity                 perpendicularity
p. 403                                                          "
note 30\7            Cosmotheros                     Cosmotheoros
p. 415                  _casual_                         _causal_
p. 416                                                          )
p. 419                                                          ]
p. 431                       _a_                                a
note 69\7                   1453                             1753
note 84\7                   Ast.                             Ass.
p. 463              Philosphical                    Philosophical
p. 471                                                          ]
p. 564                prevalance                       prevalence
Vol. 2
p. 50                    Ὑφιφάνη                          Ὑψιφάνη
                         ἄρισπον                          ἄριστον
                          οὔδιον                           εὔδιον
p. 84                                                           ]
p. 85                      viii.                             vii.
p. 115                      1853                             1823
p. 149                         ,                                .
p. 162                            Footnote number missing in text
p. 201                    stream                            steam
p. 213 and note 39\11 same number as the preceding note
p. 240               Cruikshanks                      Cruickshank
note 18\13     Mass-bestimmengen                Mass-bestimmungen
p. 264                        in                               is
note 11\14                _Stahl                            Stahl
p. 295                       the                             _the
note 78\14  the entire text of this note is missing
p. 301                   lecture                         lectures
note 87\14                   96.                             963.
note 92\14                   153                              853
p. 330                    Angels                           Angles
p. 336                     given                           giving
p. 343                                                          "
p. 394                    Surien                           Surian
p. 411       _Couérs Elmentaire_              _Cours Elémentaire_
note 136\16                Εἴδην                             Εἴδη
p. 450                dependance                       dependence
p. 457            sucking-beasts                  suckling-beasts
note 80\17                ählich                          ähnlich
note 89\17                   229                              129
p. 477                   osseuze                          osseuse
note 119\17                  229                              299*
p. 508            Lythophylaccii                    Lythophylacii
p. 511                   Stukely                         Stukeley
note 18\18          Géognastique                     Géognostique
p. 513               Sabapennine                     Sub-Apennine
p. 514                Schlotheim                      Schlottheim
p. 530                       , (                              ,)
p. 556                  Poissons                        Poisson's
p. 620                       iv.                             vii.
p. 624                         [                                (
p. 628                        in (not italicised in text)
p. 630            Nordenskiold's                   Nordenskiöld's
p. 638                       390                              474
p. 640                      then                             than
p. 641                      1828                           (1828)

* This is the page number given in the English edition. In the only
version of the text referred to that I have found, the quotation is
in a footnote on page 352 of the second edition (1805); the note
was not in the first edition.







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