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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 1.

NEW YORK:
D. APPLETON AND COMPANY,

649 & 551 BROADWAY.
1875.

TO SIR JOHN FREDERICK WILLIAM HERSCHEL,

K. G.H.

Mr DEAR HERSCHEL,

IT is with no common pleasure that I take up my pen to ded-
icate 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 Dis-
course on a kindred subject. For -I couJd not have read it without
rinding 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 be-
lieve.

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 de-
served fame which plays round your head ; but still more, to recollect.

6 DEDICATION.

as one of them said, that your head is far from being the best part
about you.

May your sojouru in the southern hemisphere be as happy and suc-
cessful 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 nebulae 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 iu
the Southern Hemisphere," I cannot refrain from congratulating you
upon having had your life ennobled by the conception and happy exe-
cution 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.

PREFACE

TO THE THIRD EDITION

TN the Prefaces to the previous Editions of this work, sev-
' eral 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 ob-
tained. 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 sci-
ence 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 en-
courage me to go through it; and I had a trust, which ]

8 PREFACE.

have as yet seen nothing to disturb, that 1 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 suffi-
ciently 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, com-
monly, 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 con-
cerning 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
haye an important place in the history of Natural Science in

PREFACE.

its most extended sense. Yet it appeared convenient to car
ry on the history of Science, so far as it depends on Observa-
tion, 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 Induc-
tive 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 I have done this without

1 Among these, I may mention as works to which I have peculiar obligations,
Tennemann's Geschichte der Philosophic; Degrando's Histoire Comparee des Sys-
temes de Philosophic ; Montucla's Histoire des Mathomatiques, with Delalande's
continuation of it; Delambre's Astronomic Ancieune, Astronomic du Moyen A.trc,
Astronomic Moderne, and Astronomic du Dix-huitieme Siecle; Bailly's Histoire
d' Astronomic Ancienne, and Ilistoire d' Astronomic Moderne; Voiron's Hi^ci"*

10 PREFACE.

scruple, since the novelty of my work was intended to con-
sist, not in its superiority as a collection of facts, but in the
point of view in which the facts were placed. I have, how-
ever, 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 au-
thors. According to the plan which I have pursued, the his-
tory of each science forms a whole in itself, divided into dis-
tinct 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.

""With all these grounds of hope, it is still impossible not,
to see that such an undertaking is, in no small degree, ardu
ous, 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 per-
forming of a Work; and that they receive this as a certain-
ty that we are not laying the foundations of any sect o; 1
doctrine, but of the profit and dignity of mankind : Fur-

1 O t/

d'Astronomie (published as a continuation of Bailly), Fischer's Geschiohte der
Physik, Gmelin's Geschichte der Chemie, Thomson's History of Chemistry, Spren-
gel'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,
must admirable and instructive.

PREFACE. 11

luermore, 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 be-
yond 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 suc-
cession of generations.' BACON LSTSTAUKATIO MAGNA, Prcef.
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 Jfind, the
other, the Interpretation of Naturt? LSTST. MAG. Pnef. ad
Part. ii.

CONTENTS

OF THE FIRST VOLUME.

*

PIG*
[KTR3DUCTION. . 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. Kesult of the Greek School Philosophy 80

Sect. 2. Cause of the Failure of the Greek Physical Philosophy 83

CONTENTS.

BOOK II.

i

HISTORY OF THE PHYSICAL SCIENCES IN ANCIENT

GREECE.

PAGI
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 Ill

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 12

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.. 13S

CONTENTS. 15
CHAPTER III. INDUCTIVE EPOCH OF HIPPARCHUS.

PAGE

Sect. 1. Establishment of the Theory of Epicyles and Eccentrics 14e

Sea. 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 1G1

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 IY.

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 CONTENTS.

PAGE

4. Greek Commentators of Plato and Others 207

6. 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 Y.

HISTORY OF FORMAL ASTRONOMY AFTER THE
STATIONARY PERIOD.

Introduction 255

CHAPTER I. PRELUDE TO THE INDUCTIVE EPOCH OF CO-
PERNICUS 257

CHAPTER II. INDUCTION OF COPERNICUS. THE HELIOCEN-
TRIC THEORY ASSERTED ON FORMAL GROUNDS . , 262

CONTENTS. 17

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

PAGE

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 Astro-
nomical Discoveries 276

Sect. 4. The Copernican System opposed on Theological Grounds 28G

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 30o

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 31fL

Sect. 2. Revival of the Scientific Idea of Pressure. Stevinus. Equilib-
rium of Oblique Forces 316

Sect. 3. Prelude to the Science of Dynamics. Attempts at the First Law

of Motion 310

VOT. L 2

18 CONTENTS.

CHAPTER II. INDUCTIVE EPOCH OF GALILEO. DISCOVERY

OF THE LAWS OF MOTION IN SlMPLE CASES.

PACK

Sect. I . Establishment of the First Law of Motion 822

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 Mo-
tions 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. PE-
RIOD OF VERIFICATION AND DEDUCTION 340

CHAPTER IV. DISCOVERY OF THE MECHANICAL PRINCIPLES

OF FLUIDS:

Sect. 1. Eediscovery 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 Oscilla-
tion. Huyghens 350

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

1. Geometrical Mechanics. Newton, &c 363

2. Analytical Mechanics. Euler 3G3

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. Mecanique Celeste, &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

CONTENTS. 19

BOOK VII.
HISTORY OF PHYSICAL ASTRONOMY.

T PAGE

CHAPTER I. PRELUDE TO THE INDUCTIVE EPOCH OF NEW-
TON 385

CHAPTER II. THE INDUCTIVE EPOCH OF NEWTON. DIS-
COVERT 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 Newtonjan 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 At-
traction 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. Rouier 463

20 CONTENTS.

PAGE

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 482

BOOK I. THE GKEEK 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 GKEECE.

Plato's Timajus and Republic 497

Hero of Alexandria. . 501

BOOK III. THE GKEEK ASTEONOMY.

Introduction 503

EARLIEST STAGES OF ASTRONOMY.

The Globular Form of the Earth 505

The Heliocentric System among the Ancients 506

The Eclipse of Thales 509

CONTEXTS. 21

BOOK IY. PHYSICAL SCIENCE IN THE MIDDLE AGES.

PAGB

General Eemarks 511

PROGRESS IN THE MIDDLE AGES.

Thomas Aquinas 512

Roger Bacon 512

BOOK Y. FORMAL ASTRONOMY,

PRELUDE TO COPERNICUS.

Nicolas of Cus 523

THE COPERNICAN THEORY.

The Moon's Rotation 524

M. Foucalt's Experiments ". 525

SEQUEL TO COPERNICUS.

English Copernicaus 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 YI. MECHANICS.

PRINCIPLES AND PROBLEMS.

Significance of Analytical Mechanics 536

Strength of Materials 538

Roofs Arches Vaults . 541

BOOK YII. PHYSICAL ASTEOXOMY.

PRELUDE TO NEWTON.

The Ancients 544

Jeremiah Horrox 545

Newton's Discovery of Gravitation 546

22 CONTENTS.

THE PRINCIPIA.

PiGE

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 . 665

INDEX OF PROPER NAMES.

The letters a, I, indicate vol. i., vol. 11., respectively.

Abdollatif, b. 443.

Aboazen, a. 222.

Aboul Wefa, a. 180.

Achard, 6. 174.

Achillini, b. 445.

Adain Marsh, a. 198.

Adanson, b. 404, 405.

Adelbold, a. 198.

Adelhard Goth, a. 198.

Adet, b. 279.

Achilles Tatius, a. 127.

^Epinus, 6. 197, 203, 209.

Agassiz, b. 429, 521, 540.

Agatharchus, b. 53.

Airy, a. 372, 442, 477 ; b. G7, 120.

Albategnius, a. 177, 178.

Albertus Magnus, a. 229, 237 ; b. 367.

Albumasar, a. 222.

Alexander Aphrodisiensis, a. 200.

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

AlphonsoX., a. 151, 178.

Amauri, a. 236.

Aminonius Saccas, a. 206, 212.

Ampere, b. 183, 243, 244, 246, 284.

Anaxagoras, a. 78 ; b. 53.

Anaximander, a. 130, 132, 135.

Anaximenes, a. 56.

Anderson, a. 342.

Anna Corunena, a. 207.

Anselm, a. 229.

Arago, 6. 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, 8"'-,

412, 417, 420, 438, 444, 455, 583
Arnold de Villa Nova, a. 228.
Arriaga, a. 335.
Artedi, b. 423.
Artephius, a. 226.
Aryabatta, a. 260.
Arzachel, a. 178.
Asclepiades, 6. 439.
Asclepigenia, a. 215.'
Aselli, 6. 453.
Avecibron, a. 232.
Averroes, a. 194, 210.
Avicenna, a. 209.
Avienus, a. 169.
Aubriet, b. 387.
Audouin, 6. 483.
Augustine, a. 197, 220, 232.
Autolycus, a. 130, 131.
Auzout, a. 474.

Babbage, Mr. b. 254, 555.

Bachman, b. 386.

Bacon, Francis, a. 273, 383, 412; b.

25, 32, 165.
Bacon, Eoger, b. 55.
Bailly, a. 199, 445.
Baliani, a. 326, 347.
Banister, b. 380.
Barlow, b. 67, 223, 245, 254.

INDEX OF PROPER NAMES.

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.
Belon, 6. 421, 476.
Benedetti, a. 314, 321, 324, 33C.
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 ; 6. 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.
Blonde], a. 342.
Bock, b. 371.
Boethius, 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.
Boue, Ami, b. 523.
Bouguer, a. 377.
Bouillet, b. 166.

Bourdon, 6. 461.

Bournon, 6. 326.

Bouvard, a. 443.

Boyle, a. 895 ; 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 ; 6. 31.
Brooke, Mr., b. 325.
Brougham, Lord, b. 80, 112.
Brown, Robert, b. 409, 474.
Brimfels, b. 368.
Bruno, Giordano, a. 272.
Buat, a. 350.
Buch, Leopold von, b. 523, 527, 539,

557.

Buckland, Dr., b. 534.
BudsEtis, a. 74.
Buffon, J. 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, 6. 489.
Cajsalpinus, 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, 6. 476.
Canton, b. 197, 198, 219.
Capelli, a. 435.
Cappeller, b. 318.

INDEX OF PROPER NAMES.

25

Cardan, a. 313, 319, 330, 335.

Carlini, a. 456.

Came, b. 538.

Caroline, Queen, a. 422.

Carpa, b. 445.

Casrasus, a. 326.

Cassini, Dominic, a. 454, 462, 479 ;

6. 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. 861.
Cbaussier, b. 463.
Cbladni, b. 40, 41 .
Christie, b. 254.
Christina, a. 390.
Chrompre, b. 304.
Cicero, a. 119.
Cigna, a. 376 ; 6. 202.
Clairaut, a. 367, 377, 410, 437, 451,

454; b. 67.
Clarke, a. 361, 424.
Cleomedes, a. 161, 167.
Clusius, 6. 378.
Cobo, 6. 379.

Colombo, Ludovico delle, a. 346.
Columbus, Realdus, b. 446, 450.
Columna, Fabius, b. 381.
Commandinus, a. 316.
Comparetti, i. 79.
Condamine, a. 453.
Constantine of Africa, b. 367.
Conti, Abbe" de, a. 360.
Conybeare, 6. 519, 525.
Copernicus, a. 257.
Cosmas Indicopleustes, a. 196.
Cotes, a. 366, 425.
Coulomb, 6. 204, 207, 209, 221.
Crabtree, a. 276, 302, 304.
Cramer, b. 35.
Cronstedt, b. 341 .
Cruikshanks, 6. 240.
Gumming, Prof., b. 252.

, b. 196.

Cuvier, b. 421, 422, 466, 478, 481, 487,
492, 516, 517, 520, 522.

D'Alembert, a. 361, 365, 367, 372, 374,

375, 378, 445; 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, ,1. 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.
DeLuc, 5. 167, 177.
De'meste, b. 319.
Democritus, a. 78 ; b. SCO.
Derham, b. 165.
Desaguliers, b. 193.
Descartes, a. 323, 328, 338, 343, i54,

387, 423 ; 6. 56, 59, 220.
Des Hayes, b. 519.
Desmarest, b. 512, 515.
Dexippus, a. 208.
Digges, a. 331.
Dillenius, b. 402.
Diogenes Laertius, a. 187.
Dioscorides, Z>. 364, 367.
Dolloncl, a. 475; b. 67.
Dominis. Antonio de, b. 59
Dubois, 6. 445.
Dufay, b. 194, &c., 201.
Du Four, b. 79.
Dufrenoy, b. 527, 532.
Dulong, 6. 150, 187.
Duns Scotus, a. 233, 237.
Dunthorne, a. 435.
Dupuis, . 125.
Durret, a. 288.

26

INDEX OF PROPER NAMES.

Dutens, a. 82.
Duvernay, b. 475.

Ebn lounis, 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.
Eustacliius, b. 445, 453.
Eustratus, a. 207.

Fabricius, a. 207.

Fabricius of Acquapendente, b. 456.

Fabricius, David, a. 300.

Fallopius, b. 445.

Faraday, Dr., 6. 245, 254, 291, 292,

296, 302.

Fennat, a. 341, 353.
Fitton, Dr., b. 524.
Flacourt, b. 379.
Flamsteed, a. 304, 409, 410, 419, 427,

435.

Fleischer, 6. 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 ; 5. 68, 98, 128.
Frederic II., Emperor, a. 236.
Fresnel, b. 72, 92, 96, 102, 114, 115, 179.
Fries, b. 418.
Frontinus, a. 250.
Fuchs, 6.334, 369.
Fuchsel, b. 513.

Grertner, b. 404.

Galen, b. 440, 443, 444, 445, 462, 404
Galileo, a. 276, 319, 322, 324, &c., 336,

342, 345.
Gall, b. 463, 465.
Galvani, b. 238, 240.
Garnbart, a. 451.
Gascoigne, a. 470.

Gassendi, a. 288, 341, 390, 392 ; b. 33.
Gauss, a. 372, 448.

Gay-Lussac, 6. 158, 169, 179, 283, 290.
Geber, a. 178, 224.
Gellibrand, b. 219.
Geminus, a. 118, 143, 166.
Generelli, Cirillo, b. 587.
Geoffrey (botanist), b. 459.
Geoffroy (chemist), b. 265.
Geoffrey Saint-Hilaire, b. 477, 480, 483.
George Pachymerus, a. 207.
Gerbert, a. 198.
Germain, Mile. Sophie, b. 43.
Germanicus, a. 168.
Gessner, 6. 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, 6. 398.
Glisson, b. 466.
Grnelin, b. 348.
Godefroy of St. Victor, a. 231
Goldfuss, 6. 519.
Goppert, b. 578.
Gothe, b. 63, 469, 473.
Gough, b. 171.
Graham, a. 471 ; b. 219.
Grammatici, 6. 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, 6. 457, 475.
Grey, b. 194.
Grignon, b. 319.
Grimaldi. . 341 ; b. 60, 79.

INDEX OF PKOPEK NAMES.

27

Grotthuss, 6. 304.

Guericke, Otto, b. 33, 193.

Guettard, b. 510.

Gulielmini, b. 317.

Guy ton de Morveau, b. 278, 281.

Hacliette, a. 350.

Hadley, a. 474.

Haidinger, b. 330.

Halicon, a. 150.

Haller, b. 401, 460.

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, 6. 446, 449, 456.
Hausmann, b. 329.
Haiiy, b. 320, &c., 325, 342.
Hawkesbee, b. 193, 195.
Hegel, a. 415.
Helmont, 6. 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 Barbaras, a. 75.
Hernandez, 6. 379.
Herodotus, a. 57 ; 6. 361, 506.
Herophilus, b. 441.
Herrenschneider, b. 145.
Herschel, Sir John, a. 467 ; 6. 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.
. . 107.

Hippocrates, 6. 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, 6. 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.

lamblichus, 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.

Kjempfer, b. 379.

Kant, b. 490.

Kazwiri, b. 583.

Keckerman, a. 235.

Keill, a. 367, 426 ; b. 264.

Kelland Mr. Philio b. 127 130.

28

INDEX OF PROPER NAMES.

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.
Konig, b. 519.
Krafft, b. 142, 225.
Eratzenstein, b. 166.
Kriege, b. 380.

Lacaille, a. 442, 454.

Lactantius, a. 195.

Lagrange, a. 367, 369, 375, 381, 444;

b. 35, 37, 39.
Lame", b. 129.
La Hire, a. 439, 463.
Lalande, a. 440, 447.
Lamarck, 6. 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.
Laimoy, a. 236.
Laurencet, 6. 484.
Lawrence, b. 565.
Lecchi, a. 350.
Leeuwenhoek, 5. 457, 460.
Legendre, b. 223.
L'H6pital, 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.
Leticippus, a. 78, 84.
Lexell, a. 447, 452.
Lhwyd, b. 508.

Libri, b. 151.

Lindenau, a. 440.

Lindley, b. 474, 519.

Linnaeus, 6. 318, 388, 423.

Linus, b. 61.

Lister, b. 609, 511.

Littrow, a. 477.

Lloyd, Professor, b. 125, 130.

Lobel, b. 381, 408.

Locke, a, 422.

Longomontanus, 1 a. 297, 302.

Louville, a. 431, 439.

Lubbock, a. 372, 373, 459.

Lucan, a. 190.

Lucas, 5. 62.

Lyell, b. 500, 529, 545, 560, 562. 590

Macleay, b. 418.

Magini, a. 270.

Mairan, a. 361.

Malpighi, 6. 456.

Mains, b. 71, 74.

Manilius, a. 168.

Maraldi, a. 439 ; b. 79.

Marcet, b. 187.

Margrave, 6. 422.

Marinus (anatomist), b. 462.

Marinus (Neoplatonist), a. 215.

Mar riot te, a. 343.

Marsilius Ficinus, a. 238.

Martianus Capella, a. 259.

Martyn, T., b. 402.

Mcestlin, a. 271, 287.

Matthioli, b. 381.

Maupertuis, a. 367, 431, 453.

Mayer, Tobias, a. 165 ; b. 146, 206, 221.

Mayo, Herbert, b. 464.

Mayow, 6. 277.

Mazeas, b. 80, 199.

MacCullagh, Professor, b. 123, 130.

Meckel, b. 486.

Mtlloni, 6. 154.

Menelaus, a. 167.

Mersenne, a. 328, 342, 347, 390 ; 6. 28.

Messa, b. 445.

Meton, a. 121.

Meyranx, b. 484.

Michael Scot, a. 226.

Michell, b. 511.

INDEX OF PROPER NAMES.

29

Michelotti, a. 350.

Miller, Professor, b. 331.

Hilton, a. 200, 275, 340.

Witscherlich, b. 33-4.

Mohs, 6. 326, 329, 345, &c., 349, 351.

Mondino, b. 445.

Mouge, b. 274.

Monnet, b. 510.

Monnier, b. 197.

Monteiro, b. 331.

Montfaucon, a. 19G.

Morin, a. 288.

Morison, b. 383.

Moro, Lazzaro, 6. 587.

Morveau, Guyton de, b. 278, 281.

Mosotti, b. 211.

Munro, 6. 476.

Murchison, Sir Eoderic, b. 530.

Muschenbroek, b. 166.

Napier, a. 276, 306.

Naudams, a. 226.

Nauinann, 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 Bleminydes, a. 207.

Nicholas de Cusa, a. 261.

Nicomachus, a. 104.

Nigidius Figulus, a. 219.

Nobili, b. 154.

Nollet, 5. 196.

Nordenskiold, b. 350.

Norman, b. 218.

Norton, a. 331.

Numa, a. 118, 261.

Odoardi, b. 513, 515.
Oersted, Professor, b. 243.
(Eyenhausen, 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 vonOhain, b. 341.

Packe, 6. 509.

Pallas, b. 476, 513.

Papin, b. 173.

Pappus, a. 188.

Paracelsus, a. 226 ; 6. 262.

Pardies, b. 61.

Pascal, a. 346.

Paulus III., Pope, a. 267.

Pecquet, 5. 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, o. 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.
Plumier, 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, fi. 458.
Pontecoulant, a. 372.
Pope, a. 427.
Porphyry, a. 205, 207.
Posidonius, a. 169.
Potter, Mr. Kichard, b. 126, 130.
Powell, Prof., b. 128, 130, 154.
Prevost, Pierre, b. 143.
Prevost, Constant, b. 589.
Prichard, Dr., b. 500, 5G5.

30

INDEX OF PROPER NAMES.

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. ; 6. 26

Ptolemy Euergetes, a. 155.

Purbach, a. 299.

Pythagoras, a. 19, 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, 6. 384, 422.

Raymund Lully, a. 226.

Reaumur, b. 509.

Recchi, b. 379.

Redi, 6. 475.

Reichenbach, a. 472.

Reinhold, a. 269.

Rennie, Mr. George, a. 350.

Rheede, b. 379.

Rheticus, a. 266, 269.

Riccioli, a. 288, 341.

Richman, 5. 142, 199.

Richter, b. 286.

Riffault, b. 304.

Riolan, b. 448.

Rivinus, b. 386.

Rivius, a. 250, 326.

Robert Grostete, a. 198, 22G.

Robert of Lorraine, a. 198.

Robert Marsh, a. 199.

Roberval, b. 33.

Robins, a. 342.

Robinson, Dr., a. 477.

Robison, b. 169, 173, 206.

Roger Bacon, a. 199, 226, 244.

Rohault, a. 391, 423.

Rome de Lisle, b. 318, 319, 320, 324,

328.

Romer, a. 464, 480; b. 33.
Rondelet, b. 421.
Eoscoe, 6. 409.

Ross, Sir John, b. 219.
Rothman, a. 264.
Rouelle, 6. 512, 515.
Rousseau, b. 401.
Rudberg, b. 127.
Ruellius, 6. 368.
Rufus, b. 441.
Rumphe, b. 379.

Saluces, a. 376.

Salusbury, a. 276.

Salviani, 6. 421.

Santbach, a. 325.

Santorini, b. 462.

Saron, a. 446.

Savart, b. 40, 44, 245.

Savile, a. 205.

Saussure, 6. 177, 513.

Sauveur, b. 30, 37.

Scheele, 6. 271.

Schelling, 6. 63.

Schlottheim, b. 514, 519.

Schmidt, b. 557.

Schomberg, Cardinal, a. 267.

Schweigger, b. 251.

Schwerd, b. 125.

Scilla, b. 508.

Scot, Michael, 5. 367.

Scrope, Mr. Poulett, b. 550.

Sedgwick, Professor, b. 533, 538.

Sedillot, M., a. 179.

Seebeck, Dr., 6. 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, 6. 174.

Sherard, b. 379.

Simon of Genoa, b. 367.

Simplicity a. 204, 206.

Sloane, b. 380.

Smith, Mr. Archibald, b. 130.

Smith, Sir James Edward, b. 403.

Smith, William, 6. 515, 521.

Snell, b. 56, 57.

Socrates, b. 442.

Solomon, a. 227: b. 361.

INDEX OF PROPER NAMES.

31

Sorge, 6. 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. 2?

Steno, b. 317, 507, 512.

Stephauus, b. 445.

Stevinus, a. 317, 336, 345, 357.

Stillingfleet, b. 403.

Stobasus, a. 208.

Stokes, Mr. C., b. 573.

Strabo, a. 203 ; b. 363, 587.

Strachey, b. 511.

Stukeley, 6. 511.

Svanberg, b. 149.

Surian, 6. 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.

Tckong-Kang, a. 135, 162.

Telauge, a. 217.

Tennemann, a. 228.

Thales, a. 56, 57, 63, 130.

Thebit, a. 226.

Thenavd, 6. 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, 3. 237.
Tragus, b. 368.

Trithemius, a. 228.

Troughton, a. 471.

Turner, b. 289.

Tycho Brahe, a. 297, 302 ; 6. 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, 6. 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, 6. 56.

Vitruvius, a. 249, 251 ; b. 25.
Viviani, a. 337, 340.
Voet, a. 390.
Voigt, b. 473.
Volte, 6. 238, 240.
Voltaire, a. 361, 431.
Voltz, 6. 533.
Von Kleist, b. 196.

Wallerius, b. 319.

Wallis, a. 276, 341, 343, 387, 395; 6

37.

Walmesley, a. 440.
Warburton, a. 427.
Ward, Seth, a. 276, 396.
"Wargentin, a. 441.
Watson, 6. 195, 196, 202.
Weber, Ernest and William, b. 43.
| Weiss, Prof., b. 326, 327.
Wells, b. 170, 177, 242.
Wenzel, b. 286.

32

INDEX OF PROPER NAMES.

Werner, b. 818, 337, 341, 514, 520,

521, 523, 584.
Wheatstone, b. 44.
Wheler, 6. 379.
Whewell, a. 459 ; b. 330.
Winston, a. 424.
Wilcke, b. 161, 198, 204.
Wilkins (Bishop), a. 275, 332, 395.
W T illiam of Hirsaugen, a. 198.
Willis, Rev. Robert, a. 246; b. 40,

47.

Willis, Thomas, b. 462, 463, 465.
Willoughby, 6. 422, 423.
Wolf, Caspar Frederick, b. 472.
Wolff, a. 361 ; b. 165.

Wollaston, 6. 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, &.
Ill, 112.

Zabarella, a. 235.
Zach, a. 448.
Ziegler, b. 174.
Zimmerman, b. 557.

INDEX OF TECHNICAL TERMS,

Aberration, a. 464.

Absolute and relative, a. 69.

Accelerating force, a. 326.

Achromatism, b. 66.

Acid, b. 263.

Acoustics, 6. 24.

Acronycal rising and setting, a. 131.

Action and reaction, a. 343.

Acuation, b. 319.

Acumination, b. 319.

Acute harmonics, b. 37.

.Etiology, 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. 184.
Almagest, a. 170.
Almanac, a. 184.
Alphonsine tables, a. 178.
Alternation (of formations), b. 538.
Amphoteric silicides, 6. 352.
Analogy (m 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, &. 238.
Anion, b. 298.
Annus, a. 113.
Anode, 6. 298.
Anomaly, a. 139, 141.
Antarctic circle, a. 131.
Antichthon, a. 82.
Anticlinal line, b. 537.
Antipodes, a. 196.

VOL. 1. 3

Apogee, a. 146.

Apotelesmatic astrology, a. 222.

Apothecfe, b. 366.

Appropriate ideas, a. 87.

Arctic circle, a. 131.

Armed magnets, 6. 220.

Armil, a. 163.

Art and science, a. 239.

Articulata, b. 478.

Artificial magnets, 6. 220.

Ascendant, a. 222.

Astrolabe, a. 164.

Atmology, 6. 137, 163.

Atom, . 78.

Atomic theory, b. 285.

Axes of symmetry (of crystals), b. 327

Axis (of a mountain chain), 6. 537.

Azimuth, a. 184.

Azot, b. 276.

Ballistics, a. 365.
Bases (of salts), b. 264.
Basset (of strata), b. 512.
Beats, 6. 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. 804.
Catasterisms, a. 158.
Categories, a. 206.
Cathion, 6. 298.
Cathode, b. 298.
Cation, b. 298.

Causes, Material, formal, efficient, fi-
nal, a. 73.

INDEX OF TECHXICAL TERMS.

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 His-
tory), 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.

Daemon, a. 214.

D'Alernbert'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, 6. 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, 6. 30.
Dispensatoria, b. 366.
Dispersion (of light), b. 126.
Doctrine of the sphere, a. 130.
Dogmatic school (of medicine), b. 139
Double refraction, 6. 69.

Eccentric, a. 145.

Echineis, a. 190.

Eclipses, a. 135.

Effective forces, a. 359.

Elective attraction, b. 265.

Electrical current, b. 242

Electricity, 6. 192.

Electrics, 6. 194.

Electrical tension, b. 242.

Electro-dynamical, 6. 246.

Electrodes, b. 298.

Electrolytes, b. 298.

Electro-magnetism, 6. 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, 6. 529.

Epicycles, a. 140, 145

Epochs, a. 46.

Equant, a. 175.

Equation of time, a. 159.

Equator, a. 130.

Equinoctial points, a. 131.

Escarpment, 6. 537.

Evection, a. 171, 172.

Exchanges of heat, Theory of, b. 14"

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.

INDEX OF TECHNICAL TERMS.

Formal optics, b. 52.
Fianklinism, b. 202.
Frcsnel's rhomb, b. 10-5.
Fringes of shadows, 6. 79, 125.
Fuga vacui, a. 347.
Full months, a. 122.
Function (in Physiology), b. 435

Galvanism, b. 239.
Galvanometer, b. 251.
Gang] ionic system, b. 403.
Ganglions, b. 463.
Generalization, a. 46.
Geocentric theory, a. 258.
Gnomon, a. 162.
Guornonic, a. 137.
Golden number, a. 123.
Grave harmonics, b. 38.
Gravitate, a. 406.

Habitations (of plants), b. 562.
Htecceity, a. 233.
Hakemite tables, a. 177.
Halogenes, b. 308.
Haloide, b. 352.
Harmonics, Acute, 5. 37.
" Grave, b. 38.

Heat, b. 139.

" Latent, b. 160.
Heccredecaeteris, 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.
Homoioineria, a. 78.
Horizon, a. 131.
Horoscope, a. 222.
Horror of a vacuum, a. 346.
Houses (in Astrology), a. 222.
Hydracids, 5. 283.
Hygrometer, b. 177.
Hygrometry, b. 138.
Hypostatical principles, &. 262.

latro-chemists, b. 263.
Ideas of the Platonists, a. 75.
Ilchanic tables, a. 178.

Impressed forces, a. 359.
Inclined plane, a. 313.
Induction (electric), J. 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, 6. 334.
Isothermal lines, b. 146, 538.
Italic school, a. 56.

Joints (in rocks), b. 537.
Judicial astrology, a. 222.
Julian calendar, a. 118.

Lacteals, 6. 453.

Latent heat, b. 160.

Laws of motion, first, a. 322.

second, a. 330.

third, . 334.
Leap year, a. 118.
Leyden phial, b. 196.
Librations (of planets), a. 297.
Libration of Jupiter's Satellites, a

441.

Linib of an instrument, a. 162.
Longitudinal vibrations, b. 44.
Lunisolar year, a. 120.
Lymphatics, b. 453.

Magnetic elements, b. 222.
equator, b. 219.
Magnetism, 6. 217.
Magneto-electric induction, b. 256.
Matter and form, a. 73.
Mean temperature, b. 146.
Mechanical mixture of gases, b. 172.
Mechanico-chemical sciences, 6. 191.
Meiocene, b. 529.
Meridian line, a. 164.
Metals, 6. 306, 307.
Meteorology, b. 138.
Meteors, a. 86.
Methodic school (of medicine), b. 439

36

INDEX OF TECHNICAL TERMS.

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. 4G9, 474.
Movable polarization. I. 105.
Multiple proportions (in Cheuv.stry),

b. 285. .

Music of the spheres, a. 82.
Mysticism, a. 209, 211.

Nadir, a. 184.

Nebular hypothesis, b. 501.

Neoplatonists, a. 207.

Neutral axes, b. 81.

Neutralization (in Chemistry), b. 2C3.

Newton's rings, b. 77, 124.

scale of color, b. 77.
Nitrous air, b. 273.
Nomenclature, 6. 389.
Nominalists, a. 238.
Non-electrics, b. 194.
Numbers of the Pythagoreans, a. 82,

216.

Nutation, a. 4G5.
Nycthemer, a. 159.

Octaeteris, a. 121.
Octants, a. 180.
Oolite, b. 529.
Optics, 6. 51, &c
Organical sciences, 6. 435.
Organic molecules, b. 4GO
Organization, b. 435.
Oscillation, Centre of, a. 35G.
Outcrop (of strata), 6. 512.
Oxide, b. 282.
Oxyd, b. 282.
Oxygen, i. 276.

Palaeontology, b. 519. *
Pulaetiological sciences, b. 499.
Parallactic instrument, a. 1G5.
Parallax, a. 159.

Percussion, Centre of, a. 357.
Perfectihabia, a. 75.
Perigee, o. 14G.
Perijove, a. 44G.
Periodical colors, b. 93.
Phases of the moon, a. 134.
Philolaic tables, a. 304.
Phlogisticated air, b. 273.
Phlogiston, 6. 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, 6. 335.
Plumb line, a. 164.
Pneumatic trough, b. 273.
Poikilite, b. 530.
Polar decompositions, &. 293
Polarization, b. 72, 74.

Circular, b. 82, 119.

Elliptical, b. 122, 124

Movable, Z>. 105.

Plane, b. 120.

of heat, b. 153.
Poles (voltaic), b. 298.

" of maximum cold, 5. 146.
Potential levers, a. 318.
Power and act, a. 74.
Precession of the equinoxes, a. 155.
Predicates, a. 205.
Predicaments, a. 206.
Preludes of epochs, . 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.
Prosthaphcresis, . 146.
Provinces (of plants and animals), b

502.

Prutenic tables, a. 270.
Pulses, b. 33.
Pyrites, b. 352.

Quadrant, a. 1G4
Quadrivium, . 199.
Quiddity, a. 234.

INDEX OF TECHNICAL TERMS.

Quinary division (in Natural History),

b. 418.
Quintessence, a. 73.

Radiata, b. 478.
Radiation, b. 139.
Rays, b. 53.
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. 1G3.
Secular inequalities, a. 370.
Segregation, 6. 558.
Seminal contagion, b. 459.
proportions, a. 79.
Sequels of epochs, a. 47.
Silicides, b. 352.
Silurian rocks, b. 530.
Simples, 6. 367.
Sine, a. 181.
Solar heat, b. 145.
Solstitial points, . 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, i. 457.
Statical electricity, b. 208.
Stationary periods, a. 48.

"planets, a. 139.
Stations (of plants), 6. 562.
Sympathetic sounds, b. 37.
Systematic Botany, b. 357.

Systematic Zoology, b. 412.
Systems of crystallization, . 328.

Tables, Solar, (of Ptolemy), a. 146

" Hakemite, a. 177.

" Toletan, a. 177.

" Ilchanic, a. 178.

" Alphousine, a. 178.

" Prutenic, a. 270.

" Rudolphine, a. 302.

' ' Perpetual (of Lansbcrg), a. 302

" Philolaic, a. 304.

" Carolinian, a. 304.
Tangential vibrations, b. 45.
Tautochronous curves, a. 372.
Technical terms, b. 389.
Temperament, 6. 47.
Temperature, b. 139.
Terminology, b. 389.
Tertiary rocks, 6. 513.
Tetractys, a. 77.
Theory of analogues, 6. 483.
Therrnomultiplier, 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), I
47G

Uniform force, a. 327.

Unity of Composition (in Comparative
Anatomy), b. 483.

Unity of plan (in Comparative Anato-
my), b. 483.

Variation of the moon, a. 179, 303.

38

INDEX OF TECHNICAL TERMS.

Vegetable alkali, b. 204.
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 mo-
tion, a. 319.
Vortices, a. 388.

Week, a. 127.
Year, a. 112.

Zenith, a. 181.
Zodiac, a. 131.
Zones, a. 136.

HISTORY

OF THE

INDUCTIVE SCIENCES.

INTRODUCTION.

'A just story of learning, containing the antiquities and originals ci
KNOWLEDGES, and their sects ; their inventions, their diverse administra-
tions and managings ; their flourishings, their oppositions, decays, depres-
sions, oblivions, removes ; with the causes and occasions of them, and all
other events concerning learning, throughout all ages of the wo'-ld ; I may
truly affirm to he wanting.

" Thu use and end of which work I do not so much design loi 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 leirned men more wise in the rise and administration of learning."

BiOON, Advancement of Learning, book ii.

INTRODUCTION.

IT is my purpose to write the History of some of the most im-
portant of the Physical Sciences, from the earliest to the most
recent periods/ I shall thus have to trace some of the most remark-
able 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 com-
pose such sciences as the Mechanics, Astronomy, and Chemistry, of
.modern times.

The completeness of historical view which belongs to such a de-
sio-n, consists, not in accumulating all the details of the cultivation of

C 1 * * O

each science, but in marking the larger features of its formation. The
historian must endeavor to point out how each of the important ad-
vances 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 ao-oreocate now constitutes a costly treasure.

oO ~ *

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 com-
manding 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 HISTORY OF INDUCTIVE SCIENCES.

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 wilder-
ness 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 Histor"
of Inductive Science should point out to us a philosophical distribu-
tion 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 execu-
tion, 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

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 syste-
matic 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 prop-
erly be selected from the general mass and termed SCIENCE. It will
be sufficient at present to say, that the sciences of which we have

1 The Philosophy of the Inductive Sciences was published shortly after the present
work.

INTRODUCTION. 43

i

nere 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. 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 op-
erations 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 de-
mands 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 knowl-
edge ; 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 con-
sequence 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 Avere
bound together under the form of laws and principles. And even at

For the Antithesis of Facts and Ideas, see the Philosophy, book i. ch. 1, 2, 4, 5.

44 HISTORY OF INDUCTIVE SCIENCES.

i

tins day, the tribes of uncivilized and half-civilized mau, over the
whole face of the earth, have before their eyes a vast body o'f 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 knowl-
edge for the last three hundred years abundantly teaches us.

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 prov-
inces 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,
\ 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 occa-
sion to remind the reader of this reflection.

Successive Steps in Science. But there is another remark which
we must also make. Such sciences as we have here to do with are

'Concerning Sufcfssivc Generalisations in Science, see the ffiilo&..p7ty, book i. ch
2, sect. 11.

INTRODUCTION. 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 contradic-
tory. 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

Nee manet nt fuer.it nee formas servat easdem,
Sed tamen ipsa eadein est.

All changes, naught is lost ; the forms are change:!,
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.

Tims 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 develop-
ment 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.

O

Terms record Discoveries* 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
Borne 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

Concerning Technical Twins, see rhiljsonly, book i. ch. S.

46 HISTORY OF INDUCTIVE SCIENCES.

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 re-
corded by the change of the current coin which has accompanied them.

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 Avider 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 influ-
enced the fortunes of physical philosophy, and to which we may con-
sider the rest as subordinate and auxiliary. These primary movements,
when the Inductive process, by which science is formed, has been exer-
cised 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 beeu obscurely and

INTRODUCTION. 47

doubtfully discerned. And again, when this step lias 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 suc-
cessfully 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? Since the advance of science consists in collect-
ing by induction true general laws from particular facts, and in com-
bining several such laws into one higher generalization, in which they
still retain their truth ; we might form a Chart, or Table, of the prog-
ress 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 neces-
sarily exhibit all the principal doctrines of the science ; for each genera]
truth contains the particular truths from which it was derived, and
may be followed backwards till we have these before us in their sepa-
rate state. And the last and most advanced generalization would
have, in such a scheme, its proper place and the evidence of its valid-
ity. 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 substan-
tial contents of the science in question. By forming, therefore, such
Inductive Tables of the principal sciences of which 1 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 his-

5 Inductive charts of the History of Astronomy and of Optics, sucn ns are here
-eferrcd to, are given in the Philosophy, book xi. ch. 6.

4:8 HISTORY OF INDUCTIVE SCIENCES.

tory 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.

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, iu 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 enter-
prises 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 dis-
tinct 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
the^r 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 -When the

Scientific Ideas depend upon certain Fundamental Ideas, which are cnmnerated
in the PJiilosophy, book i. ch. 8.

INTRODUCTION. 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 intel-
lectual operations have much that is common and much that is dif-
ferent. 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 iu 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 lim-
ited, and always identically the same; the latter have grown up in the
mind from a thousand dim and diverse suggestions, and the obscurity
a<d 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.

Such common Notions are sufficient for the common practical con
duct 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 specula-
tive 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 ; how-
ever much we urge and agitate them, they only revolve in stationan
VOL. I. 4

50 HISTORY OF INDUCTIVE SCIENCES.

whirlpools. But the mind is capable of acquiring scientific Ideas,
which are better fitted to undergo discussion and impulsion. When
our speculations arc 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 correspond-
ence 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 ob-
jects, but speculations previously delivered ; the object is not to inter-
pret 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 Philos-
ophy ; whether their agreement in such a mode of seeking knowl-
edge 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
Srst waking of science, and that of its midday slumber.

What has been said thus briefly and imperfectly, would require great
ietail and much explanation, to give it its full significance and author-
ity. 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

INTRODUCTION. 51

;he 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 tthat has hitherto been said, is in-
tended as a slight outline of the Geography of that Intellectual World,
of which we have here to study the History.

The name v^hich 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 His-
tory ; 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, thii Philos-
ophy 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.

BOOK 1

HISTORY

OF THE

GREEK SCHOOL PHILOSOPHY,

WITH HEFEREXCE TO

PHYSICAL SCIENCE,

Ti's yap ap\a ii^aro vatmXias ;
T<j til Ktv&vvos Kpa.TC.fatf d<57
TOJ Otjntv a\ois

'Eirti 6' if.

Kptfuaaav dyitvpaf \mcpQtv
Xpvaiav %tipta<!l Xa/3(iv <ftid\av

v Trpiijtvq vuTip Oupai't&dv
oavvov Zrjia, icai iiKvntipovs
piiras, avifiuv r' f/ca/\i,
Nuvraj T, Kai Tr6vTou KAci)0otff,
T' cv<f>f)ora, Kai
/jolpav.
PINDAR. Pyth. iv. 124, 349.

V? hence came their voyage ? them what peril held
With adamantine rivets nrmlj r 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.

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 prin-
ciples. 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 rfoipo;. Cut
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' to have been first assumed by Pythagoras. Yet he, in Herod-
otus, instead of having this title, is called a powerful sophist 'EXXyjviJv
oj -TW d.<fdve<f<ra.ru tfoyHfry IIudayop?j ; 2 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

1 Cic. Tusc. v. C. = Herod, iv. 95.

56 THE GKEEK SCHOOL PHILOSOPHY.

placed Pythagoras at the origin of the Italic School, .one of the t\vc
main lines of succession of the early Greek philosophers : but the
other, the Ionic School, whioh 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
xophi, or " wise men of Greece."

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 jiniverse ; and to
these were soon added all the great questions -which our moral condi-
tion 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 in-
quiries. 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 ori-
gin of all things, according to Anaxirnenes, air ; and Heraclitus con-
sidered fire as the essential principle of the universe. It has been con-
jectured, 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

PRELUDE. 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 (apx^) 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. 1
But such precarious analyses of these obscure and loose dogmas of early
antiquity are of small 'consequence to our object.

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 remark-
able 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, 4 " 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 satisfac-
tory 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."

"VVe 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
t'elt rio want of a theory. Not so the Greeks ; they had their reasons
to render, though they were not such as satisfied Herodotus. " Some

Metaph. i. 3. Herod, ii. 19.

58 THE GREEK SCHOOL PHILOSOPHY.

of the Greeks," he says, " who wish to be considered great philos
ophers ('EXXrjvwv TIVSJ E-tfitf^oi /SouXo^svoi ysvsV^ai tfoipi'/jv), have pro-
pounded 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 f 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 oppo-
site 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 (dvStfio'TTjfxovso'rc'p^),
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 ot
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, never-
theless, 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 pro-
ceed from snow ?" He then offers several other reasons " to show," as
he says, " to any one capable of reasoning on such subjects (UvSpi
ye Xrjyi^stfQai TOIOUTWV ififi oi'ou TS t'ovTi), that the assertion cannot be
true. The winds which blow from the southern regions are hot ; the
inhabitants are black; the swallows and kites (iWJvoi) 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 upor

PRELUDE. 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 ; /or, 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."

' O

I need aot 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 pro-
poses, 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. " lu winter the sun is carried by the seasons away
from his former course, and goes to the upper parts of Libya. And
therein 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 pro-
ceeds, " 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 (fXxs.i sir' swurov TO Uwp), 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 in-
creased by showers and rain torrents so that they are in flood till the
summer comes ; and then, the rain failing 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
vay, I have been led to think the sun is the cause of the occurrence
in question.'' 1 AVe mny remark that the historian here appears to

60 THE GREEK SCHOOL PHILOSOPHY.

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 specula-
tions, 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 evi-
dence. 5 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 phe-
nomena of the same kind. We may be well excused, therefore, for
believing that they could not impart to the Greeks what they them-
selves did not possess ; and so far as our survey goes, physical philos-
ophy has its origin, apparently spontaneous and independent, in the
active and acute intellect of Greece.

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 neces-
sary 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 immedi-

* Thirlwall, Hist. <?/., ii. 130 ; and, as there quoted, Ritter, Gescliichte der Philos-
ip/iie, i. 159-173.

PEELUDE. 61

ately lead man to profound physical knowledge, answered some nobler
and better purpose in bis constitution and government. The fact un-
doubtedly 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, ob-
viously 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, un-
meaning ; such as motion and velocity, force and pressure, impetus
and momentum (po#r,). And the next step in philosophizing, neces-
sarily 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 apd 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 Attrac-
tion, as shown in such cases, is a tendency to lessen all expanded and

62 THE GREEK SCHOOL PHILOSOPHY.

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 sum-
mer, and therefore could not be the cause of its overflow. He would
thus have corrected his first loose conjecture by a real study of na-
ture, 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 beer,
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 look-
ing abroad into the world of sense. They took for granted that phi-
losophy must result from the relations of those notions which are in-
volved 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 accord-
ing 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. 5

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.

6 The course by which the Sciences were formed, and which is here referred to
is that which the Greeks did not follow, is described in detail in the Philosophy,
oook xi., Of the Ccr.struction of Science.

ITS FOUNDATION. 63

CHAPTER II.
THE GREEK SCHOOL PHILOSOPHY.

Sect. I. The general Foundation of the Greek School Philosophy.

physical philosophy of the Greek Schools was formed by look-
-*- in at the material world through the medium of that common

^ o

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 classi-
fying and analyzing the conceptions which it involves, could not over-
come 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 lan-
guage 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. 1 When he was asked, "What is the c/rcatesl
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 in-
quiries is, that we, say thus or thus in common language. Thus, w r hen
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 enumer-
ates many of these ; 2 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 in-
cluded 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 conclu-
sion, 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

1 Pint. Cnv. Sfpt. Sap. Dioj. Laert. i. 35. * Pliy?L\ Ausc. iv. 3.

04 THE GREEK SCHOOL PHILOSOPHY.

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.

Again, 3 in a question concerning mechanical action, he says, ''When
a man moves a stone by pushing it with a st ; .ck, ive say both that the
man moves the stone, and that the stick moves the stone, but the lat-
ter more properly?

Again, we find the Greek philosophers applying themselves to ex-
tract 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 con-
ceptions 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 philos-
ophizing ; for the philosopher whose name it bears, is represented as
arguing with an Athenian named Aristotle, 4 and, by a process ot
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 Timceus, 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 uni-
verse. The philosopher is thus led to maxims which agree with those

3 Physic. Ausc. viii. 5.

This Aristotle is not the Stagirite, who was forty-five years younger than Plato,
out one of the " thirty tyrants," as they were called.

ARISTOTELIAN PHYSICS. 65

of the Aristotelians, that there can be no void, that things seek their
own place, and the like. 5

Another mode of reasoning, very widely applied in these attempts,
was the doctrine of contrarieties, in which it was assumed, that adjec-
tives or substantives which are in common language, or in some ab-
stract mode of conception, opposed to each other, must point at some-
fundamental antithesis in nature, which it is important to study. Thus
Aristotle 6 says, that the Pythagoreans, from the contrasts which
number suggests, collected ten principles, Limited and Unlimited,
Odd and Even, One and Many, Plight 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 opposi-
tions of the same kind.

The physical speculator of the present day will learn without sur-
prise, that such a mode of discussion as this, led to no truths of real or
permanent value. The whole mass of the Greek philosophy, there-
fore, 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, there-
fore, to give some account of these doctrines in their most fully devel-
oped 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 "Meteoro-
logies," though full of physical explanations of natural phenomena,
does not exhibit the doctrines and reasonings of the school in so gen-
eral a form ; the same may be said of the " Mechanical Problems."
The treatises on the various subjects of Natural History, " On Ani-
mals," " On the Parts of Animals," " On Plants," " On Physiognom-
onics," " On Colors," " On Sound," contain an extraordinary accumu-

6 Timoeus, p. 80. ' Metaph. 1. 5.

VOL. I. 5

56 THE GREEK SCHOOL PHILOSOPHY.

lation 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 Alex-
ander 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 net 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 mean-
ing 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

ARISTOTELIAN PHYSICS. C

-

empty, and therefore without a void there could be no motion : and,
on the other hand, there is no void, for the interval between bodies
are filled with air, and air is something. These opinions had even
been supported by reference to experiment. On the one hand, Auax-
agorus 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 : 7 In a void there cov\ld be no difference of tip 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 ob-
servation would be compelled to conform to the usual combinations of
phrases, as these had become associated by the modes of apprehension
previously familiar.

It is not intended here to intimate that the common modes of ap-
prehension, which are the basis of common language, are limited and
casual. They imply, on the contrary, universal and necessary condi-
tions of our perceptions and conceptions ; thus all things are neces-
sarily apprehended as existing in Time and Space, and as connected
by relations of Cause and Effect ; and so far as the Aristotelian phi-
losophy 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, 5 where he proves
that there never was a time in which change and motion did not

O

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

* O O ' O '

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 it
time be eternal, motion must be eternal." But he sometimes intro-

7 Physic. Ausc. iv. 7, p. 215. Ib. viii. 1, p. 253

6S THE GREEK SCHOOL PHILOSOPHY.

duces 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 opin-
ions 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 :" 9 this follows from the relation

O

of causes and effects. Again, " Motion must go on constantly, and,
therefore, must be either continuous or successive. Now what is con-
tinuous 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.

I proceed with Aristotle's argument. 10 " 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 con-
ceived, 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.

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 /?/?/, is much
older than Aristotle, and was probably one of the earliest of philosophi-
cal dogmas. The great master of this philosophy, however, puts the
opinion in a more systematic manner than his predecessors.

' Physio. Ausc. via. G. p. 253. lo lb. viii. 8.

ARISTOTELIAN PHYSICS. 89

"We seek," he says, 11 "the principles of sensible things, that is, ot
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.

"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
thev are combinations of the four first, which therefore he infers to be
the four elementary qualities.

" 12 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."

It may be remarked that this disposition to assume that some com-
mon elementary quality must exist in the cases in which we habitually
apply a common adjective, as it began before the reign of the Aristo-
telian 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 com-
position 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 begin-
nings of that revival ; I mean the doctrines concerning motion.

These are still founded upon the same mode of reasoning from adjec-
tives ; 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

De Gen. et Corrupt, ii. 2. 1S Ib. iii. 3.

TO THE GREEK SCHOOL PHILOSOPHY

this way, they defined what was absolutely (txTXws) heavy and light.
We now know that things which rise by their lightness do so onlv
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 1 bodies.

O

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.'"

The tendencies of bodies downwards and upwards, their weight,
their fall, their floating or sinking, were thus accounted for in a man-
ner which, however unsound, satisfied the greater part of the specula-
tive 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

DC Ccelo. iv. 4.

ARISTOTELIAN PHYSICS. 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' 4

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 calct, ultima friget.
Hot at the first, then barely warm, then cold.

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, 15 " 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 sur-

O

rounding resistances, but to the body itself.

One of the doctrines which was the subject of the wannest discus-
sion between the defenders and opposers of Aristotle, at the revival ol
physical knowledge, was that in which he asserts, 16 " That body is
heavier than another which in an equal bulk moves downward
quicker." The opinion maintained by the Arisotelians at the time ot
Galileo was, that bodies fall quicker exactly in proportion to their
weight. The master himself asserts this in express terms, and reasons
upon it. 17 Yet in another passage he appears to distinguish between
weight and actual motion downwards: 18 " In physics, we call bodies
heavy and light from their power of motion ; but these names are not
applied to their actual operations (eve'pysiai^) except any one thinks

4 Alsted. Encyc. torn. i. p. 637. I5 Phys. Ausc. viii. 10. 10 De Coelo, iv. 1, p. 308
17 Ib. iii. 2. " Ib. iv. 1, p. 807.

72 THE GREEK SCHOOL PHILOSOPHY.

momentum (poir>5) to be a word of botli applications. But heavy an<3
light are, as it were, the embers or sparks of motion, and therefore
proper to be treated of here."

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 l>y any means useless, may easily be so
used as to lead to mere verbal refinements instead of substantial
knowledge.

o

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.' 9 " 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.

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 20 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."

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

Phys. ii. 3. " De Coelo, i. 1,

ITS TECHNICAL FORMS. . d

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,
ancl 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. I/
things which move in a circle move contrary to nature, it is marvel
lous, 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 " quintet 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 lano-uage involves. But though the Grecian

o o ^

philosopher began by studying words in their common meanings, he
soon found himself led to fix upon some special shades or applicatious
of these meanings as the permanent and standard notion, which they
were to express ; that is, he made his language technical. The inven-
tion 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 Philoso}^. 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 \ve can employ, to sug-
gest one of the most comprehensive and fundamental antitheses -with
which philosophy has to do ; the opposition of sense and reason, of

74 THE GREEK SCHOOL PHILOSOPHY.

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 lano-nage, we

*/ O O '

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
(djvaiitg, Jvs'pysict). This distinction is made the basis of most of the
physical philosophy of the school ; being, however, generally intro-
duced 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, im-
possible 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
ivTks-)(}\a. Thus the noted definition of Motion in the third book
of the Physics, 51 is that it is " the Entelechy, or Act, of a movable
body in respect of being movable ;" and the definition of the Soul is 23
(hat 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, ij)se
citrsus actionis, is employed by some ; primus actus is employed by
many, but another school use primus actus of a non-operating form.
Budaeus uses efficacia. Cicero 83 translates it " quasi quandam continu-
atam motioueui, et perennem ;" but this paraphrase, though it may

ys. iii. 1. ^ De Animfl. ii. 1. Tusc. i. 10.

ITS TECHNICAL FORMS. 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 appli
cations of the term. Hermolaus Barbaras 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 com-
mon and familiar substitute for this word : the mocking fiend, how-
ever, suggested only a word equally obscure, and the translator, discon-
tented with this, invented for himself the word pcrfedihabia.

AVe 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 employ-
ment 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 com-
fortable subsistence to many poor philosophers, should now be hunted
down like so many wolves, without a possibility of retreat. He con-
sidered 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. 3 *

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 per-
haps greater celebrity than any of.the terms of Aristotle. I mean the
Ideas of Plato. The account which Aristotle gives of the origin ol
these will serve tt explain their nature. 25 " 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

24 Martinus Scriblcrus, cap. vii.

K Arist. Metaph. i. 6. The same account is repeated, and the subject discussed,
Metnph. xii. 4.

76 THE GREEK SCHOOL PHILOSOPHY.

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 defi-
nition 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."

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, 20
"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 (slS-ft) of which things partake and receive applications
according to that of which they partake : thus those things which par-
take of Likeness are called like ; those things which partake of Great-
ness are called great ; those things which partake of Beauty and Jus-
tice are called beautiful and just" To this Socrates assents. And in
another part of the dialogue he shows that these Ideas are not in-
cluded in our common knowledge, from whence he infers that they are
objects of the Divine mind.

In the Phasdo the same opinion is maintained, and is summed up in
this way, by a reporter of the last conversation of Socrates, 27 sivai ci
ExaoVov TWV EI'OUV, xaj Todruv r'aXXa (jtsraXctfA/Savovra aurwv TOUTWV <rr,v
sVcdvufiiav '/tf^siv ; " 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."

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 :

20 Parmenid. p. 131. 27 Phsedo, p. 102.

ITS TECHNICAL FORMS. 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 lisp? TOU Tlpwrou
Yu^poiJ, " 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,
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 phe-
nomena, fls they were, are still more obscure than the Ideas of the PLi-
tonists. There were, indeed, considerable resemblances in the way ir
which these two kinds of notions were spoken of. Plato called his
Ideas ^ln^t^es, monads ; and as, according to him, Ideas, so, according
to the Pythagoreans, Numbers, were the causes of things being what
they are. 28 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 Pythago-
reans followed their notion out into much greater development than
any other school, investing particular numbers with extraordinary at-
tributes, and applying them by very strange and forced analogies.
Thus the number Four, to which they gave the name of Tetractyb,
was held to be the most perfect number, and was conceived to corre-
spond to the human soul, in some way which appears to be very im-
perfectly understood by the commentators of this philosophy.

Arist. Metr.ph. 5. 6.

78 THE GREEK SCHOOL PHILOSOPHY

It has been observed bv a distinguished modern scholar, 29 that the

J ~

place which Pythagoras ascribed to his numbers is intelligible only by
supposing that he confounded, first a numerical unit with a geometri-
cal 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 mio;ht have led to results well

7 O

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 disclo-
sures of chemistry and crystallography, the importance of such a line
of inquiry.

4. Technical Forms of the Atomists and Others. The atomic doc-
trine, of which we have just spoken, was one of the most definite of
the physical doctrines of the ancients, and was applied with most per-
severance 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 phys-
ical inquiry; and, on this account, has been thought worthy of an
historical disquisition by Bacon.*

The technical term, Atom, marks sufficiently the nature of the opin-
ion. 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,

Thirhvall's Hut. Gr. ii. 142.

50 Parmenidis et Telesii et prsecipue Dcmocriti Pliilosophia, &c., Works, vol.
ix. GIT.

ITS TECHNICAL FORMS. 70

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
klea 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 Xoyoi rfepfxa-nxo/, 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 ear-
lier 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 acuteuess, invention, and range of thought ; and,
above all, they had the merit of first completely unfolding the specula-
tive faculty of starting in that keen and vigorous chase of knowledge
out of which all the subsequent culture and improvement of man's in-
tellectual stores have arisen. The sages of early Greece form the
heroic age of science. Like the first navigators in their own mythol-
ogy, 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 un-
locked 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.

SO THE GREEK SCHOOL PHILOSOPHY

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 appli-
cation 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 philosophi-
cal 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 Aris-
totelian School. Real truths, when once established, remain to the
cud 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 phys-
ical doctrine now received, of which we trace the anticipation in Aris-
totle, in the way in which we see the Copernican system anticipated
by Aristarchus, the resolution of the heavenly appearances into circu-
lar 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 "Prob-
lems," 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

ITS FAILURE. 8]

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 distinct-
ness 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, 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 ? 2 Is it because the wedge is
composed of two opposite levers?" "Why, 3 when a man rises from a
chair, does he bend his leg and his body to acute angles with hi*
thigh ? Is it because a right angle is connected with equality and
rest?" "Why* can a man throw a stone further with a sling than with

u O

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 iii
motion ?" " Why, 5 if a circle be thrown on the ground, does it first
describe a straight line and then a spiral, as it fulls? Is it that the ait
first presses equally on the two sides and supports it, and afterwards
presses on one side more ?" " Why 5 is it difficult to distinguish a mu-
sical note from the octave above ? Is it that proportion stands in tho
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, ay_clear
or permanent apprehension of the general principles which such an
interpretation implies.

Thus the Aristotelian physics cannot be considered as otherwise than
a complete failure. It collected no general laws from facts ; and con-
sequently, 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 thev saw : though thev

/ O ' / O

1 Mech. Prob. 4. Jb. is. a jh. 31. < Ib. K

B Utpl "A\vx. 11- rirpi 'Apfiov. 1-1.

VOL. 16

32 THE GREEK SCHOOL PHILOSOPHY.

often venture so far to trust their principles as to infer from them prop-
ositions 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 remi-
niscence. The Pythagorean tenet that ten is a perfect number, 7 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 sug-
gestion, the music of the spheres.

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 wri-
ters estimate their claims much more highly than they are stated here.
Among such writers we may notice Dutens, who, in 17 60, published his
"Origin of the Discoveries attributed to the Moderns; in which it is
shown that our most celebrated Philosophers have received the great-
est 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 Timaeus, in Plato's dialogue, says of the Creator of the
world, 8 " that he infused into it two powers, the origins of motions,
both of that of the same thing and of that of different things;" Du-
tens 9 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 10 that it required all the penetration of
Newton and his followers to detect this law in the scanty fragments by
which it is transmitted.

Argument of this kind is palpably insufficient to cover the failure Oi
the Greek attempts at a general physical philosophy; or rather we

' Arist. Metapli. i. 5. Tim. 96. 3d ed. p. 83. l Ib. o. 88.

CAUSE OF ITS FAILURE. S3

may say, that such arguments, since they are as good as can be
brought iu 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 (he 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 requi-
site 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 obser-
vations ; 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 physi-
cal 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 man-
ner that all our knowledge must begin from experience, but also stated
iu language much resembling the habitual phraseology of the most
modern schools of philosophizing, that particular facts must be col-
lected; that from these, general principles must be obtained by induc-
tion; and that these principles, when of the most general kind, are
axioms. A few passages will show this.

'The way" must be the same," says Aristotle, in speaking of the
rules of reasoning, " with respect to philosophy, as it is with respect to

11 Anal, Prior, i. 30.

84 THE GREEK SCHOOL PHILOSOPHY.

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 sup-
ply 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 observa-
tion supplies the principles of astronomical science. For the phenom-
ena 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 (ra virdp%ovra) belonging to
each subject, it is our task to mark out clearly the course of the
demonstrations. For if in our natural history (Kara rfjv loroptav] 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."
These facts, ra vrrdpxovra, he, at other times, includes in the term
sensation. Thus, he says, 12 " 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 univer-
sal propositions, Induction from particulars. But we cannot have
universal theoretical propositions except from induction ; and we can-
not make inductions without havin^ 1 sensation : for sensation has to do

O '

with particulars."

In another place,' 3 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, rela-
tive to us, are those which are nearer to the sensation ; but the princi-
ples absolutely prior are those which are more remote from the sensa-
tion. The most general principles are the more remote, the more par-
ticular are nearer. The general principles which are necessary to
knowledge are axioms."

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, 14
" Thus, proceeding in violation of sensation, and disregarding it, be-
cause, as they held, they must follow reason, some came to the conclu-
sion that the universe was one, and infinite, and at rest. As it
appeared, however, that though this ought to be by reasoning, it

12 Anal. Post. i. 13. 13 Ib. i. 2. 1J DC Gen. et Cor. i. 8.

CAUSE OF ITS FAILURE. So

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.

2. Nor was this recognition of the fundamental value of experience
a mere profession. The Greek philosophy did, in its beginning, pro-
ceed 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 thai

86 THE GREEK SCHOOL PHILOSOPHY.

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, iu
reality, the treatises of Aristotle which we have mentioned, are as re-
markable 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. "VVe may easily show how unprofit-
able an arbitrary or random classification is, however orderly and sys-
tematic 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, trans-
forming these striking appearances into fiery swords and spears, bears
and dragons, armies and chariots. The facts so classified were, not-
withstanding, 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 specta-
tors had no steady conception of the usual order of such phenomena.
For, however much we may fear to be misled by preconceived opin-
ions, 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 want-
ing 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. Jvo one who knows any thing of the

CAUSE OF ITS FAILURE. 87

.listory of the ancient Greek mind, can question, that in acutencs?, 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 phi-
losophical schools 1

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

The peculiar characteristics of scientific ideas, which I have endeav-
ored 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. AVe 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 pro-
ceeding from every point of the sun's disk and passing through every
point within the boundary of the hole. By attending to the conse-
quences of this mode of conception, it will be seen that each point oi
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 suppos-
ing 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

THE GREEK SCHOOL PHILOSOPHY.

of the circular form of the sun's image : but these circular images be
come larger and larger as they are farther 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.' 5 " Is
it because light is emitted in a conical form ; and of a cone, the base

O

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 th.it his explana-
tion 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.

G. Again, to pass to a more extensive failure : why was it that Aris-
totle, knowing the property of the lever, and many other mechanical
truths, was unable to form them into a science of mechanics, as Archi-
medes afterwards did ?

i

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 diffi-
culties 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 con-
cave. In the next place, it has, at the same time, opposite motions,
for it moves forward and backward at the same time. For the circum-
ference, setting out from any point, comes to the same point again, sc

5 Problem. 15, oca ^aOri^arlKris, &c.

CAUSE OF ITS FAILURE. 89

tli.it 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 ap
plies 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, tin
latter, contrary to nature. Now in the smaller circle, the motion, con-
trary 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 " unnatu-
ral" 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 under-
taken. 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 amono; them.

O

In such Ideas the ancients were very poor, and the stunted and de-
formed growth of their physical science was the result of this penury.
The Ideas of Space and Time, Number and Motion, they did in-
deed possess distinctly ; and so far as these went, their science was
tolerably healthy. They also caught a glimpse of the Idea of a Me-
dium by which the qualities of bodies, as colors and sounds, are per-
ceived. But the idea of Substance remained barren in their hands ;

90 THE GREEK SCHOOL PHILOSOPHY.

in speculating about elements and qualities, they went tlie 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 mod-
ern times, regulate many parts of physics and chemistry.

If this statement should seem to any one to be technical or arbi-
trary, \ve must refer, for the justification of it, to the Philosophy oi
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.

o

[2d Ed.] This account of the cause of failure in the physical specu-
lations of the ancient Greek philosophers has been objected to as un
satisfactory. 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 theii
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 Ideal 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

CAUSE OF ITS FAILURE. 91

which are enumerated. They did not fail because they ncg.ected tc
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 tlu-y
failed because they did not take the right ideas in each case. And sc
long as they were in the wrong in this point, no industry in collecting
facts, or ingenuity in classing them and reasoning about them, couH
lead them to solid truth.

Nor is this account of the nature of their mistake without its in-
struction 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 n. to x. of the Philos-
oploj, 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 Con-
ceptions and the Colligation of Facts, the former must precede the
latter. In Book xir. 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 Pres-
sure, 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 THE GREEK SCHOOL PHILOSOPHY.

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 mechan-
ism of the Medium 1

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 gen-
eral 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

O

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.

BOOK II.

HISTORY

OF THE

PHYSICAL SCIENCES

JX

ANCIENT GREECE.

/?poro?j Trc<t>rjv Kal ptyas 1:600;.

Prom. Vinct.

t to earth the spark of heavenly fir?,
1,'cncealed at first, and small, but spreading soot
Among the sons of men, and burning on,
Teacher of art and use, and fount of power.

INTRODUCTION.

IN order to the acquisition of any such exact and real knowledge oi
nature as that which we properly call Physical Science, it is requi-
site, as has already been said, that men should possess Ideas both dis-
tinct 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 activ-
ity 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 in). 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 his-
tory of Astronomy are such that this science could not, with a view to
our purposes, be made co-ordinate with Mechanics or Optics.

96 PHYSICAL SCIENCES IX AXCIEXT GREECE.

CHAPTER I.

EARLIEST STAGES or MECHANICS AND HYDROSTATICS.

Sect. 1. Mechanics.

A STRONOMY 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 re-
markably 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 here-
after ; at present we must consider the original advance.

The great step made by Archimedes in Mechanics was the establish-
ing, 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 experiment-
al 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

MECHANICS AND HYDROSTATICS. 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.

O

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 idea^
which are requisite to apprehend it clearly. But when we are so pre-
pared, 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 reason-
ings, we perceive that it is the idea of Pressure ; Pressure being con-
ceived 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, iveiyht, 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 what-
ever. But the causes which produce such pressure are capable of pro-
ducing 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 mo-
tion 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
VOL. I. 7

98 PHYSICAL SCIENCES IN ANCIENT GREECE.

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 con-
sequently 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 dis-
tinguished from the mechanical doctrine of Motion, which is termed

O '

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 revi-
val 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 in-
volves, 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 mov-
able 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.

MECHANICS AXD HYDROSTATICS. 9S

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, sornetjnes 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 Hydro-
statics 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 con-
cerning 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 surround-
ing 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 condi-
tion 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 =o 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 recom-

O * '

mendation, 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 PHYSICAL SCIENCES IN ANCIENT GREECE,

CHAPTER II.

EARLIEST STAGES OF OPTICS.

FT1HE progress made by the ancients in Optics was nearlj proportional
J- 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 Reflec-
tion 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 car-
ried. 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 argu-
ments are mentioned by which this was established. We are told in
the Proem, "In explaining what concerns the sight, he adduced cer-
tain 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 car-
ried 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.

OPTICS. 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 these visu;d
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,
\ve often cannot see it when it is under our nose ; which it was con-
ceived 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 th.?n they are not seen with
their proper color." 1

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 classifica-
tions 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

1 De Anim. ii. 6.

102 PHYSICAL SCIENCES IX ANCIEXT GREECE.

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 Propo-
sitions 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 Jhe object, if the illuminating body be less, and
v ice 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 ob-
tained a knowledge of a principle, they followed it to its mathematical
consequences with great acuteuess. The subject of concave mirrors is
pursued further in Ptolemy's Optics.

The Greek writers also cultivated the subject of Perspective specula-
lively, 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 Refrac-
tion 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 ap-
pear 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 dvcaXorfis (Meteorol. iii. 2), but appa-
rently in a very vague manner. It is not evident that he distinguished
Refraction from Reflection. His Commentators however do distin-
guish these as tfiaxXcttfig and <xvaxX<xc'i. See Olympiodorusin Schnei-
der's Edofjce Physicce, vol. i. p. 397. And Refraction had been the
subject of special attention among the Greek Mathematicians. Archi-
medes 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 0})tics of Euclid. We do not
find this fact explained in that wcrk as Ave now have it ; but in Ptol-
emy's Optics the fact is explained by a flexure of the visual ray : it is

OPTICS. 103

.noticed that this flexure is different at different angles from the per
pendicular, 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 re-
fraction 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 experiences de physique bier
faites, ce qui est sans exemple chez les anciens."

Ptolemy's Optical work was known only by Roger Bacon's refer-
ences to it (Opus Ma jus, p. 286, <kc.) till 1810 ; 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 ot
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 Encyclopaedia Bri-
tannica. Ptolemy shows great sagacity in applying the notion of
Refraction to the explanation of the displacement of astronomical ob-
jects 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.

Cleomecles, 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 Ernpiricus, a century later, says, "The air being dense, by the
refraction of the visual ray, a constellation may be seen above tin
horizon when it is yet below the horizon." But from what follows, it

lO-i PHYSICAL SCIENCES IN AXCIEXT GREECE.

appears doubtful whether he clearly distinguished Refraction and Re-
flection.

In order that we may not attach too much value to the vague ex-
pressions of Cleomedes and Sextus Empiricus, we may remark that
Gleomedes 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 influ-
ence, 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 Refrac-
tions 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), "Ptolemteus in libro de Opticis, id est, de
Aspectibus, seu in Perspectiva sua, qui prius quarn Alhazen dedit hauc
sententiam, quam a Ptolema3O 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 risibili extriusecus ad visum manantibus." (Opt. Lib. i. cap.
5.) Vitello says of his Table of Refractions, " Acceptis instrumenta-
-litcr, prout potuimus propinquius, angulis omnium refractionum . . .
invenimus quod semper iidem sunt anguli refractionum : . . . secun-
dum hoc fecimus has tabulas." " Having measured, by means of in-
struments, 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
ungle ; and hence we have constructed these Tables."

HARMONICS. 105

CHAPTER III.
EARLIEST STAGES OF HARMONICS.

A MONG the ancients, the science of Music was an application 01
* Arithmetic, as Optics and Mechanics were of Geometry. The
ftory which is told concerning the origin of their arithmetical music,
is the following, as it stands in the Arithmetical Treatise of Nicom-
achus.

Pythagoras, walking one day, meditating on the means of measur-
ing 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 in-
accurate ; for the musical intervals thus spoken of would not be pro-
duced 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 the-
ory 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 G, or 2 to 1 ; a Fifth,
corresponding to the proportion 12 to 8, or 3 to 2 ; and a Fourth, cor-
responding 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
act, for the rate of vibration of a string, on which its note depends, is,

106 PHYSICAL SCIENCES IN ANCIENT GREECE.

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 Oc-
tave, Fifth, and Fourth. In order to produce these intervals, the
appended weights must be, not as 12, 9, 8, and 6, but as 12 6|-, 5^,
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 Semi-
tone 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 conse-
quences 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 pub-
lished by Meibomius. 1 These arithmetical elements of Music are to the
present day important and fundamental portions of the Science of
Harmonics.

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
\vas 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 sound?,
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

2T'.tsicx Scriptores septan, 1C52.

HARMONICS. 107

jnust 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 tb,e arithmetical, if it were found possible. When the connection
was once suggested, it was easy to devise experiments by which it
might be confirmed.

o

"The philosophers of the Pythagorean School, 2 and in particular,
Lasus of Hermione, and Hippasus of Metaponturn, made many suck
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.

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 Avhich 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 subjects, as
in Harmonics, much was written, the works thus produced consisted
of deductions from the fundamental principles, by means of arithmet-
ical 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 compre-
hensive character of their attempts, and some of tie causes which
limited their progress in positive science. They speculated and

2 Montucla, iii. 10.

108 PHYSICAL SCIENCES IN ANCIENT GREECE.

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.

o o

This conviction is eminently conspicuous in the writings of Plato.
In the Republic, in the Epinomis, and above all in the Timceus, 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 suc-
ceeding 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 Timceus 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 pre-
sented 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 luhy 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 Pliccdo, 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
Timceus 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.

EOOK 1H,

HISTORY

0?

REEK ASTRONOMY-,

ij 30 XT'/ ~ f ; ' r << &* f

iriiv is TOVTOV &iavorj9]/vai 7ovin\:riov, dif ovre atypov <rn TTOTC TO Oelov,
ovre. ayvoci xcv TIJV avdpioirtvqv <j>vaiv' dXA' oKtv Sri, SttidaKovTof auraJ. \iva.Ko\o\iQi'iGii
<al iiaOi'/acTui ra ctSuaKoiJitva. PLATO, Epinomis, p. 538. t

Nor should any Greek have any misgiving of this kind ; that it is not
fitting for ITS 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
-vithout purpose, and that they know the nature of man : they know that
jy their guidijics and aid, man may follow and comprehend the lessons
which are vcnr.J:?afed him on such subjects?.

INTRODUCTION.

earliest and fundamental conceptions of men respecting the ob-
J- jects 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 Constella-
tions, 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 knowl-
edge, men were able, at an early and unenlightened period, to con-
struct 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
t\vo 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 conse-
quence of these causes, the knowledge of man respecting the heavenly
bodies took, from the earliest period of his history.

112 THE GREEK ASTRONOMY.

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 recur-
rence of light and darkness, of comparative warmth and cold, of noise
and silence, of the activity and repose of animals ; the rising, mount-
ing, 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 ob-
vious 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 por-
tion 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 arrang-
ing 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

EARLIEST STAGES OF ASTRONOMY. 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 ex-
tremely different in different countries ; and the contrasts and resem-
blances 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 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.

In general, nations have marked this portion of time by some word
which has a reference to the returning circle of seasons and employ-
ments. Thus the Latin annus signified a ring, as we see in the deriva-
tive annulus : the Greek term iviavrbg implies something which re-
turns 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 gyms.

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 method?

1 Ideler, Lerl. Trans. 1S13. p. 51.
VOL. I.-8

114. THE GREEK ASTRONOMY.

of practical numeration on which such a system of terms is always
founded. 2 The South American Indians, the Koussa Caffres and Hot-
tentots, 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, can-
not, as we do, include in their notion of a year the fact of its consist-
ing 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 con-
sidered as the earliest scientific process which we can trace in the his-
tory 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.

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 indefiniteuess
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 at-
tended 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 lio-ht. The motions of the sun, the

o o

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 rpo-al ?}e/ltoto, the turnings of the sun, are used re-
peatedly 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

The phenomena would be different in different climates, but the
recurrence would be common to all. Any one of these kinds of phe-
nomena, noted with moderate care for a year, would show what was
the number of days of which a year consisted ; and if several years

1 Arithmetic in Encyc. Metrop. (by Dr. Peacock), Art. 8. s Ibid. Art. 82.

4 "HftaTa -nivrfiKotiTa fisru rpoiras fit\loio

(\84vTos Bipcos. Op. et D'us, 661.

ITS EARLIEST STAGES. 11 3

rrere included in the interval through which the scrutiny extended
the knowledge of the length of the year so acquired would be pro-
portionally more exact.

Besides those notices of the sun which offered exact indications ot
the seasons, other more indefinite natural occurrences were used ; as
the arrival of the swallow (%ehidtjv) and the kite {lariv). 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

Among the Greeks the seasons were at first only summer and
winter (#epo and ^efjttwv), the latter including all the rainy and cold
portion of the year. The winter was then subdivided into the xeipuv
and lap (winter proper and spring), and the summer, less definitely,
into Bepog and 6-upa (summer and autumn). Tacitus says that the
Germans knew neither the blessino-s nor the name of autumn, " An-

O '

tumni perinde nornen ac bona ignorantur." Yet harvest, hcrbst, is
certainly an old German word. 6

In the same period in which the sun goes through his cycle of posi-
tions, 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 w r est after sunset ; but it is noted that w r hen 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, w r ere, in countries where the sky is usually
clear, employed at an early period to mark the seasons of the year,
Eschylus 7 makes Prometheus mention this among the benefits of which

Ideler, i. 210. Ib. i. 343.

O&K ?iv yap avrolg ovre \clftaro; riK/jap,

Of r' avBtfiialovs %pos, ov&t KapTripov

Qipov; (3i$atoV oAV arep yvw^rj; TO ttHv

Zjrf>!7<7ov. care <5// c(jtiv di'uroXuj tyS)

AcTO-di' ecita, rds re cvaKpirov; cvaet;. Prom. F. 454.

116 THE GREEK ASTRONOMY.

he, the teacher of arts to the earliest race of men, was the coin
munieator,

Thus, for instance, the rising 8 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
clays which compose the year; and to fix the precise season from the
appearance of the stars.

A knowledge concerning the stars appears to have been first culti-
vated with the last-mentioned view, and makes its first appearance in
literature with this for its object. Thus Hesiod directs the husband-
man when to reap by the rising, and when to plough by the setting
of the Pleiades. 9 In like manner Sirius, 10 Arcturus," the Hyades and
Orion, 12 are noticed.

" Ideler (Clironol. i. 242) says tliat this rising of the Pleiades took place at a time
of the year which corresponds to our llth 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 testas incipit, occasu hiems ;
semestri spatio intra se messes vindemiasque et omnium maturitatem complexre.'
(II. N. xviii. 60.)

The autumn of the Greeks, <Jrupa, was earlier than our autumn, for Homer calls
Sirius do-n/p (ircopii-of, which rose at the end of July.

'ArXayci'/o)!/ fE
O' d/o;rou' apiroto <5t,
Aj <5;/ TOI VVKTCIS T KOI rjfiara
KcKpv<piiTai, avrts At TtpiTrAo/u/i'oi; ertavrnv
'I'a'ii/oi/rai. Op. et Lies, 1. 3S1.

Ib. 1. 413.

11 Eur 1 civ & ($r/KOVTa pcru TpoTra; ifiXloio
KTc^ici) Zu'f fyaTa, fit'/ fta r<5r' a
;, rpoXnrlav icpov f>6ov '

Op. ctDi<-S, 1. 562.

i.Cr' av o' 'Qpiuiv Kul 'Seipio; fj uctrov\9>l
Ovfavov, Aoxrurp'ji' (5' ioi&i) froSoodnTyhos ^uj.

Ib. 007.
12 . . . . . . avraa iirijv >i

n\ijidi:s 'ICiiiss TC rb Tt aOlios 'flpiuros

AtJi-uo-ii'. 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 call!']
ra. Ideler, Hist. Uhtersuchungren, p. 200.

ITS EARLIEST STAGES. 117

By such means it was determined that the year consisted, at lc-;i~t,
rearly, of 365 days. The Egyptians, as we learn from Herodotus,
claimed the honor of this discovery. The priests informed him, lie
says, " that the Egyptians were the first men who discovered the y;ir,
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
..lay of the seventh month (Gen. viii. 4), that is, 5 months of 30 days.

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.)

Ix 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 becrinuing of the former would take

*/ o o

place at different periods of the latter ; it would ivander into various
seasons, instead of remaining fixed to the same season ; the term yea);
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 we find this knowledge diffused among all civil-
ized nations, and various artifices used in making the correction. The
method which we employ, and which consists in reckoning an addi-

'3 Ib. ii. 4.

14 Syncellus (Chronographia, p. 123) says that according to the legend, it was King
Ascth who first added the 5 additional days to 860, for the year, iu the eighteenth
century, B. c.

11 S THE GEEEK ASTEOXOMY.

tional day at the end of February every fourth or leap year, is an ex-
ample 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 octaetens 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 Gerninus, 15 " 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 3651 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

Other nations did not regulate their civil year by intercalation at
short intervals, but rectified it by a reform when this became neces-
sary. The Persians are said to have added a mouth 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 vari-
ous causes, not properly done ; and the consequence was, that the
reckoning fell into utter disorder, in which state it was found by Julius
Caesar, 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

O /

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 Cal-
endar, thus reformed, came into use, January 1, B. c. 45.

Sect. 4. Attempts at the Fixation of the Month.

THE cii\:le 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

Uranol. p. 83. 16 Censorinus de Die Jfatali. c. 13

ITS EARLIEST STAGES. 119

as the circle of changes of the seasons is designated oy 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 ab-
sent, 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 lan-
guages, 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
HTJV in like manner is related to prjvr], 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

The mouth 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 pre-
serve, 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 h>7] not vea, " the old and new," as
belonging to both the waning and the reappearing moon : 18 and their

" Cicero derives this word from the verb to measure : " quia mensa spatia, confi-
eiunt, menses nominantur ;" and other etymologists, with similar views, connect the
above-mentioned words with the Hebrew manak, to measure (with which the
Arabic word almanack is connected). Such a derivation would have some analogy
with that of atinus, &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 s
terb denoting the very abstract and general notion, to measure.

18 Aratus says of the moon, in a passage quoted by G&minus, p. 33

"A.ICI 6' d'AXo0i' u'AArz xap

As still her shifting visage changing turn?,
By her we count the monthly round of morns.

120 THE GREEK ASTRONOMY.

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 sys-
tem of intercalation became a religious duty.

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.

aysiv TUS

OvSiv 6p6;, dAA' avta re Kal Karia
"IZor' dirtiXcti; tyrialv avrtj TOV; dcui'S
'HvjV av ij/evaO&ai Seiiri'ov Ka-iwcLv
Tij; /oprjjj pfj Tvxdvrct Kara \6yov TUJV j

J\"ubes, 615-19.
CHORUS OF CLOUDS.

The Moon by us to you her greeting sends,
Bat 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. 13

The correction of this inaccuracy, however, was not pursued sepa-
rately, but was combined with another object, the securing a corre-
spondence between the lunar and solar years, the main purpose of al!
early cycles.

Sect. 5. Invention of Lunisolar Years.

THERE are 12 complete lunations in a year; which according to
the above rule (of 29-| days to a lunation) would make 354 days, leav-
ing 12i 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 Herod-
otus 50 relates a conversation of Solon, implying a still ruder mode of

19 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.

20 B. i. c. 15.

ITS EARLIEST STAGES. 121

intercalation. This can hardly be coasidered as an improvement in
the Greek calendar already described.

The first cycle which produced any near correspondence of the
reckoning of the moon and the sun, was the Ociaeteris, 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 365^ clays 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 per-
sons and times ; probably different persons proposed different forms oi
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 29231; hence
in 16 years there was a deficiency of 3 days, with regard to the mo-
tions of the moon. This cycle of 16 years (Hecccedecaeteris), with 3
interpolated days at the end, was used, it is said, to bring the calcula-
tion 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 agree-
ment : and we have thus a cycle of 160 years. 21

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
year's ; 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
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;

21 Gemirms. IJeler. K Ideler, Hist. Unters. p. 203.

122 THE GREEK ASTRONOMY.

(the former time is less than 6940 days by 9^ hours, the latter, by T|
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 \vith great exactness.

In order that 235 months, of 30 and 29 days, may make up C940
days, we must have 125 of the former, which were called/^ months,
and 110 of the latter, which were termed liollow. An artifice was
used in order to distribute 110 hollow months among 6940 days. It

o /

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, llth, 14th, 17th, and 19th; others, the
3d, 5th, 8th, llth, 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 dif-
ference between the calendar day and the celestial phenomenon which
ought to correspond to it. It is most probable that the length of the
mouth 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

The exact length of a certain number of months being thus known,
the discovery of a cycle which should regulate the calendar with suf-
ficient 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 prob-
ably more efficacious than method. It is very possible that the Cycle
of Melon is correct more nearly than its author w T as aware, and more

23 Thucyd. vii. 50. 'H atX^i'V \K\t'u:tC tr<ty\avt yap Travo-Ajji/of ovaa. iv. 52. ToD
JX/uu tK\tir(S TI i-yei'CTo xepl vovjuiviav. ii. 23. Nou/oji'i'a Kara tre\jjv>iv (uaircp Kai fi6vov
isoKS.1 ilvai ylyvcadai Svvarov) & fjMos f/Ai7r f<ru piorjufiplav Kal TruAtv av l-\t]p<j)dri, yc-
Knt aafifiuv Tir&v tK<f>avcvTtnv.

ITS EAELIEST STAGES. 123

nearly than lie could ascertain from any evidence and calculation
known to him. It is so exact that it is still used in calculating tin-
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 correspond-
ing to the current year. 24

Metou'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." In this corrected
period, four cycles of 19 years were taken, and a clay 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 Galippic period is used in Ptolemy's Almagest,
in stating observations of eclipses.

The Metonic and Calippic periods undoubtedly imply a very con-
siderable 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.

o

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 alto-
gether 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 observa-
tion, 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

34 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 mouths of 23
and' 80 days. The Siamese also have this period. (Astron. Lib. U. K.)

25 Delamb. A. A. p. 17.

124: THE GREEK ASTRONOMY.

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 \vhicli 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 arith-
metical 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, G. The Constellations.

SOME tendency to consider the stars as formed into groups, is inevit-
able 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 Hesiocl, and at a still earlier period, as we find in
the book of Job. 25

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 com-
munication. The arbitrary nature of these figures shows that they

89 Job xxxviii. 31. " Canst thou bind the sweet influences of Chima (the .Plei-
ades), 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 maketli Arcturus, Orion, and Pleiades, and the chambers
of the south."

Dupuis, vi. 545, think? that ^ isch was !', the goat and kids. See Hyde, Uluqk-
SeigA.

ITS EARLIEST STAGES. 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 " seem to ha\ v
been almost purposely named and delineated to cause as much confu-
sion 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 indi-
cate 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

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 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 ; 3C
the river among the stars which the Greeks called the Eridanus, the
Egyptians asserted to be the Nile. Some conceive that the Signs ot
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 husband-
man. If we take the position of the heavens, which, from the knowl-
edge 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 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 :

27 Sir J. Herschel.

16 So also the Greeks, Homer, II. xvra. 437.

"Apxrov tjv KUI ajia^av iniK\r]ntv Ka\iovaiv.
The Northern Bear which oft the Wain they call,
"ApKros was the traditional name ; a^n^a, that suggested by the form.

29 Dupuis, vi. 543. The Indian zodiac contains, in the place of our Capricorn, a
am and a fish, which proves the resemblance without chance of mistake. Bailly,
i. p. 157. 30 Dupuis, vi. 549. 31 Laplace, Hist. Astron. p. S.

126 THE GREEK ASTRONOMY.

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.

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 asso-
ciated with the stars. 32 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.

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 nat-
ural 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 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.

Sect. H i. The Planets.

WHILE men were becoming familiar with the fixed stars, the planets
must have attracted their notice. Venus, from her brightness, and

82 Dupuis, vi. 546. & Ib. vi. 546.

ITS EARLIEST STAGES. 127

from her accompanying the sun at no great distance, and thus appear-
ing as the morning and evening star, was very conspicuous. Pythag-
oras is said to have maintained that the evening and morning star
are the same body, which certainly must have been one of the earli-
est 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 lumina-
ries 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 mo-
tions 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

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,

'< Achilles Tutius (Uranol. pp. 135, 136), gives the Grecian and Egyptian names

f the planets.

Egyptian. Greek.

Saturn Nc/jta/wg- Kj/oi'ou c!crri/p rjiaivuv

Jupiter 'O<7[f>i(5of AIOJ <j>aidtav

Mars 'Hf>aK\eou; 'Apios

Venus 'A-tipoS

Mercury '

128 THE GREEK ASTRONOMY.

Egyptians. 35 The same week is found in India among the Braurius ;
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.

The notion which led to the usual designations of the days of the
week is not easily unravelled. The days each correspond to one ol
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 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 con-
sider 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 per-
haps not worth our while here to examine further the steps of this
process ; it would be difficult to determine with certainty Avhy 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 pro-
duced this result ; and we may probably consider the Week, with
Laplace, 37 as "the most ancient monument of astronomical knowl-
edge." 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, accord-
ino- 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 super-
stition.

Sec. 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

" Laplace, Hist. Astron. p. 16. 36 PMlol. Mas. No. 1. 37 Hist. Ast. p. 17.

ITS EARLIEST STAGES. 129

,he 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 specula In';
astronomy, and was occasioned and rendered important by the scien-
tific 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 Bight, it would be readily seen, might be repre-
sented 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 !
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 tinu
of night varies gradually from night to night, so as to go through its
cycle of appearances once a year. All this would obviously agrei
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 perpet-
ually 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 amon<;
the stars on the surface of the concave sphere. The sun by his bright-
ness 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 ali
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 tho
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 noc-
turnal 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 amouo- the stars will be clcarlv seen, when it is considered that no

O f

VOL. I.

130 THE GREEK ASTRONOMY.

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 that the stars which occupy oue 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

O O O / O

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 deter-
mine the position of the sun each night, and thus trace his path in a
year.

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 59 states that Anaximander, 40 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.

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
exactlymidway between these poles was called theJSquator (larjuepivoc:).

38 Delamb. A. A. p. xiii. 39 Lib. ii. c. (viii.)

40 Plutarch, De Plac. Phil. lib. ii. cap. xii. says Pythagoras was tlie author of
this discovers".

ITS EARLIEST STAGES. 131

The two circles parallel to this which bounded the sun's path among
the stars were called Tropics (rpoTTLKa't), 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 (dpit-utoc,
from a'pKTOf, the Bear, the constellation to which some of the prin-
cipal 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." The sun's path or circle of the signs is called the Zodiur,
or circle of animals ; the points where this circle meets the equator
are the Equinoctial Points, the clays and nights being equal w T hen 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 (ttokovpoi, 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.

The Horizon (ppi&v] 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 Phamomena (3>aiv6[.ieva). "We possess two
treatises written by Autolycus 42 (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 Hepl Ktvovjj,ei'7]g
I.6aipag, "On the Moving Sphere," he demonstrates various properties
of the diurnal risings, settings, and motions of the stars. In another

" 43

work, Hepl 'ETUTO/IWV Kal A^'crewr 1 , "On Risings and Settings,
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
or rice vers& ; 45 and also their oji/x/ru/f risings and settings when they
cease to be visible after sunset, or beo-in to be visible after sunrise. 46

o

41 The Arctic and Antarctic Circles of modern astronomers are different from
these.

43 Dclambre, Asiron. Ancienne, p. 19.

13 Delambre, Astron. Anc. p. 25. 44 Cosmical rising and setting.

45 Aeronyeal rising and setting ; (aKpoivKtos, happening at the extremity of tht
night.)

40 IM'aical rising and setting.

132. THE GREEK ASTRONOMY.

Several of the propositions contained in the former of these treatises
are still necessary to be understood, as fundamental parts of astronomy

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

"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 as-
sumed 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 differ-
ent 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 con-
sidered both monstrous and heretical.

Yet the different positions of the horizon at different places, neces-
sarily led the student of spherical astronomy towards this notion of the
earth as a round body. Anaximander 43 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

Ast. Anc. p. 53. See Brucker, Hist. Pldl vol. i. p. 450.

ITS EARLIEST STAGES. 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 sug-
gest 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.

We find this doctrine so distinctly insisted on by Aristotle, that we
may almost look on him as the establisher of it. 49 " 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, 60
"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 interposi-
tion 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 laro-e : for when we make a small removal to the south or the

^ o

Vorth, the circle of the horizon becomes palpably different, so that the
stars overhead undergo a great change, and are not the same to those

o o o '

that travel to the north and to the south. For some stars are seen in
r>vpt or at Cyprus, but are not seen in the countries to the north ot

O* i. v J.

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 -Mo connect the region in
the neighborhood of the pillars of Hercules iritli that toivards India,
and who assert that in this way the sea is OXE, do not assert things
very improbable. They confirm this conjecture moreover by the

Arist. de, Cctlo, lib. ii. can. x:v. c.l. Casaub. p. 2: i. ; p. 291 C.

134 THE GREEK ASTRONOMY.

elephants, which are said to be of the same species (yevof) towards
each extreme ; as if this circumstance was a consequence of the con-
junction 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."

When this notion was once suggested, it was defended and confirm-
ed by such arguments as we find in later writers : for instance, 51 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 em-

O

ployed 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.

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 spheri-
cal, 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
mouth. For the convex side of the crescent-moon, and her full edo-e

7 ~

when she is gibbous, are always turned towards the sun. And this
explanation, once suggested, would be confirmed, the more it was ex-
amined. 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;

riiuy, Mil. Hist. ii. LXV.

ITS EARLIEST STAGES. 135

the only difference is, that the dark part of the rnoon is usually not
visible at all.

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

|

Sect. 11. Eclipses.

ECLIPSES of the sun and moon were from the earliest times 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 discov-
ered 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 proba-
bly 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 beo-innin<r. 5S Prob-

O O

ably this was the first instance of the prediction of peculiar astronom-
ical 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 pre-
dict 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 IK;
single observation or fact connected with astronomy in the Chinese

M Probl. Cap. xv. Art. 7.

63 The eclipses of the sun are more difficult to calculate ; since they depend upon
.he place of the spectator on the earth.

136 THE GREEK ASTRONOMY.

nistories ; and their astronomy lias never advanced beyond a very rude
and imperfect condition.

We can only conjecture the mode in which the Chaldeans discovered
their Period of 18 years; and we may make very different supposi-
tions with regard to the degree of science by which they were led to
it. We may suppose, with Delan#bre, 54 that they carefully recorded
the eclipses which happened, and then, by the inspection of their regis
ters, discovered that those of the moon recurred after a certain period.
Or we may suppose, with other authors, that they sedulously deter-
mined the motions of the moon, and having obtained these with con-
siderable 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.

It appears probable rather that such a period was discovered by no-
ticing the recurrence of eclipses, than by studying the moon's motions.
After 6585^- 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 Stores 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 applica-
tions and inferences, of which we may mention a few.

Prediction of Eclifises. The Cycles which served to keep in order
the Calendar of the early nations of antiquity, in some instances en-
abled 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, sa} T s, " We never see an eclipse happen which
has not been predicted by those who made use of the Tables." (VTTO

~U)V KdVOVtK&V.)

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

A. A. p. 212.

ITS EARLIEST STAGES. 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 thai-
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. Anaximeues is said by Pliny to have
first taught this art in Greece ; and both he and Anaximander are re-
ported 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 col-
lected 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
aave already perhaps entered too much in detail. AA'e have been

138 THE GEEEK ASTROXOlir.

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 lo
contemplate them engaged in a worthier employment, namely, in add-
ing to these discoveries.

CHAPTER II.

PRELUDE TO THE IXDUCTIVE EPOCH OF HIPPARCHUS.

"ITHOUT pretending that \ve 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. Be-
fore, 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 explana-
tion felt.

In the steps previously made in astronomical knowledge, no inge-
nuity had been required to devise the view which was adopted. The
motions of the stars and sun were most naturally and almost irresisti-
bly 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-correc-
tion. 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 emergiug again in the
morning.'" A continued attention to these stars would, however,

1 Cic. de Nat. D. lib. ii. p. 450. " Ea qnte Saturni stella dicitur, ^ai'rui que a
Grsccis nominator, ]uo? a terra abest pluriinum, xxx fere annis cursum suurn con

PltELUDE TO THE EPOCH OF HIPPARCHUS. 130

t

detect a kind of intricate regularity in their motions, which might
naturally be described as " a dance." The Chaldeans are stated by
Diodorus 2 to have observed assiduously the risings and settings of the
planets, from the top of the temple of Belus. By doing this, the}
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. 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.

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 pro-
duced ; 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 barvk 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 sup-
pose that a person, holding a lamp in his hand in the dark, and at a

fieit; in quo cursu multa mirabiliter efficiens, turn antecedeodo, turn retardando,
*um vespertinis temporibus delitescendo, turn rnatutiuis se rursum aperieudo, mliil
immutat sempiternis sceculomm retatibus, quin eadem iisdem temporibus efficiat."
And so of the other planets.
2 Del. A. A. \. p. 4. 3 pi iu . //. 3- ji. p . 204.

1-10 THE GREEK ASTRONOMY.

distance, so that the lamp alone is visible, should run on turning him-
self 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
Parnphylian, who, being supposed to be killed in battle, revived when
he was placed on the funeral pyre, and related what he had seen dur-
ing 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" (Eplnomis),
he again describes the various movements of the sky, so as to show a
distinct acquaintance with the general character of the planetary mor
tions ; and, after speaking of the Egyptians and Syrians as the original
cultivators of such knowledge, he adds some very remarkable exhorta-
tions to his countrymen to prosecute the subject. "Whatever we
Greeks," he says, " receive from the barbarians, we improve and per-
fect ; there is good hope and promise, therefore, that Greeks will cany
this knowledge far beyond that which was introduced from abroad."
To this task, however, he looks with a due appreciation of the quali-
ties 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 acquaint-
ance 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:"

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

The theory, once suggested, probably /nacle rapid progress. Sim-
plicius 5 relates, that Eudoxus of Cnidus introduced the hypothesis of
revolving circles or spheres. Calippus of Cyzicus, having visited Pole-

s, pp. OSS, 090. 5 Lib. ii. de Cotlo. Eullialdns, p. 18.

PRELUDE TO THE EPOCH OF HIPPARCHUS.

aiarchus, an intimate friend of Eucloxus, they went together to Athens,
and communicated to Aristotle the invention of Eudoxus, and -with
Lis help improved and corrected it.

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
rnoon, 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 dep'end being the same, the eclipses will occur
in the same order. In GoSog- days there are 239 revolutions of anom-
aly, 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,

THE GREEK ASTRONOMY.

they could hardly avoid discovering the anomaly or unequal motion o'
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 6 is
probably right in attributing all such observations to the Greeks.

The sun's motion wouJd 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 some-
times 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. Ac-
cordingly, 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 de-
served 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 sim-
plicity 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 inter-
preted, in the arguments by which the opinion was defended, that the

8 Astro nomie Ancienne, i. 212.

PRELUDE TO THE EPOCH OF HIPPARCHUS. 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 occa-
sions 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 repre-
sented by equable and circular motions."

These conjectures and assumptions led naturally to the establish-
ment 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. 7 " 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 perpen-
dicular 8 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 report-
ed 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.

The hypothesis, in this form, does not appear to have been reduced
to measure, and was, moreover, unnecessarily complex. The resolution

7 Mctapli. xi. 8.

8 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,

' f < Trjs olKciordrrj; 0iAo<7c>i'uj rwv

THE GREEK ASTRONOMY.

of t'he 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 yearly 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 the-
ory by Hipparchus. There had also been a preparation for this step,
on the other side, by the collection of Facts. "We know that observa-
tions 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 ob-
servations, which went back 1903 years, and which Aristotle caused
Callisthenes to brino- to him in Greece. All the Greek observations

O

which are of any value, begin with the school of Alexandria. Aris-
tyllus and Timocharis appear, by the citations of Hipparchus, to have
observed the Places of Stars and Planets, and the Times of the Sol-
stices, 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 Equi-
noxes.

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 besran 331 B. c. These are the dates used

i/ O

by Hipparchus and Ptolemy.

INDUCTIVE EPOCH OF HIPPARCHUS.

CHAPTER III.

INDUCTIVE EPOCH or HIPPARCHUS.

Sect. 1. Establishment of the Theory of Epicycles and Eccentrics.

A LTHOUGH, as we have already seer,, at the time of Plato, the
* Idea of Epicycles had been suggested, and the problem of its gen-
eral 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 ac-
count for their apparently irregular motions. We may best under-
stand 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, tho 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 Eccen-
tricity. It may easily be shown by geometrical reasoning, that tho
Inequality of apparent motion so produced, is exactly the same in
VOL. I. 10

146 THE GREEK ASTRONOMY.

detail, as the inequality which follows from the hypothesis of a smal.
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 Surfs Eccentric. When Ilipparchus 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) 1 give the Anomaly, or inequality of the
sun's motion ; and this they exhibit by means of the Prostha2)heresis,
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.

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 perceiv-
ing 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 94i days, and the time from the sum-
mer tropic to the autumnal equinox 92^- days, from these phenomena
alone he demonstrates that the straight line joining the centre of the
?uu's eccentric path with the centre of the zodiac (the spectator's eye)
:'s nearly the 24th part of the radius of the eccentric path ; and that

Syntax. 1. iii.

INDUCTIVE EPOCH DF HIPPARCHUS. 147

its apoyee precedes the summer solstice by 24^ 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 irregulari-

O

ties ; but when the hypothesis of an Eccentric or an Epicycle had suf-
ficed 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 hypoth-
eses 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 vis-
ible 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 run-
ning round the middle of the skv. 2 In each revolution, the motion in

O *>

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 know T u 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, fur 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 moou's revolution among the

1 The reader will find au attempt to make the nature of this path generally iutel-

igible in the Companion to the Ei-il'dii Almanac for 1314.

148 THE GREEK ASTRONOMY.

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.

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 astrono-
mer, 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 65 85^ 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 in-
stance, 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. 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 Nabouassar, 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. 4

3 Ptol. Si/n. iv. 10.

4 Ptolemy uses the hypothesis of an epycicle for the moon's first inequality ; bat
Ilippnrchus employs an eccentric.

INDUCTIVE EPOCH OF HIPPARCHUS. 149

The moon's motions are really affected by several oilier 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
ao-es, did not contain so many, says Ptolemy, as those which he has
transmitted to us of his own. "Hence 5 it was," he acids, "that while
he labored, in the most assiduous manner to represent the motions of
the sim 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.

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

3 S'jnt. ix. 2.

150 THE GREEK ASTRONOMY.

possessed. There is, indeed, no philosopher who is so uniformly spokei.
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 6 most
truth-loving and labor-loving person," one who had shown extraordi-
nary 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 youi
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 7 that it is
unfortunate for the memory of Aristarchns that his work has come to us
entire, and who cannot refer 8 to the statement of an eclipse rightly pre-
dicted by Halicon of Cyzicus without adding, that if the story be true,
Halicoii was more lucky than prudent ; loses all his bitterness when
he comes to Hipparchus. 9 " 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 astrono-
mers whose observations are inexact, " a long period and the continued
efforts of many industrious men are requisite to produce good instru-
ments, but energy and assiduity depend on the man himself."

Hipparchus was the author of other great discoveries and improve-
ments 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.

8 Syi. ix. 2. 7 Astronomie Ancienne, i. 75.

Ib. i. IT. 9 Ib. i. 186.

INDUCTIVE EPOCH OF HIPPARCHCS. 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, per-
haps, opinions in popular circulation, which might lead men to think
lightly of the merit of introducing or establishing the Doctrine of Epi-
cycles. 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. 10

He his fabric of tlie 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," when this complex system was explained to him;
that " if God had consulted him at the creation, the universe shouk!
have been on a better and simpler plan." In addition to this, the sys-
tem 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 perpet-
ually in motion ; an imagination which is presumed to be incredible
and monstrous.

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 an-
other reason, much more important to the purpose of this work ;

Paradise Lost, viii. " A. D. 1252.

152 THE GREEK ASTRONOMY.

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 rna)
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 prog-
ress 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 suc-
ceeding 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 fun-
damental 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 revolu-
tion, 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 a, few observations, it de-
duces from these, results agreeing with all observations, however
numerous and distant. To express an inequality by means of an epi-
cycle, implies, not only that there is an inequality, but further, that
the inequality is at its greatest value at a certain known place, dimin-
ishes 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 epi-
cycle 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 pro-
cesses by which modern astronomers deal with such motions. Their
universal method is to resolve all unequal motions into a series of

INDUCTIVE EPOCH OF HIPPARCHUS. 153

terms, or expressions of partial motions ; and these terms involve sines
and cosines, that is, certain technical modes of measuring circular mo-
tion, 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 iu 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 appli-
cability 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, 12 "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 in-
consistency will result T'

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 ; 13 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 geo-
metrical conceptions, in which view they are true representations of
[he apparent motions.

12 fynt. xiii. 2. 13 Ibid. iii. 3.

154 THE GEEEK ASTRONOMY.

It is true, that the real motions of the heavenly bodies are simpler
than the apparent motions ; and that \ve, 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 ol
the moon amona; the stars will be.

O

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 astron-
omers to the proper methods of making it more exact and complete,
to point out new objects of attention and research ; and that, afte/
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 astronomi-
cal theory, Copernicus, adopted the theory of epicycles ; that is, he
employed that which we have spoken of as its really valuable charac-
teristic. "We 14 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."

In this sense, therefore, the Hipparchian theory was a real and in-
destructible truth, which was not rejected, and replaced by different
truths, but was adopted and incorporated into every succeeding astro-
nomical theory ; and which can never cease to be one of the most im-
portant 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 b*
the conditions of every real advance in progressive science ; P auielv

14 Copernicus. De -Rev. 1. i. c. 4.

INDUCTIVE EPOCH OF HIPPARCHUS. 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 lumi-
naries. 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 analvsis 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 Longi-
tude 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 infer-
ences 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 decrees behind

O 'A O ' O

the equinoctial point in his own time, and had been eight degrees be-
hind the same point at an earlier epoch. The suspicion was thus sug-
gested, that the longitudes of all the stars increase perpetually; but
Ilipparchus had too truly philosophical a spirit to take this for granted.
He examined the places of Eegulus, and those of other stars, as he had
clone 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 Ilipparchus conceived this change ol
relation of the heavens, is manifested by the question which, as we are
cold by Ptolemy, he examined and decided ; that this motion of the

156 THE GREEK ASTRONOMY.

heavens takes place about the poles of the ecliptic, and uot 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 Eegulus, zodiaca.
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 pub-
lished 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 con-
structing 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 astron-
omers. 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 adapt-
ed to call up many questionings in the minds of speculative men ;
for, after this, nothing could be supposed constant till it had been as-
certained to be so by clo'se 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 suggest-
ed, 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, sys-
tematized, 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.

SEQUEL TO THE EPOCH OF HIPPABCHUS. 157

CHAPTER IV.

SEQUEL TO THE INDUCTIVE EPOCH OF HIPPARCHUS.

Sect. 1. Researches which verified the Theory.

fTUIE discovery of the leading Laws of the Solar and Lunar Motions,
-L and the detection of the Precession, may be considered as the
great positive steps in the Hipparchian astronomy ; the parent dis-
coveries, from which many minor improvements proceeded. The task
of pursuing the collateral and consequent researches which now of-
fered 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 as-
tronomy.

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, ex-
cept 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 clays, 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 THE GREEK ASTRONOMY.

1. Fixity of the Stars. The question necessarily arose after the dis-
covery 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 con-
stantly the same relative position. In order to determine this funda-
mental 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 alinca-
tions 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, 1 who
speaks of it with admiration as a wonderful and superhuman task
(" ausus rem etiam Deo improbam, annumerare posteris stellas"), as-
serts the undertaking to have been suggested by a remarkable astro-
nomical event, the appearance of a new star ; " novam stellam et aliam
in cevo suo genitam depreheudit ; ejusque motu, qua die fulsit, ad
dubitationem est adductus anne hoc ssepius fieret, moverenturque et
e:e quas putamus affixas." There is nothing inherently improbable in
this tradition, but we may observe, with Delambre, 2 that we are not
informed whether this new star remained in the sky, or soon disap-
peared 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 enumer-
ation of 475 of the principal stars, according to the constellations in
which they are, and were published about sixty years before Hip-
parchus.

2. Constant Length of Years. Hipparchus also attempted to ascer-
tain whether successive years are all of the same length ; and though,
with his scrupulous love of accuracy, 3 he does not appear to have

Xat. Hist. lib. ii. (xxvi.) = A. A. i. 200. 3 Ptolem. Synt. iii. 2.

SEQUEL TO THE EPOCH OF HIPPARCHUS. 15

thought himself justified iu asserting that the years were always ex
actly 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.

3. Constant Length of Days. Equation of Time. The equality ot
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 astron-
omers. 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 suffi-
ciently exact, must have led to its being corrected or rejected.

Among these we may notice the researches which were made con-
cerning 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 ex-
amined by Hipparchus, who invented aparallactic instrument for tha
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 THE GEEEK ASTRONOMY.

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 pro-
cess 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 alto-
gether 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 obser-
vations 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, iu some degree falsified
in consequence of the reigning opinion. In fact, however, the imper-
fection 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

SEQUEL TO THE EPOCH OF HIPPARCHUS. 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 ^ of the radius of the orbit ; but its real
amount is only half as great ; this difference is a necessary conse-
quence of the supposition of uniform circular motions, on which the
Epicyclic Hypothesis proceeds.

"We see, therefore, that this part of the nipparchian theory carries
in itself the germ of its own destruction. As soon as the art of celes-
tial measurement was so far perfected, that astronomers could be sure
of the apparent diameter of the moon within J^ or -^ 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 mijst 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 ele-
ments, into the theory which occupies men during the period ; the
improvement of instruments, and the methods of observing and ex-
perimenting, are principal features in such periods. We shall, there-
fore, mention some of the facts which bear upon this point.

The estimation of distances among the stars by the eye, is an ex-
tremely inexact process. In some of the ancient observations, how-
ever, this appears to have been the method employed ; and stars are
described as being a cubit or two cubits from other stars. W T e may
form some notion of the scale of this kind of measurement, from what
Cleomedes remarks, 4 that the sun appears to be about a foot broad :
an opinion which he confutes at length.

A method of determining the positions of the stars, susceptible ol
a little more exactness than the former, is the use of alineations, al-
ready 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 j3 and a of
Ursa Major, are hence often called " the pointers."

< Del. A. A. i. 222.
VOL. I. 11

162 THE 'GREEK ASTRONOMY.

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, 5 from
a memoir of Gautil, first printed in the Connaissance des Temps foi
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 summei
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 6 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."

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 ex-
pression of the circumference required some progress in trigonometry ;
for instance, a table of the tangents of angles.

7 O O

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 SCO 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 hemi-
sphere was placed with its rim horizontal, and a style was erected in
Fnch a manner that the extremity of the style was exactly at the centre
of the sphere. The shadow of this extremity, ou 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.

Lib. U. K. Hist. Ast. p. 5. 8 Del. A. A. i. 257.

SEQUEL TO THE EPOCH OF HIPPARCHUS. 163

this instrument was in fact used rather for dividing the day into
portions of time than for determining position.

Eratosthenes 7 observed the amount of the obliquity of the sun's
path to the equator : we are not informed what instruments lie 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 ob-
servations. If a circular rim or hoop were placed so as to coincide
with the plane of the equator, the inner concave edge would be en-
lightened 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 instru-
ment appears to be referred to by Hipparchus, as quoted by Ptolemy. 8
" 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.

A solstitial armil is described by Ptolemy, consisting of two cir-
cular rims, one sliding round within the other, and the inner one fur-
nished 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

* o

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 annils 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 -|^ of the circumference. 9

It was soon remarked that the whole circumference of the circle

l)elambre, A. A. i. SG. 8 Ptol. Synt. iii. 2.

Delambre, A. A. i. 87. It is probable that his observation gave liini 47 2 /i

47 2 ' 3 148 11-13 11 11

degrees. The fraction - = Q = =.^- which b very nearly -

164 THE GREEK ASTRONOMY.

was not wanted for such observations. Ptolemy 10 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 perpen-
dicular 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.

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? 1

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, 12 the observer looked along the face of the circle oi
the armil, so as to see its two edges apparently brought together, and
the star apparently touching them. 12

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. 14 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.

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, 15 that Hipparchus, after having

J0 Synt. i. 1.

11 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.)

"Delanib. A. A. \. 185.

13 Ptol. Synt. i. 1. T fl<r:r/) KoAA);/'io; dufiorepais avrwi' raTf ixiipaviiai; 5 darr,p 11

. v. 1. Del. A. A. 151.

SEQUEL TO THE EPOCH OF HIPP ARCH US. 165

abserved, for some time, right ascensions aud 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.

To the above instruments, may be added the diopira, and the
parullactic 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

O ' *-^

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. 13

" 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, 5-g- 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, 57^ degrees more forwards than the moon in longitude."
From these data the longitude of Regulus is calculated.

o o

From what has been said respecting the observations of the Alex-
andrian 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.

Del. A. A. ii. 248.

166 THE GREEK ASTRONOMY.

Sect. 4. Period from Hipparchus to Ptolemy.

WE have now to speak of the cultivators of astronomy frou\ cJi
time of Hipparchus to that of Ptolemy, the next great name winch
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 sup-
posed that their studies Avere carried on under considerable advan-
tages, inasmuch as they all enjoyed the liberal patronage of the kings
of Egypt. 17 The "divine school of Alexandria," as it is called by
Sy'nesius, 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.

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 Gemiuus, 13 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 Calippie
Period. We have likewise "The Circular Theory of the Celestial
Bodies" of Cleomedes, 19 of which the principal part is a development
of the doctrine of the sphere, including the consequences of the glob-
ular form of the earth. We have also another work on " Spherics"
by Theoclosius of Bithyuia, 20 which contains some of the most import-
ant propositions of the subject, and has been used as a book of in

Delamb. A. A. ii. 240. " B. c. 70. 19 B. c. 60. "" u.c. 50.

SEQUEL TO THE EPOCH OF HIPPAHCHUS. 167

Btruction even in modern times. Another writer on the same subject
is Menelaus, who lived somewhat later, and whose Three Books on
Spherics still remain.

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. 21 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 re-
sults ; and this branch of science also appears to have been formed by
Hipparchus, 24 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 : buf it is extraor-
dinary that the writers whom we have mentioned as coming after
Hipparchus, namely, Theodosius, Cleornedes, and Menelaus, do not
even mention the calculation of triangles, 23 either plain or spherical ;
though the latter writer 24 is said to have written on " the Table ol
Chords," a work which is now lost.

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, ss
who lived 270 B. c. at the court of Antigonus, king of Macedonia, de-
scribed the celestial constellations in two poems, entitled " Phenome-
na," and " Prognostics." These poems were little more than a versifi-
cation 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 connec-
tion 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 ex

"> Delamb. A. A. ii. 37. -= A. A. i. 117. M A. A. i. 240.

94 A. A. ii. 37. 25 A. A. i. 74.

168 THE GREEK ASTRONOMY.

tant; 26 Germanicus Caesar, 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. 27 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 expo-
sition ; but have no value in the history of science. AYe 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.

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 M
boundless progress in science to which man was destined. Though
this belief was no more than a vague and arbitrary conjecture, it sug-
gested other conjectures in detail, some of which, having been verified,
have attracted much notice. For instance, in speaking of comets, 28
Seneca says, " The time will come when those things which are now
hidden shall bt brought to light by time and persevering diligence.
Our posterity will wonder that we should be ignorant of what is so ob-
vious." " The motions of the planets," he adds, " complex and seem-
ingly confused, have been reduced to rule ; and some one will come
hereafter, who will reveal to us the paths of comets." Such convic-
tions and conjectures are not to be admired for their wisdom ; for
Seneca was led rather by enthusiasm, than by any solid reasons, to en-
tertain 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.

An important practical application of astronomical knowledge \vas
made by Julius Caesar, 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.

26 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
Arc/uiologia, vol. xviii.

27 Montucla, i. 221. 2S Seneca, Qit. X. vii. 25.

SEQUEL TO THE EPOCH OF HIPPARCHUS. 169

Sect. 5. Measures of the Earth.

THERE were, as we have said, few attempts made, at the period of
idiich we arc speaking, to improve the accuracy of any of the deter-
minations of the early Alexandrian astronomers. One question nat-
urally excited much attention at all times, the magnitude of the earth,
its figure being universally acknowledged to be a globe. The Chal-
deans, 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 bot-
tom by the sun's rays. At Alexandria, on the same clay, the sun was,
at noon, distant from the zenith by a fiftieth part of the circumference.
These two cities were north and south from each other : and the dis-
tance 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" says that the mathematicians
make the circumference 400,000 stadia. Hipparchus conceived that
the measure of Eratosthenes ought to be increased bv about one-tenth. 30

o

Posiclonius, the friend of Cicero, made another attempt of the same
kind. At Rhodes, the star Canopus but just appeared above the hori-
zon; at Alexandria, the same star rose to an altitude of Jg-th 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.

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, 31 the vast plain of Singiar, in Mesopotamia, was
the scene of this undertaking. The Arabian astronomers there divided

o

themselves into two bands, one under the direction of Chalid ben Ab-
dolmalic, and the other having at its head Alis ben Isa. These two

o

parties proceeded, the one north, the other south, determining the dis-
\ance by the actual application of their measuring-rods to the ground,

= a >t C<do, ii. ad tin. 30 Plin. ii. (cviii.) S1 Montu. 3") 7.

170 THE GREEK ASTRONOMY.

till each was found, by astronomical observation, to be a degree from
the place at which they started. It then appeared that these terres-
trial 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 thick-
ness of six grains of barley.

Sect. Q. Ptolemy's Discovery of Evection.

Br 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

O '

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 wri-
ters, 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 Hip-
parchus; his works contain ninety -nine hundre.dths 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, cor-
rection, and extension of the theory which he leceived. I speak of
Ptolemy, whose work, " The Mathematical Construction" (of the heav-
ens), 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 re-
ceived our first knowledge of it from the Arabic writers. The "Mer/iste
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 Eccen-
trics, of the observations and calculations which were employed in

SEQUEL TO THE EPOCH OF HIPPAECHUS. 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 conse-
quences of this theory, the work is a splendid and lasting monument
of diligence, skill, and judgment. Indeed, all the other astronomical
w r orks of the ancients hardly add any thing whatever to the informa-
tion 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 Hip-
parchus 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 astio-
nomical 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, ho
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
Evcction, 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 dis-
tances from the sun at different times. "These," he 52 says, "some-
times agreed, and sometimes disagreed." But by further attention to
the facts, a rule was detected in these differences. " As my knoAvledge
became more complete and more connected, so as to show the order oi
this new inequality, I perceived that this difference w r as small, or noth-
ing, 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 inequal-

32 Synth, v. 2.

172 THE GREEK ASTRONOMY.

ity 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 epicy-
clical hypothesis.

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 epi-
cycle, already employed to explain the first inequality, with the hy-
pothesis 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 ; 33 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. 34

The discovery of the Evection, and the reduction of it to the epi-

33 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 in-
equality more simply than his method did.

34 I will insert here the explanation which my German translator, the late distin-
guished 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 (2a i). At New and Full Moon, a
is or 180, and thus the Evection is 1. 3. sin I. At both quarters, or dichot-
omies, a is 90 or 270o, and consequently the Evection is + 1. 3 . sin I. The
Moon's Elliptical Equation of the centre is at all points of her orbit equal to G. 8 .
sin I. 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 great-
est inequalities of the moon's motion the quantity 6 . 3 . sin J 1 . 3 . sin b, or 5 .
sin J : 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 ob-
served the moon in her quarters, found for the sum of thoee Inequalities at those
points the quantity 6 . 3 . sin 5 + 1 . 3 . sin 6, or 7 . 6 . sin b ; and thus made tho
eccentricity of the moon as much too great at the quarters as the observers ol
eclipses had made it too small. He hence concluded that the eccentricity of the
Moon's orbit is variable, which is not the case.

SEQUEL TO THE EPOCH OF HIPPARCHUS. 173

cyclical theory, was, for several reasons, an important step in astron-
omy ; some of these reasons may be stated.

1. It obviously suggested, or confirmed, the suspicion that the mo-
tions 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 oi
theory to observation, we find, not only the stated phenomena, for
which the theory does account, but also residual phenomena, which
i emain 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

O ' O

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 gravita-
tion. The moon's first inequality arises from a different cause ; from
the same cause as the inequality of the sun's motion ; from the mo-
tion in an ellipse, so far as the central attraction is undisturbed by any
other. This first inequality is called the Elliptic Inequality, or, move
usually, the Equation of the Centre?'* All the planets have such in-
equalities, 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

S5 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 uni-
formly round the Sun as a centre in a circular orbit in the same time. An imagi-
nary 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 Longi-
tude of the mean Planet at a given time is easily found, because its motion is uni-
form. 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 quan-
tity which must be added to or subtracted from a mean quantity, to make it
to the true quantity; or rather, a quantity which must be added to or subtracts; 1
from a variably increasing quantity to make it increase equally.

174 THE GREEK ASTRONOMY.

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.

3. The Epicyclical Hypothesis was found capable of accommodating
itself to such new discoveries. These new inequalities could be repre-
sented 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 boen similarly exhibited ; and even Newton 36
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.

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 posi-
tion and connection of the heavenly bodies, which were suggested by
one set of phenomena, were not confirmed by the indications ot
another set of phenomena ; for instance, those relations of the epi-
cycles which were adopted to account for the Motions of the heavenly
bodies, were not found to fall in with the consequences of their ap-
parent 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. 37

36 Principle, lib. iii. prop. xxxv.

37 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 con-
'ains, when the moon is nearest the earth, 2010 seconds; when she is farthest ofl

SEQUEL TO THE EPOCH OF HIPPARCHUS. 175

Sect. 7. Conclusion of the History of Greek Astronomy.

I MIGHT HOW 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 sitn and moon have such inequalities. And this in-
equality 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 Eccentrici-
ties 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 pecu-
liarities which might not at first sight occur to the reader. The eclip-
tical 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 Eccen-
tricity 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. 38

1762 seconds ; that is, 24S seconds, or 4 minutes 8 seconds, less than in the former
case. [The two qantities are in the proportion of 8 to 7, nearly.] LMroio's 2iote.

3B 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,
:iii<l 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 Epi

176 THE GREEK ASTRONOMY.

^

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 pre-
tended 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 acquaint-
ance 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 ex
tending from Ptolemy to Copernicus ; we have no advance in Greek
astronomy after the former; no signs of a revival of the power of dis-
covery till the latter. During this interval of 1350 years, 39 the princi-
pal 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 chano-e. The Arab astronomer had been the scrupulous but

O

unprofitable servant, who kept his talent without apparent danger
of loss, but also without prospect of increase. There is little in Ara-

cycle was to the Periodic Time of the Epicyclical Centre on the Deferent, as the
synodlcal 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 P.lanet'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 synodlcal 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 versa. Littrow's Notes.

" Ptolemy died about A. D. 150. Copernicus was living A. D. 1500.

SEQUEL TO THE EPOCH OF HIPPARCHUS. 177

bic 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.

When the sceptre of western Asia had passed into the hands of the
Abasside caliphs, 40 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 success-
ors of Alexander the Great. Astronomy attracted peculiarly the fa-
vor 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." The
translation of the " Megiste Syntaxis" of Ptolemy, which thus became the
Almagest, is ascribed to Isaac ben Homain in this reign.

The greatest of the Arabian Astronomers comes half a century later.
This is Albategnius, as he is commonly called ; or more exactly, Mu-
luimmed ben Geber Albatani, the last appellation indicating that h-
was born at Batan, a city of Mesopotamia. 42 He was a Syrian prince,
whose residence was at Aracte or Kacha 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 obser-
vations led him to conceive that some improvements might be made in
their results. He found it necqssary 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.

These, however, did not prevent the publication of others. Under
the Caliph Hakcm (about A. D. 1000), Ebon lounis published Tables
of the Sun, Moon, and Planets, which were hence called the Hakemitc
Tables. Not long after, Arzachel of Toledo published the Tolctan Ta-

Gibbon, x. SI. Id. x. 36. <- Del. Astronomie dit Moyen Age, 4.

VOL. I. 12

178 THE GREEK ASTRONOMY.

bles. 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, Ulngh 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 16G5, 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 aus-
pices 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 es-
sence, and the rectitude of the quality of their motion." His system
consists, according to Delambre, 43 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, 44 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 ele-
ments, such as the obliquity of the ecliptic and the inclination of the
moon's orbit.

We must, however, notice one or two peculiar Arabian doctrines.
The most important of these is the discovery of the Motion of the
Sun's Apogee by Albategnius. He found the Apogee to be in longi-
tude 82 degrees ; Ptolemy had placed it in longitude 65 degrees. The
difference of 17 degrees was beyond all limit of probable error of cal-
culation, though the process is not capable of great precision ; and the
inference of the Motion of the Apogee was so obvious, that we cannot

Delambre, M. A. p. 7. 4J J/. A. p. ISO, &e.

SEQUEL TO THE EPOCH OF HIPPAECHUS. 179

Hgree with Delambre, in doubting or extenuating the claim of Alba-
tegnius 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 llth 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 ac-
quaintance 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 posi-
tion of the stars, and that for this purpose, it was necessary to conceive
two circles of about eight degrees radius described round the equinoc-
tial 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. 45 It
appears that Mohammed- Aboul Wefa-al-Bouzdjani, an Arabian astron-
omer of the tenth century, who resided at Cairo, and observed at
Lao-dad 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 sup-
posed 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

43 Sedillot, Nouvelles Kech. sar 1'Hist. cle 1'Astron. cliez les Arabes. Xouveau
Journal A*iatique. 1S36.

180 THE GREEK ASTRONOMY.

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 Muliazal 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."

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 cir-
cumstance 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

o

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 i> difficult to estimate too highly, in abolishing the

SEQUEL TO THE EPOCH OF HIPPARCHUS. 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 AVO
now employ. 46 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 oi
the Arabic word gib, which signifies a fold, the two halves of the chord
being conceived to be folded together.

The p-reat obligation which Science owes to the Arabians, is to

O O

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 instru-
ment is its index, which possesses an angular motion. Some of the
stars still retain their Arabic names; Aldebaran, 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 independ-
ently 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. 405), to have discovered the first equation of tin.'
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.

Mont. i. 376.

BOOK IV.

HISTORY

PHYSICAL SCIENCE IS THE MIDDLE AGES ;

OE,

VIEW OF THE STATIONARY PERIOD

OF

INDUCTIVE SCIENCE.

'

In vain, in vain ! the all-composing hour
Eesistless 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.

Dundad, B. iv.

INTRODUCTION.

WE liave 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 enumer-
ate 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 dis-
tino-uishino: features of the intellect and habits of those times. We

O O

must endeavor to delineate the character of the Stationary Period,
and, as far as possible, to analyze its defects and errors ; and thus ob-
tain some knowledge of the causes of its barrenness and darkness.

O

We have already stated, that real scientific progress requires dis-
tinct 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 tin-
profitably, 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 enthu-
siastic temper, which, when introduced into speculation, tends to sub-
ject 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 A^es.

186 PHYSICAL SCIENCE IX THE MIDDLE AGES.

CHAPTER I.
Ox THE INDISTINCTNESS OF IDEAS OF THE MIDDLE AGES.

firm and entire possession of certain clear and distinct general
-L 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 pre-
cision 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, con-
ceiving clearly the motions and combinations of motion which entej
into his theory, saw that the relative lengths of the seasons were suffi-
cient 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. TVhen 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

INDISTINCTNESS OF IDEAS. 187

jeeble 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 Laertius 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 ap-
propriately been called the Encyclopoedia 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 apprehen-
sion 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 mat-
ters may or must have its weight, is here of no force ; and the tech-
nical precision of ideas which the terms of a sound physical theory
usually demand, renders a mere statement of the doctrines very impei'-
fectly intelligible to readers familiar Avith common notions only. To
dwell upon such collections of opinions, therefore, both implies, and
produces, in writers and readers, an obscure and inadequate apprehen-
sion 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 state-
ments 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 sound physical
speculation.

188 PHYSICAL SCIENCE IX THE MIDDLE AGES.

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, Bibli-
ographical Notices, and similar writers. All such writers are worth-
less 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 de-
pended. 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 exam-
ple, that of Pappus, in the eighth Book of his Mathematical Collec-
tions, 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 ap-
prehension 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 stqyport 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 mechan-
ical 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

INDISTINCTNESS OF IDEAS. 18D

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 Archi-
medes 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 in-
creased as the inclination became greater. Thus his views were vague ;
he had no clear conception of mechanical action, and he tried a gee-
metrical conjecture. This is not the way to real knowledge.

Pappus (who lived about A. D. 400) was one of the best mathemati-
cians 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 spec-
ulative 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 Aris-
totelian school, concerning Motion and Power ; and, being thus em-
ployed among doctrines in which there was involved no definite mean-
ing capable of real exemplification, they, of course, could not acquire
sound physical knowledge. "We have already seenr 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 man-
ner, to facts, the vagueness of their notions was not corrected by any
collision with observation. The physical doctrines which they extract-
ed 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 con-
tinued 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 mechan-
ics 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 PHYSICAL SCIENCE IN THE MIDDLE AGES.

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 un-
tried, men heard and repeated them, without perceiving the incon-
gruities 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 experi-
ment. We have an example of the confusion of thought to which
the Aristotelians were liable, in their doctrine concerning; fallino- bodies.

' O O

" 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 Rernora, a little fish which was
said to be able to stop a large ship merely by sticking to it. 1 Lucan
refers to this legend in a poetical manner, and notices this creature
only in bringing together a collection of monstrosities ; but Pliny re-
lates the tale gravely, and moralizes upon it after his manner. " What,"
he cries, 2 " 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

tj J V

1 Lucan is describing one of the poetical compounds produced in incantations.

Hue quicquid fcetu genuit Natura siuistro

Miseetur: non spuma canum quibus unda timori est

Viscera non lyncis, noil durse nodus hysenoa

Defuit, et cervi pasti serpente medullas ;

Non puppes retinens, Euro tendente rudentes

In mediis Echineis aquis, oculique draconum.

Etc. Phcirsalia, iv. 670.

Pliu. Hist. -V. xxxii. 5.

INDISTINCTNESS OF IDEAS. 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 cap-
tive 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 Gains, the emperor, when he was sail-
ing 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 in-
dignant that this animal should interpose its prohibition to his prog-
ress, when impelled by four hundred rowers. It was like a slug ; and
had no power, after it was taken into the ship."

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 archi-
tecture. All architecture, to possess genuine beauty, must be mechan-
ically 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 mechan-
ical 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 PHYSICAL SCIENCE IN THE MIDDLE AGES.

column, turned back to the wall, and adhered to it in the intervening
space. The splendid remains of Palmyra, Balbec, Petra, exhibit end-
less 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.

O

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 ineas^e, 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 has been obliged to exercise great ingenuity, in
order to discover the method by which Ibn lounis proved his solution
of certain difficult problems.

b. Indistinctness of Ideas shoivn by Skeptics. The same unsteadi-
ness 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

3 Debmb. M. A. p. 125-8.

INDISTINCTNESS OF IDEAS. 193

fire 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 unprofit-
able 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 Astrol
ogers, against the Musicians, as well as against Grammarians, Ehet-
ovicians, 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, how-
ever, that his objections are rather to the metaphysical grounds, than
to the details of the sciences ; he rather denies the possibility of spec-
ulative truth in general, than the experimental truths which had been
then obtained. Thus his objections to geometry and arithmetic arc-
founded on abstract cavils concerning the nature of points, letters,
unities, (fee. 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 dogma?,
though even the former had nothing which excited his. admiration.

C3 O

The skepticism which denies the evidence of the truths of wind
the best established physical sciences consist, must necessarily involve
a very indistinct apprehension of those truths ; for such truths, prop-
erly exhibited, contain their own evidence, and are the best antidote
VOL. I. 13

I'J-i PHYSICAL SCIENCE IX THE MIDDLE AGES.

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 witn Algazel or Algezeli, who is adduced bv Deererando 4

o o */ o

ns 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 AlgazeVs Destructions of
the Philosophers. It appears that he contested the fundamental prin-
ciples 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.

[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 Philosophigues chcz les Arabes, et notamment
sur la Doctrine cV Algazzali, par August Schmolders. Paris. 1842.
From this book it appears that Degerando's account of Algazzali is
correct, when he says 5 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 revela-
tion, but also to the free exaltation of a mystical enthusiasm." It is
remarked by Dr. Schmolders, following M. de Hammer-Purgstall, that
the title of the work referred to in the text ought rather to be Mutual

O

Refutation of the Philosojihcrs : 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. Schmolders has published,
On the Errors of Sects, (&c., contains a kind of autobiographical ac-
count 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 Degerando, Hist. Comp. de Systemes, iv. 224.

Hist. Comp. iv. p. 227. 6 Essai, p. 33.

INDISTINCTNESS OF IDEAS. 195

0. JTtyitct 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 compara-
tively 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 pre-
sented to men's minds, and the serious task?, 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 philoso-
phy is that which teaches us our moral duties and religious hopes. 7
Thus Eusebius savs, 8 "It is not through ignorance of the things ad-

*> ' O O O

mired by them, but through contempt of their useless labor, that we
think little of these matters, turning our souls to the exercise of better

* O

things." When the thoughts were thus intentionally averted from
those ideas which natural philosophy involves, the ideas inevitably be-
came very indistinct in their minds; and they could not conceive that
any other persons could find, on such subjects, grounds of clear con-
viction and certainty. They held the whole of their philosophy to be,
as Lactantius 9 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 \vhieh 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.

7. Question of Antipodes. TVith 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

Brucker, iii. 817. 3 /Voy;. Ev. xv. 61. 9 List. 1. iii. init.

196 PHYSICAL SCIENCE IX THE MIDDLE AGES.'

We have some remarkable examples of this; and a very notable one
is the celebrated question of the existence of Antipodes, or persons in-
habiting 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 geomet-
rical necessity, from a clear conception of the various points of knowl-
edge 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 in-
evitable 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 re-
ferred 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 ex-
perience* 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 in the fourth century, argues this
matter in a way very illustrative of that impatience of such specula-
tions, 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 down-
wards, 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.

In the sixth century, indeed, in the reign of Justinian, we find a
writer (Cosmas ludicopleustes") who does not rest in this obscurity of

< Inst. 1. iii. 23.

11 Montfaucon, Collect io Nova Patnim, t. ii. p. 113. Cosmas Indicopleustcs.
^hristiaiiorum Opiuiones dc Mundo, sive Topograpliia Christiana.

INDISTINCTNESS OF IDEAS.

representation ; but in this case, the distinctness of his 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 (who
flourished A. D. 400) the opinion is treated on other grounds ; and with-
out 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 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 prel-
ate was shocked at the assumption, as it seemed to him, of a world of
human beiuo-s, out of the reach of the conditions of salvation ; and

O '

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 bish-
opric, 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' 4 notes the
opinion of the rotundity of the earth as an ." unsafe" doctrine, only a
few years before Columbus visited the other hemisphere.

8. Intellectual Condition of the Religious Orders. It must be rec-
ollected, 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, enter-
tained the true opinion of the figure of the earth. Thus Boethius 15 (in
the sixth century) urges the smallness of the globe of the earth, corn-

is Civ. D. xvi. 9.

13 It appears, however, that scriptural arguments were found on the other
St. Jerome says (Comm. in Ezech. \. 6), si'rakingr of the two cherulnms with four
faces, seen by the prophet, and the interpretation of the vision : "Alii vcro qui
philosophorum stultam scquuntur sapientiam, >\\w homi.<pheria in duobus tempi'
cherubim, nos et antipodes, quasi supine el I'li'lentcs homines suspieantur."

11 Montfauc. Pair. t. ii. 15 U i I 'ons. ii. pr. 7.

1

198 PHYSICAL SCIENCE IN THE MIDDLE AGES.

pared 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 acquaint-
ance 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 con-
struction. 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 steadi-
ness the elementary ideas on which it depends, we may here mention,
after Montucla, 16 Adelbold, whose work On the Sphere was addressed
to Pope Sylvester, and whose geometrical reasonings are, according to
Montucla, 17 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; Robeit of Lorraine,
who was made Bishop of Hereford by William the Conqueror, in con-
sequence of his astronomical knowledge. lu the next century, Add-
hard Goth, an Englishman, travelled among the Arabs for purposes of
study, as Gerbert had clone in the preceding age ; and on his return,
translated the Elements of Euclid, which he had brought from Spain
or Egypt. Robert Grostete, Bishop of Lincoln, was the author of an
Epitome on the Sphere ; Eoger Bacon, in his youth the contemporary
of Robert, and of his brother Adam Marsh, praises very highly their
knowledge in mathematics.

" 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

Mont. i. 502. l: Ib. i. 503.

INDISTINCTNESS OF IDEAS. 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 iu 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 in-
spires 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 iu
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 specu-
lative subjects had time and opportunity to become clear and steady.
The studies which were cultivated under the name of the Seven Liberal
Arts, iKrcssarily tended to favor this effect. The Trivium indeed,
which consisted of Grammar, Logic, and Rhetoric, had no direct bear-
ing 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

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 1
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 tlu/
earth is flat, and the waters of the sky sustained above a material floor,
through which in showers they descend. Yet the true doctrines oi

O /

13 Brack, iii. 597.

19 Roger Bacon, iu liis Specula Mathematica, cap. i. says, " llarum scicnth.riiii
porta et clavis cst mathematics, qiuim sancti a, principle) mundi invcnerunt, etc.
Cnjus ncgligcntia jam per ti-lginta itl qttii</r<{</i/</,i annos destruxit totuin studiuir
Latinorum." I do not know on what occasion this neglect took place.

200 PHYSICAL SCIENCE IX THE MIDDLE AGES.

astronomy appear to have had some popular circulation. For instance,
a French poem of the time cf Edward the Second, called Ymage du
Monde, contains a metrical account of the earth and heavens, accord-
ing to the Ptolemaic views ; and in a manuscript of this poem, pre-
served in the library of the University of Cambridge, there are repre-
sentations, 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 doivn,. 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 w : hat he there sees. After they have
crept through the aperture in which Lucifer is placed, the poet says,

" To Icvai gli occhi e credetti vedere
Lucifero com' io 1' avea lasciato,
E vidile le gambe in su tenere."

" Questi come e fitto

Si sottasopra?"

"Qnando mi volsi, tu passast' il punto
Al qual si traggou cl' ogni parte i pesi."

Info-no, xxxiv.

"I raised mine eyes,

Believing that I Lucifer should see

"Where lie 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." GARY.

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.

THE COMMEXTATORIAL SPIRIT. 201

The philosophical notions of up and dowu are too much at variance
wit ii 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,
aud 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 MlDDLE 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

O '

those who became acquainted with, them could not but give to them,
there appeared a disposition among men to lean on the authority ol
some of these teachers; to study the opinions of others as the only
mode of forming their own ; to read nature through books ; to at-
tend 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, aud
highly characteristic of the stationary period; it gave, in a great de-
gree, a peculiar bias and direction to the intellectual activity of many
centuries; and the kind of labor with which speculative men were oc-
cupied in consequence of this bias, took the place of that examination
of realities which must be their employment, in order that real knowl-
edge may make any decided progress.

In some subjects, indeed, as, for instance, in the domains of morals,
poetry, aud the art?, whose aim is the production of beauty, this op-
position 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 PHYSICAL SCIENCE IN THE MIDDLE AGES.

prevail in men's minds are the material upon which we must work,
ihe 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 in-
dications so strong as to be truly remarkable ; for instance, in the
efforts of the antiquarians of almost every European country to assim-
ilate 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^/iysicaZ philos-
ophy 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 re-
placed by C9mmentators ; 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 au-
thority of thoughtful and sagacious men, a disposition which men in
general neither reject nor think they ought to reject in practical mat-
ters, naturally clings to them, even in speculation. It is a satisfaction
to us to suppose that there are, or have been, minds of transcendent pow-
ers, of wide and wise views, superior to the common errors and blind-
ness of our nature. The pleasure of admiration, and the repose of con-
fidence, 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 tlie 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 stu-

THE COMMENTATORIAL SPIRIT. 203

dying Aristotle or Plato. Moreover, a large portion of this employment
is of a kind the most agreeable to most speculative minds; it coi.
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, 1
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.

How natural it is to select a great writer as a paramount anthoiitv,
and to ascribe to him extraordinary profundity and sagacity, we mny
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 ami
sciences, has, as we know, found favor even in modern times. To pa^
over earlier instances of this feeling, we may observe, that Strabo begins
his Geography by saying that he agrees with Hipparchns, 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 ; bat
in phrases which, to most persons, might appear the mere play of a
poetical fancy, or a casual selection of circumstances, he finds unques-
tionable evidence of a correct knowledge of general geographical
truths. Thus, 2 when Homer speaks of the sun " rising from the soft
ind deep-flowing ocean," of his "splendid blaze plunging in the ocean;"
of the northern constellation

" Alone uiiwashen by the ocean \vi\\c ;''

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.

1 Dcgeran Jo, flist. des Syst. de P kilos, iii. p. 1C4. 2 Strabo, . p. 5.

20i PHYSICAL SCIENCE IN THE MIDDLE AGES.

2. Character of Commentators. The spirit of commentation, as has
already been suggested, turns to questions of taste, of metaphysics, o.
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

o

physical science for their subject (as Proclus, who commented on
Euclid's Geometry, and Simplicius, on Aristotle's Physics), these com-
mentaries were, in fact, rather metaphysical than mathematical. It
does not appear that the commentators have, in any instance, illus-
trated the author by bringing his assertions of facts to the test of
experiment. Thus, when Simplicius comments on the passage con-
cerning a vacuum, which we formerly adduced, he notices the argu-
ment 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. 3

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 ho does not seek to obtain ad-
ditional 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 CommeutatorVemployment 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 under-
rate the relative value of other kinds of mental exertion. He may

3 Simplicius, p. 170.

THE COMMENTATOEIAL SPIRIT. 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 por-
tion 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 con-
cluding a course of lectures on Euclid, delivered at Oxford. 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."

"We here speak of the peculiar province ot 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

' O

learned men in the stationary period, which came under this descrip-
tion, belong to another class.

o

3. Greek Commentators on Aristotle. The commentators or dis-
ciples 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 mas-
ter ; 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, 5 who nourished in the third century, wrote a book
on the PrcdlcaUcs, which was found to be so suitable a complement

' Exolvi per Dei gratiam, Domini auditores, promissum ; liberavi fid em
explicavi pro meo modulo, defiuitiones, petitiones, communes sententias, et octc
I'riores propositions Elementorum Euclidis. Hie, annis fessus, cyclos artemqiie
repono. Buhle, Arist. i. 2S4.

206 PHYSICAL SCIENCE IN THE MIDDLE AGES.

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, Jiabit,
action, passion.

At a later period, the Aristotelian commentators became more ser-
vile, 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 Aphrodisicnsis, who lived at the end of the
second century, is of this class ; " sometimes useful," as one of the
recent editors of Aristotle says ; 8 " but by the prolixity of his interpre-
tation, by his perverse itch for himself discussing the argument ex-
pounded 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, 7 as Alexander, Ammonius, and others, em-
ployed 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 8 entertained the design of translating into

o o

Latin the whole of Aristotle's and Plato's works, and of showino- their

' o

agreement ; a gigantic plan, which he never executed. Others em-
ployed 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, 9
who had pretended to incorporate his doctrines iuto those of the New
Platonic school, or even to reconcile him with Plato himself on the
subject of ideas. Others, again, wrote Epitomes, Compounds, Ab-
stracts ; and endeavored to throw the works of the philosopher into
Borne simpler and more obviously regular form, as John of Damascus, in

Ib. i. 2S3. ? ih. i. 311.

8 Degernmlo, Hist. <les Syst. iv. 100. 9 Ib. iv. 155.

THE COMMEXTATORIAL SPIRIT. 207

the middle of the eighth century, who made abstracts of some of Aris-
totle'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 Arnrou, the conqueror of Egypt ; the latter
was at first secretary to the Caliph, but afterwards withdrew to a
monastery. 10

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 philos-
ophy. Leo, the Isaurian, who was a zealous Iconoclast, abolished
also the schools where general knowledge had been taught, in com-
bination with Christianity, 11 yet the line of the Aristotelian commen-
tators was continued, though feebly, to the later ages of the Greek
empire. Anna Comneua 12 mentions a Eustratus who employed him-
self 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 Bleniniydes 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, 13 &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 dis-
dained the authority of their predecessors. He could hardly help
remarking in how different a spirit philosophy had been pursued since
their time.

4. Greek Commentators of Plato and others. I have spoken prin-
cipally 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 com-
mented on by Ammonius ; Plotinus's Enneads were commented on by
Proclus and Dexippus. Psellus'' 1 the elder was a paraphrast of An*

10 Deg. iv. l.v). ' Ib. iv. 185. '-' Ib. iv. Hi7. 13 Ib. iv. 103. Dcg. iv. 1G9.

208 PHYSICAL SCIENCE IX THE MIDDLE AGES.

totle ; 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 meu, the emperor Leo, surnarned the Philos-
opher, aud Photius the patriarch, who exerted themselves to restore
the study of literature at Constantinople. We still possess the Collec-
tion of Extracts of Photius, which, like that of Stobaeus and others,
shows the tendency of the age to compilations, abstracts, and epitomes,
the extinction of philosophical vitality.

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 direc-
tion, 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 Linnaeus, Avon 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 dragmno; the car of

o oo o

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 conscious-
ness, 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

THE COMMENTATOEIAL SPIRIT. 209

vmpathy 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 en-
riched 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 iu the East, before the growth of the Saracen power. In
the sixth century, a Syrian, Uranus, 15 encouraged by the love of phi-
losophy manifested by Cosroes, had translated some of the writing?
of the Stao-irite : about the same time, Sergius had given some trans-

o o o

lations in Syriac. In the seventh century, Jacob of Edessa translated
into this language the Dialectics, and added Notes to the work. Such

O O '

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.

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
Hfysticism. But they are, for the most part, sufficiently strong exam-
ples of the peculiar spirit of commentation, to make it fitting to notice
them here. At the head of them stands 16 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 iu 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. 17 Avicenna (Ebn Siua)

Deer. iv. 106. '' Ib. iv. 1ST. " Ib. iv. 203.

VOL, I. 14

210 PHYSICAL SCIENCE IX THE MIDDLE AGES.

was at once the Hippocrates and the Aristotle of the Arabians ; ana
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. Aviceuna is
conceived, by some modern writers, 13 to have shown some power of
original thinking in his representations of the Aristotelian Logic and
Metaphysics. Averroes (Ebn Eoshd) of Cordova, was the most illus-
trious of the Spanish Aristotelians, and became the guide of the school-
men, 19 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 servil-
ity with which he maintains that Aristotle 20 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

O

directed against an Arabian skeptic, of the name of Algazel, whom we
have already noticed.

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 dogma-
tism ; 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
jf science ; but we must previously consider some other features in the
character of the Stationary Period.

lg Deg. iv. 206. 19 Ib. iv. 247. Averroes died A. D. 1206. 20 Ib. iv. 243.

TH$IR MYSTICISM. 211

CHAPTER III.
OF THE MYSTICISM OF THE MIDDLE AGES.

JT lias 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 ; fur, 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 con-
nection and causation, men attempted to reduce such occurrences
under spiritual and supersensual relations and dependencies ; they re-
ferred 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 As-
trology, the study of the Composition of bodies became Alchemy,
Mathematics became the contemplation of the Spiritual Eelations 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 employ-
ments and the thoughts of the times now under our notice. This
tendency materially affected both men's speculations and their labors
in the pursuit of knowledge. By its direct operation, it gave rise to
the newer Platonic philosophy among the Greeks, and to correspond-
ing 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 im-
peded 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 PHYSICAL SCIENCE IX TI^E MIDDLE AGES.

tendencies of thought which accompanied the retrogradation of induc-
tive 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 appli-
cable to such cases ; not to general rules capable of direct verifica-
tion ; 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. JWeoplatonic Tkcosophy. The Neivcr Platonism is the first ex-
ample of this Mystical Philosophy which I shall consider. The main
points which here require our notice are, the doctrine of an Intel-
lectual 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 consti-
tute, 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 employ-
ment 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 Neoplatouic philoso-
phy requires our notice as one of the most remarkable forms of this
Mysticism.

Though Ammonias Saccas, who flourished at the end of the second
century, is looked upon as the beginner of the Neoplatouists, his disci-
ple Plotinus is, in reality, the great founder of the school, both bv his

THEIR MYSTICISM. 213

works, winch, still remain to us, and by the enthusiasm which his char-
acter 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. 2*0). His disciple, Porphyry, has giv.-n
us a Life of him, from which we may sec how well his habitual manners
were suited to make his doctrines impressive. " Plotinus, the philoso-
pher of our time," Porphyry thus begins his biography, " appeared like
a person ashamed that he was in the body. In consequence of tin*
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 inclosed 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 disci-
ple 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 1 in the classes of things which it in-
cludes. To the Intelligible World, man's mind ascends, by a triple
road which Plotinus figuratively calls that of the Musician, the Lover,
the Philosopher. 2 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."

The conclusion of the work is, 3 as might be supposed, upon the ap-
proach 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

1 vi. Euneatl, iii. 1. - ii. E. ii. 2. 3 vi. Enn. ix. 3.

21-t PHYSICAL SCIENCE IX THE MIDDLE AGES.

look from him we revolve about him : we do not always look at liiin,
but when we do, we have satisfaction and rest, and the harmony which
belongs to that divine movement. In this movement, the mind be-
holds the fountain of life, the fountain of mind, the origin of being, the
cause of good, the root of the soul." 4 " There will be a time when this
vision shall be continual ; the mind being no more interrupted, nov
suffering any perturbation from the body. Yet that which beholds is
not that Avhich is disturbed ; and when this vision becomes dim, it
does not obscure the knowledge which resides in demonstration, and

O '

faith, and reasoning ; but the vision itself is not reason, but greater
than reason, and before reason." 5

The fifth book of the third Enneacl has for its subject the Daemon
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 Daemon which they say
accompanies each man." 6 These daemons were, however (at least by
later writers), invested with a visible aspect and with a personal char-
acter, 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 dsemous or genii
visible ; and the Treatise on the Mysteries of the Egyptians, which is
attributed to lamblichu?, gives an account of the secret ceremonies,
the mysterious words, the sacrifices and expiations, by which this was
to be done.

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 devo-
tional exaltation, combined with the grossest superstitious of Paganism.
The successors of lamblichus appeared rather to hold a priesthood,
than the chair of a philosophical school. 7 They were persecuted by
Coustantine and Constantius, as opponents of Christianity. Sopater, a

4 vi. Enn. ix. 9. 5 vi. Erm. ix. 10. Ficinus. Comm. in. v. Enn. iii.

~ Dcg. iii. 407.

THEIR MYSTICISM. 2U

Svrian philosopher of this school, was beheaded by the former
ror on a charge that he had bound the -winds by the power of magii .'
But Julian, who shortly after succeeded to the purple, embraced with
ardor the opinions of lamblichus. Proclus (who died A. D. 48V) was
one of the greatest of the teachers of this school ; 9 and was, both in his
life and doctrines, a worthy successor of Plotinus, Porphyry, and Tam-
blichus. We possess a biography, or rather a panegyric of him, by his
(liscij.l<! 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, puri-
ficatory, 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 t he-
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 prac-
tices 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 doc-
trines of his sect. He appears before us rather as a hierophant than ;,
philosopher. A large portion of his life was spent in evocations, puri-
fications, fastings, prayers, hymns, intercourse with apparitions, and
with the gods, and in the celebration of the festivals of Paganism, es-
pecially 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.

The reader will find an.intcresting view of the School of Alexandria,
in M. Uarlholemy Saint-Hilaire's Riqtport on the Memoires sent to th.-
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 iu 1844. M. Saint-Hilaire has prefixed to i\u$, Rapport a dis-
sertation 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 Science?, has led me to do. Although he finds much to ad-

* Gibbon, iii. 352. 9 Dej. iii. 41?.

216 PHYSICAL SCIENCE IN THE MIDDLE AGES.

mire in the Alexandrian philosophy, he declares that they were incapa-
ble 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." Plotiuus 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, es-
pecially in him ; and which we may call Mystical Arithmetic. Like
all the kinds of Mysticism, this consists iu the attempt to connect our
conceptions of external objects by general and inappropriate notions of
goodness, perfection, and relation to the divine essence and govern-
ment ; instead of referring such conceptions to those appropriate ideas,
which, by due attention, become perfectly distinct, and capable of be-
ing 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 concern-
ing number have decidedly a mystical character. The mere mathe-
matical relations of numbers, as odd and even, perfect and imperfect,

THEIR MYSTICISM. 217

abundant and defective, were, by a willing submission to an enthu-
siastic 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 10 k
said to have written a treatise on the number ten : Telauge, the daugh-
ter 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 virtuou?,

N<i< //a TOV aftcrlpa ^u^a Trapadtivra TCTpaKTvv
Tiayav aevvdov

By him who stainpt The Four upon the mind,
The Four, the fount of nature's endless stream,

In Plato's works, we have evidence of a similar belief in religious
relations of Number; and in the new Platouists, this doctrine was es-
tablished 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." " The intelligi-
ble and intellectual gods produce all things triadically ; for the monads
in these latter are divided accorxliuo- to number : and what the monad

o

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.

The relations of space were dealt with in like manner, the Geomet-
rical properties being associated with such, physical and metaphysical
notions as vague thought and lively feeling could anyhow connect

O O O v

with them. We may consider, as an example of this, 12 Plato's opinion

Mont. ii. 123. 1! Prod. v. 3, Taylors translation. Stanley, Hist. Phil.

218 PHYSICAL SCIENCE IX THE MIDDLE AGES.

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 parti-
cles 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 .he zodiac. In
such examples we see how loosely space and number are combined or
confounded by these mystical visionaries.

These numerical dreams of ancient philosophers have been imitated
by modern writers ; for instance, by Peter Bun go 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, 13 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.

3. Astrology. Of all the forms which mysticism assumed, none was
cultivated more assiduously than astrology. Although this art pre-
vailed 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 de-
cree of the senate, both during the times of the republic and of the ern-
oire. 14 The recurrence of this act of legislation shows that it was not

o

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 de-
termine the course of a man's character and life from the configuration
>f the stars at the moment of his birth. We do not possess any of the

3 Montncla, i. 511. 14 Tacit. Ann.u. 32. xii. 52. Hist. I. 22, II. 62.

THEIR MYSTICISM. 210

speculations of the early astrologers ; and we cannot therefore be cer-
tain 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 (arroppomc) 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 associa-
tion, 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.

That common sense of mankind which teaches them that theoretical
opinions are to be calmly tried by their consequences and their accord-
ance 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, 15 rejected the pretensions of the Chaldeans; and Cicero
himself reasons against them with arguments as sensible and intelligent

o o o

as could be adduced by a writer of the present day ; such as the dif-
ferent fortunes and characters of persons born at the same time ; and
the failure of the predictions, in the case of Pompey, Crassus, Casar,
to whom the astrologers had foretold glorious old age and peaceful
death. He also employs an argument which the reader would per-
haps 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 ?"

Pliny argues on the same side, and with some of the same argu-
ments.' 5 "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

The impression made by these arguments is marked in an anecdote
told concerning Publius Nimdius Figulus, a Roman of the time oi

o o o

Julius Cffisar, whom Lucan mentions as a celebrated astrologer. It is.

15 Cic. de Div. ii. 42. 1C Hist. Rat. vii. 49.

220 PHYSICAL SCIENCE IN THE MIDDLE AGES.

said, that when an opponent of the art urged as an objection the dif-
ferent 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 17 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 ex-
amples 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 nar-
rative. 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 Capreas. They reached this place by a narrow path,
accompanied by a single freed man of great bodily strength ; and on
their return, if the emperor had conceived any doubts of their trust-
worthiness, 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 ex-
amined 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.

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

17 Ann. vi. 22

THEIR MYSTICISM. 221

out unstable minds of the later philosophical schools of Alexandria,
Athens, and Rome. \Ye have a treatise on astrology by Proclus,
which will serve to exemplify the mystical principle iu 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 oi
the astrological work. A few notices of the commentary of Proclus
will suffice. 18 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 : lie 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 accord-
ing to her light; the advance of the sea, and its recess, are regulated
by her risino- and setting: and along with her, fruits and animals wax

J CTJ O ' O

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'-
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, \vhich, 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

" I. 2. 19 I. 4.

222 PHYSICAL SCIENCE IX THE MIDDLE AGES.

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.

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 ety-
mological 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 especia.
influences and subjects assigned to them. In particular, each sign was
supposed to preside over a particular part of the body ; thus Aries Lad
the Lead 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 hon-
ors, friends and enemies, were distributed.

AVe need not attempt to trace the progress of this science. It pre-
vailed 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 astron-
omers, was also a great astrologer; and his work on the latter subject,
11 De Magnis Conjunctionibus, Annornm Revolutionibus ac eorum Pcr-
fectionibus," Avas long celebrated in Europe. Aboazen Haly (the wri-
ter of a treatise " De Judiciis Astrorum"), who lived in Spnin in the
thirteenth century, w r as 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

O '

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 pro-
fessors 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
vhat avast accumulation of well-observed facts is requisite to establish

THEIR MYSTICISM. 22

any true rule ; and it is well known Low long, in spite of facts, false
and groundless rules (as the dependence of tlie 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 con-
nection 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 reason-
ing, could, of course, never be got rid of; and the bewildering feeling
of earnestness and solemnity, with which the connection of the heav-
ens with man was contemplated, never died away. In other respects
however, the astrologers fell into a servile commentator! al 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 na-
tions 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 ori-
ginating sound and rational general principles. The Arts may have
had their birth in all parts of the globe ; but it is only Europe, at par-
ticular favored periods of its history, which has ever produced Sciences.

~YV"e 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 unno-
ticed, Alchemy and Magic.

AVe may observe, before we proceed, that the deep and settled in-
fluence 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, Tvcho Brahe,

224 PHYSICAL SCIENCE IN THE MIDDLE AGES.

Francis Bacon, are examples of this. These, or most of them, rejected
all the more obvious and extravagant absurdities "with which the sub-
ject had been loaded ; but still conceived that some real and valuable
truth remained \vhon all these were removed. Thus Campanella, 2c
whom we shall have to speak of as one of the first opponents of Aris-
totle, wrote an "Astrology purified from all the Superstitions of the
Jews and Arabians, and treated physiologically."

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 ap-
plication was to physical properties. This is the form in which the
subject is presented to us in the earliest writings which AVC possess on
the subject of chemistry ; those of Geber 21 of Seville, who is supposed
to have lived in the eighth or ninth century. The very titles of Ge-
ber'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 Perfec
tion." 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 rep
resented 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 conquer-
ors, 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? 2 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 oper-
ations were described in phraseology of this sort, the enthusiasm of the

20 Bacon, De Aug. iii. 4. =' Thomson's Hist, of diem. i. 117.

42 Boyle, Thomson's Hist. Ch. \. 25. Ciirolus Musitanus.

THEIR MYSTICISM. 225

'uncy would bo added to that of the liopes, and observation would not
be permitted to correct the delusion, or to suggest sounder and more
rational views.

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 sub-
stantial 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, it
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. Marjlc. 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. In-
capacity and indisposition to perceive natural and philosophical causa-
tion, an enthusiastic imagination, and such a faith as can devise and

O '

maintain supernatural and spiritual connections, 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.
VOL. I. 13

226 PHYSICAL SCIENCE IX THE MIDDLE AGES.

is an additional exemplification of those habits of thought which pre
vented the progress of real science, and the acquisition of that com-
mand 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 prac-
tical knowledge, is a feature of those times, which shows how exten-
sive 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 ad-
mired, 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.
Naudseus, 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
Villa Nova, 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,

THEIR MYSTICISM. 227

Popes Sylvester the Second and Gregory the Seventh, had been in-
volved in the wide calumny. In the same way in which the vulgar
jonfouuded the eminent learning and knowledge which had appeared
in recent times, with skill in dark supernatural arts, they converted
into wizards all the best-known names in the rolls of fame ; as Aris-
totle, 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 intel-
lectual 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 astrol-
ogers, 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 w~ere stronger minds, which
threw off in a greater or less degree this train of delusive and unsub-
stantial ideas, is true ; as, on the other hand, Mysticism, among the
vulgar or the foolish, often went to an extent of extravagance arid super-
stition, of which I have not attempted to convey any conception. The
lesson which the preceding survey teaches us is, that during the Sta-
tionary Period, Mysticism, in its various forms, was a leading character,
both of the common mind, and of the speculations of the most intel-
ligent and profound reasoners; and that this Mysticism was the oppo-
site 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 ob-
tained had no enduring value ; they did not exhibit a permanent
record of old truths, nor a firm foundation for new. Experience col-
lected 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 tc
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 PHYSICAL SCIENCE IX THE MIDDLE AGES.

CHAPTER IV.
OF THE DOGMATISM or THE STATIONARY PERIOD.

j~N speaking of the character of the age of commentators, we noticed
J- 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 ac-
credited writings, resolved that no one should find there, or in any
other region, any other truths; speculative men became tyrants with-
out 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. 1 The general nature of the process may be briefly stated to
have been the following.

The tendencies of the later times of the Roman empire to a com-
menting 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 intel-
lectual mechanism of the Greek, fixed and augmented the prevalent
feebleness and barrenness of intellect. Men forgot, or feared, to con-
sult nature, to seek for new truths, to do what the great discoverers of
ether times had clone ; 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

1 Dr. Ilampden, in the Life of Thomas Aquinas, in the Enc-yc. Metrop, Degerando,
Hist. Coiiifiin'e, vol. iv. Also Tennemann, Hist, of Phil. vol. viii. Introduction

DOGMATISM OF THE STATIONARY PERIOD. 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 arc, 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 great e.-l
fame ; and two of those, who most occupied the attention of students,
Plato and Aristotle, w r ere, on several points of this nature, very diverse
from each, other in their tendency. The attempt to reconcile these
philosophers by Boethius and others, AVO 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 lead-
ing 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 reconcil-
ing them to their heavenly Master, but also to be a Philosophy in the
widest sense in which the term had been used ; a consistent specula-
tive 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, Avith no due apprehension of the
necessary ministry of Observation, and Reason dealing with observation,
by \vhich alone such a system can be embodied. It Avas held without
any regulating principle, that the philosophy Avhich had been be-
queathed to the world by the great geniuses of heathen antiquity, and
the Philosophy which was deduced from, and implied by, the Revela-
tions 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. 2 Anselm, in the eleventh century, again brought it forward ; : '
and Bernard de Chartres, in the thirteenth. 4

This view was confirmed by the opinion Avhich prevailed, concern-
ing the nature of philosophical truth ; a view supported by the theory

- iv. o5l. 3 Ib. iv. SSS. * Ib. iv. 41S.

230 PHYSICAL SCIENCE IN THE MIDDLE AGES.

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 analyzing 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. 5 I have already
explained, in some measure, the fallacy of this belief, which consists,
as has been well said, 6 " 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.

Thus a Universal Science was established, with the authority of a
Religious Creed. Its universality rested on erroneous views of the re-
lation 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 Eeligion
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 Philoso2)hy 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 Platouists
had no inconsiderable share. Various causes contributed to the eleva-
tion of Aristotle to this distinction. His Logic had early been adopted
as an instrument of theological disputation ; and his spirit of systemati-
zation, 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 philos-
ophy of which we now speak, so far as it pretends to deal with physics.

2. Scholastic Dogmas. But before the complete ascendency of Aris-
totle was thus established, when something of an intellectual waking

Detr. iv. 4' '7. " Enc. Hit. 807.

DOGMATISM OF THE STATIONARY PERIOD. 231

took place after the darkness and sleep of the ninth and tenth centu-
ries, the Platonic doctrines seem to have had, at first, a strong attrac-
tion for men's minds, as better falling in with the mystical speculations
and contemplative piety which belonged to the times. John Scot
Erigena 7 may be looked upon as the reviver of the New Piatonism in
the tenth century. Towards the end of the eleventh, Peter Damien, !
in Italy, reproduced, involved in a theological discussion, some Neopla-
tonic ideas. Godefroy 9 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. " Phi-
losophers 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 Chartrcs, 10 in his Megascosmus and Micro-
cosmus, 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 psychol-
ogy his special study." He says the faculties of the mind are "the
senses, the imagination, the reason, the memory, the understanding,
and the intelligence."

o

Physics does not originally and properly form any prominent part of
the Scholastic Philosophy, which consists mainly of a series of quet
tions 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
abserve, that in speaking of the division of the waters above the fir-

7 Deg. iv. 35. slb.iv.SG7. 9 Ib. iv. 413. io Ib. iv. 410. " Ib. iv. 41'.

232 PHYSICAL SCIENCE IX THE MIDDLE AGES.

mament, from the waters under the firmament, he gives one opinion,
that of Becle, that the former waters are the solid crystalline heavens
in which the stars are fixed, 12 " for crystal, which is so hard and trans-
parent, is made of water." But he mentions also the opinion of St.
Augustine, that the waters r.bove the heavens are in a state of vapo:
{yaporaliter) and in minute drops ; " if, then, water can, as we see it-
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 dropt
and still lighter vapors ? But in whatever manner the waters are
there, we do not doubt that they are there."

The celebrated Summa Theoloyice of Thomas Aquinas is a work of
the same kind ; and any thing 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. L, 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 philos-
opher." 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, 13 "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."

The Question concerning Corporeal Action, in Aquinas, is divided
into six Articles ; and the conclusion delivered upon the first is, 14 thai
" Body being compounded of power and act, is active as well as pas-
sive." Against this it is urged, that quantity is an attribute of body,
and that quantity prevents action ; that this appears in fact, since a
'arger body is more difficult to move. The author replies, that "quan-

12 Lib. ii. Distinct, xiv. De opere stcundx dlel.

13 Jldalff/icus, lil). ii. cap. 16. H Summa, P. i. Q. Hi Art. 1.

DOGMATISM OF THE STATIONARY 1'EilIOD. 233

tity does not prevent corporeal form from action altogether, but pre-
vents it from being a universal agent, inasmuch as the form is individ-
ualized, which, in matter subject to quantity, it is. Moreover, the
iliu-tration 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 Coelo and De Mumlu'' (we
see that he quotes familiarly the physical treatises of Aristotle) ;
" second, because it is false that pouderousness 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 some-
thing is drawn from power into act."

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 oi
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 uuiversals are obtained from individuals. But the
schoolmen, founding their speculations on the received modes of con
sidering such subjects, to which both Aristotle and Plato Lad con-
tributed, 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 15 solves the difficulty by the
aid of the Aristotelian distinction of Matter and Form. The individ-
ual derives from the Form the property of bciny something, and from
the Matter the property of being that particular thing. Duns Scotus, 13
the great adversary of Thomas Aquinas in theology, placed the prin-
ciple of Individuation iu " a certain determining positive entity," which
his school called Hcecccitij or thisness. " Thus an individual man u
Peter, because his humanity is combined with Petreity." The force

De?. iv. 570. la Ib. iv. 523.

234 PHYSICAL SCIENCE IX THE MIDDLE AGES.

of abstract terms is a curious question, and some remarkable exper-
iments in their use had been made by the Latin Aristotelians before
this time. In the same v?Ay in which -we talk of the quantity and
quality of a thing, they spoke of its quiddity} 1

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 phi-
losophy 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 argu-
ments : and though these notional and verbal relations were invested
with a most complex and pedantic technicality, they did riot, 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 mul-
tiplied 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 ol
conceiving its nature.

Having thus taken upon themselves the task of raising and discuss-
ing questions by means of abstract terms, verbal distinctions, and logi-
cal 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 ad-
mired, might recur without limit. John of Salisbury 18 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, 19 " was equally ap-
plicable to the period of centuries." The same knots were tied and

17 Dcg. iv. 494.

1S He studied logic at Paris, at St. Gencvieve, and then left them. " Duodecen-
nium mihi elapsum est diversis studiis occupatum. Jucundum itaque visum est
veteres quos reliqueram, et quos adhuc Dialectica detinebat in monte, (Sanctra
Genovefte) revisere socios, conferre cum eis super ambiguitatibus pristinis ; ut
nostrum invicem collatione mutua commetiremur profectuin. Invent! sunt, qui
fuerant, et ubi ; neque euim ad palmam visi sxint processisse ad qujestiones pris-
tinis dirimendas, neque propositiuncnl.ini um.m adjecerant. Quibus_ urgebaut
Bthnulis eisdem et ipsi urgebantur," &c. Metulogicus, lib. ii. cap. 10.

Middle Ages, iii. 537.

DOGMATISM OF THE STATIONARY PERIOD. 235

untied ; the same clouds were formed and dissipated. The poet's cen
sure 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.

It will therefore be unnecessary to go into any detail respecting the
history of the School Philosophy of the thirteenth, fourteenth, and fif-
teenth centuries. We may suppose it to have been, during the inter-
mediate 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 scho-
lastic 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 form-
ing : 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 exist-
ence, 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. 20 " Zabarella
maintains that the proximate cause of the motion of elements is
the form, in the Aristotelian sense of the term : but to this sen-
tence we," says Keckernian, "cannot agree; for in all other things
Iheform 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 author! tv :
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

Keckerman, p. 142S.

236 PHYSICAL SCIENCE IX THE MIDDLE AGES.

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

o *

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,
wLen 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 na-
ture abhors a vacuum ; that some bodies have a positive levity in
others, as oil in water ; and the like.

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 fluc-
tuations. 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 Aris-
totle's works, and more especially his metaphysical writings, had been
translated into Latin, and were explained in the schools of the Univer-
sity of Paris, as early as the beginning of the thirteenth century. 21 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
mio-ht a'ive occasion to other heresies not vet invented." The Logic

O D * -*

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

21 Moslieim, iii. 157.

DOGMATISM OF THE STATIONARY PERIOD. 23 T

Arabic, certain books of Aristotle, and of other ancient sages ; and wo
have a letter of Peter de Viueis, in which they are recommended to
the attention of the University of Bologna : probably the same recom
raendation was addressed to other universities. Both Albertus Mag-
nus and Thomas Aquinas wrote commentaries on Aristotle's works ;
arid as this was done soon after the decree of Gregory the Ninth,
Launoy is much perplexed to reconcile the fact with the orthodoxy ol
the two doctors. Campauella, who was one of the first to cast oft the
authority of Aristotle, says, " We are by no means to think that St.
Thomas aristotkized ; 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 authors with profound deference. 22 For instance, Aqui-
nas 03 attempts to defend Aristotle's assertion, that if there were no
resistance, a body would move through a space in no time ; and the
e-ame defence is given by Scotus.

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 Parish When Ramns, in 1543, pub-
lished 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, 25 " que le dit llamus avoit ete temeraire, arrogant
et impudent ; et que parcequ'en son livre cles animadversions il repre-
nait Aristotle, estait evidemment counue et manifesto son ignorance."
The books are then declared to be suppressed. It was often a com-
plaint of pious men, that theology was corrupted by the influence of
Aristotle and his commentators. Petrarch says, 26 that one of the Ital-
ian learned men conversing with him, after expressing much contempt
fur the Apostles and Fathers, exclaimed, " Utinam tu Averroen pati
posses, ut videres quauto ille tuis his nugatoribus major sit !''

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

M Deg. N. 475. T. Piccoloiniui, ii. 335. 24 Launoy, pp. 10S, 123.
-" LaunDy, p. 132. " Hallam, J/. A. in. 5G6.

238 PHYSICAL SCIENCE IX THE MIDDLE AGES.

powerful school of Platonists (not iSTeoplatonists) 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 ascend-
ency of Aristotle was about to be overturned ; but, in physics at least,
his authority passed unshaken through this trial. It was not by dis-
putation 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 direc-
tion ; 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

O '

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

PROGRESS OF THE ARTS. 239

upon each other, and upcu 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
t-ask of tracing the progress of the latter.

CHAPTER V.

PROGRESS OF THE ARTS ix THE MIDDLE AGES.

ART A\D 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 mid-
dle 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 mys-
ticism of thought, of servility and dogmatism of character, the powers
and acquirements to which we owe so many of the most important in-
ventions which we now enjoy ? Parchment and paper, printing and
engraving, improved glass and steel, gunpowder, clocks, telescopes

210 PHYSICAL SCIENCE IN THE MIDDLE AGES.

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 Pe-
riod. 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 mas-
ters of the middle ages not only made some small progress in Astron-
omy, 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 disadvan-
tages, shall not greater works, produced in an earlier state of kuowl-
eclo-e, 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 for-
mer 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
snumerated, though at the present day they may be portions of our
sciences, are no evidence that the sciences then existed ; but only that

PROGRESS OF THE ARTS. 24:1

iliose 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 tc
deny science to great artists. It may be said, that the grand structures
of Cologne, or Arniens, 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 amono- the builders ot

o

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 ot
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, there-
fore, 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 ol
the sciences which we are reviewing ; and no facts or subordinate
truths belong to our scheme, except so far as they lead 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 pro-
cesses of art like those which we have referred to, namely, the inven-
tions of the middle ages, let us ask, what principle each of them
VOL. I. 16

242 PHYSICAL SCIENCE IX THE MIDDLE AGES.

illustrates? "\Yhat 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 for-
wards 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 man-
ufactures 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 con-
sequence of the indistinct notion of science which has commonly pre-
vailed. Thus Gibbon, in speaking of the knowledge of the period now
under our notice, says, 1 "Much useful experience had been acquired in

decline and Fall, vol. x. p. 43.

PROGRESS OF THE ARTS. 243

ihe 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 pur
poses of distillation, analyzed the substances of the three kingdoms o.
nature, tried the distinction and affinities of alkalies and acids, and con-
verted 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
iustice 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

O

did they teach ? We need not wonder if Gibbon, whose views of the
boundaries of scientific chemistry were probably very wide and indis-
tinct, could include the arts of the Arabians within its domain ; but
they cannot pass the frontier of science if philosophically defined, and
steadily guarded.

The judgment which we are thus led to form respecticg the chemi-
cal 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 botony, 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 mathe-
matics, we have already described.

3. Experimental Philosophy of the Arabians. Tire estimate to which
we haye 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. "\Ve can deliver no just decision,
except we will consent to use the terms of science in a strict and pe
cise sense : and if we do this, we shall find little, either iu the particu-

24-i PHYSICAL SCIENCE IX THE MIDDLE AGES.

lar discoveries or general processes of the Arabians, which is important
in the history of the Inductive Sciences. 2

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 im-
plies. 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 Ara-
bians. 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 sub-
jects 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

2 If I might take the liberty of criticising an author who has given a very inter-
esting view of the period ia question (Mahometamism Unveiled, by the Eev. 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
iises 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.

PROGRESS OF THE ARTS. 243

ind manufactures, luxury aud art, medicine and engineering-, in which
there were not going- ou innumerable processes, which may be termed
Experiments ; and, in addition to these, the Arabians adopted the pur-
suit of alchemy, and the love of exotic plants and animals. But so far
from their being, as has been maintained, 3 a people whose " experi-
mental intellect" fitted them to form sciences which the " abstract in-
tellect" of the Greeks failed in producing, it rather appears, that several
of the sciences which the Greeks had founded, were never even com-
prehended 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.

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 author-
ity 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,
ihat the Roman writers, and Seneca in particular, speak with an en-
thusiastic 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

3 Jtj/tomdanism Unveiled, ii. 271.

246 PHYSICAL SCIENCE IN THE MIDDLE AGES.

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. 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 a?
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. 5

5. Architecture of the Middle Ages. But though we are thus com-
pelled 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 scien-
tific ideas among them ; and which, therefore, may be considered as
the prelude to the period of discovery. I mean their practical archi-
tecture, 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 or-
namental architecture had been horizontal masses resting on vertical
columns : when the arch was introduced by the Romans, it was con-
cealed, or kept in a state of subordination : and the lateral support
which it required was supplied latently, marked by some artifice.
But 'the strup-o-le between the mechanical aud the decorative construe-

~O

lion 9 ended in the complete disorganization of the classical style. The

-i Hallam's Middle Ages, iii. 549. Forster's Hahom. U. ii. 313.

5 In the Philosophy of the Inductive Sciences, I have given an account at consider-
able length of Eoger 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.

6 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 espe-
cially so long as there were readers of Archimedes. Boethius had translated the

PROGRESS OF THE ARTS. 247

inconsistencies and extravagances, of which we have noticed the occur-
rence, 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 an
exercised by masters without skill, and without feeling for real beauty.

TVhen, 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 re-
vived 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 sigui-
ficant relations of parts, is never satisfied except the weights appear to
be duly supported, 7 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 me-
chanical construction. All the ornamental parts were made to enter
into the apparent construction. Every member, almost every mould-
ing, 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 cu-
riously slender forms of the separate parts. The arch and the vault,
no longer trammelled by an incompatible system of decoration, but
favored by more tractable forms, were only limited by the skill of the
builders. Every thing showed that, practically at least, men possessed
and applied, with steadiness and pleasure, the idea of mechanical pres-
sure and support.

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 ;

mechanical works of Archimedes into Latin, as we learn from the enumeration ot
his work by his friend Cassiodorus (Variar. lib. i. cap. 45), " Heclianicwn etiam
Archimedem latialem siculis rcddidisti." But Mtcliunicus 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
Vjy King Theodoric to Boethius, '.o urge him to send the king a water-clock.

7 Willis, pp. 15-21. I have throughout this description of the formation of the
Gothic style availed myself of M; "Willis's well-chosen expressions.

248 PHYSICAL SCIENCE IX THE MIDDLE AGES.

and tlms Architecture prepared the way for Mechanics. But this ad-
vance 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 iu the mean time, and per-
haps 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 gen-
eral terms, exhibit those principles with a far less impressive simplicity
and elegance than those of the thirteenth. We may hereafter inquire
whether we fiud 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 man-
ner 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 sup-
port of pillars so slender, that the incumbent weight seemed, as it were,
suspended in the air by an invisible hand." 8 This pleasure in the con-
templation of apparent impossibilities is a very general disposition among
mankind ; but it appears to belong to the infancy, rather than the ma-
turity of intellect. On the other hand, the pleasure in the contempla-
tion of what is clear, the craving for a thorough insight into the rea-
sons of things, which marks the European mind, is the temper which
leads to science.

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 remark-

8 Mahometan Ism Unveiled, ii. 255.

PEOGRESS OF THE AKTS. 240

ably connected and definite artificial system. Xor can \vc doubt that
it was exercised by a class of artists who formed themselves by laborious
studv 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 instruc-
tion, and of a body of rules of practice, is proved beyond dispute by
the great series of European cathedrals and churches, so nearly iden-
tical in their general arrangements, and in their particular details.
The question then occurs, have these rules and this system of instruc-
tion 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 ?

o

We are not to be surprised, if, during the most flourishing and vig-
orous period of the art of the middle ages, we fiud none of its precepts
in books. Art has, in all ages and countries, been taught and trans-
mitted 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
o'.vu 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 Archi-
tecture 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 cornmentatorial spirit of the
middle ages inspired. They are Translations of Vitruvius, with Anno-
tations. In some of these, particularly that of Cesare Cesariano, pub-
lished 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 PHYSICAL SCIENCE IN THE MIDDLE AGES.

must needs be their masters, led these writers to subordinate the mem-
bers of their own architecture to the precepts of the Roman author.
We have Gothic shafts, mouldings, and arrangements, given as paral-
lelisms 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 iu
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 signifi-
cations. 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 mys-
tical turn of thought. 9

O

We thus fiud 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 fig-
ures, for which fantastical reasons are given, may really involve prin-
ciples of beauty or stability. But independently of this, we find, in
the best works of the architects of all ages (including engineers), evi-
dence 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 exer-

9 The plan which he lias given, fol. 14, lie has entitled " Iclinosrraphia Funda-
menti sacras ^Edis baricephalse, Germanico more, a Trigono ac Pariquadrnto per-
Btructa, uti etiarn ea quas nunc Milani videtur."

The work of Cesariano was translated into German by Gtialter Eivius, and pub-
lished at Nuremberg, iu 1548, under the title of Vitrvvius Tc-utsch, with copies oi
the Italian diagrams. A few years ago, in ail article in the Wiener Jahr1u.cli.er
(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 iu Eng-
land.

PROGRESS OF THE ARTS. 251

eised if it were not so. Hence the writings of architects and engineer*
during the middle ages do really form a prelude to the works on scien-
tific mechanics. Vitruvius, in his Architecture, and Julius Fronting,
who, under Vespasian, wrote On Aqueducts, of which he was super-
intendent, 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 exam-
ple, Leonardo da Vinci wrote on the equilibrium of water. And thus
we are led up to Stevinus of Bruges, who was engineer to Prince Mau-
rice 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 \vhieii
the middle ages offered to the progress of science, I now proceed to
the history of the progress, when that progress was once again n
suined.

BOOK V

HISTORY

OF

FORMAL AS T RON MY

AFTER THE STATIOXAEY PEFJOD.

Cyclopum educta caminis
Mcenia conspicio, atque adverse fornice portas.

His demum exactis, perfecto niunere Diva?,

Devenere locos Iretos et amoeua vireta
Fortunatorum nemorutn sedesque beatas.
Largior hie canipos jether et lumine vestit
Purpureo : solemque stuim, stia sidera norunt.

VIRGIL, sEn. vi. GOO

They leave at length the nether gloom, and stand

Before the portals of a better laud :

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 ;

Aud, purged from mists that veil our earthly skies,

Shine suns and stars unseen by mortal eyes.

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 sta-
tionary period of human knowledge, began at last to yield to the in-
fluence of the principles which tended to progression. The indistinct-
ness 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 atten-
tion to what had been said concerning them : and thus, as science rose

O '

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 upou
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 dog-
matism of the schools. When they began to feel that they could dis-

256 INTRODUCTION.

cover 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, intel-
lectual and civil, of the established schools of philosophy. This clear-
ness 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 rela-
tions 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 uni-
verse, the relations of space and time ; but Kepler, Galileo, and others,
were led, by controversies and other causes, to give a gradually in-
creasing 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 in-
tense 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 pro-
pounding of the Copernican theory occasioned. But it may be ob-
served 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 a-s they were exhibited by the ancient theories, or

PRELUDE TO THE EPOCH OF COPERNICUS. 257

might be represented by obvious modifications of those theories. I
speak of new Inequalities, new Phenomena, such as Copernicus, Gali-
leo, 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.

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 dis-
covered, that is, suggested as a theory plausible at first sight, long be-
fore 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 Ptol-
emaic 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 Hdio-
YOL. I. 17

258 HISTORY OF FORMAL ASTRONOMY.

centric Theory (that which places the centre of the celestial motions it
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 oi
the heliocentric theory? That the relative motions are the same, on
that and on the other supposition. So far, therefore, the two hypoth-
eses are exactly on the same footing. But, it is urged, on the helio-
centric 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 appear-
ances. Both these arguments, simplicity on the one side, and obvious-
ness on the other, are vague, and we may venture to say, both inde-
cisive. 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 Coper-
nican 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, with-
out these appendages, would not approach the Ptolemaic, in the accu-
rate explanation of facts ; and as those who had placed the sun in the
centre had never, till the time of Copernicus, shown how the inequal-
ities 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 imllixhed 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 2^'oposed 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

PRELUDE TO THE EPOCH OF COPERNICUS. 259

the Hipparchian or Ptolemaic theories by a long series of great astron-
omers of all civilized countries.

But, though the astronomers who, before Copernicus, held the helio-
centric 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 vi^or of their minds ; and

O ' O

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 astro-
nomical knowledge of the time.

O

The most ancient of the Greek philosophers to whom the ancients
ascribe the heliocentric doctrine, is Pvtha^oras ; but Diogenes Laer-

/ O O

tins 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, Arisfcvrchus. " Aristarchus of Samos," says he, 1
" 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 8
asserts that this, which was only a hypothesis in the hands of Aris-
tarchus, 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 " 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 it is a worthy subject of contem-
plation, 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 a.nd verifying the Hipparchian theory. .

Next to the Greeks, the Indians appear to have possessed that

1 Archim. Annarl*. = Quest. Plat. Delamb. A. A. vi

8 Quoted by Copernic. i. 7. 4 Quest. Nat. vii. 2.

260 HISTORY OF FORMAL ASTRONOMY.

original vigor and clearness of thought, from -which true science
springs. It is remarkable that the Indians, also, had their heliocentric
theorists. Aryabatta 5 (A. D. 1322), and other astronomers of that
country, are said to have advocated the doctrine of the earth's revo-
lution on its axis ; which opinion, however, was rejected by subse-
quent philosophers among the Hindoos.

Some writers have thought that the heliocentric doctrine was de-
rived 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 nation"
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. Eeal science, depending on a clear view of the
relation of phenomena to general theoretical ideas, cannot be commu-
nicated 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 un-
Hkc4y 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 prin-
ciples of connection and relation. Thus, as it had been urged in

' Lib. U. K. Hist. Ast. p. 11.

PRELUDE TO THE EPOCH OF COPERNICUS. 261

favor of the geocentric doctrine, that the heaviest body must be in the
centre, it was maintained, as a leading recommendation of the oppo-
site 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 3 informs us,
built a circular temple over the ever-burning Fire of Vesta ; typifying,
not the earth, but the Universe, which, according to the Pythago-
reans, 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 Cle-
anthes said, that Aristarchus the Samian ought to be tried for im-
piety, because he removed the Hearth of the Universe." This, how-
ever, seems to have been intended as a pleasantry.

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 com-
monly 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 Docta lynorantia, 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 ly Copernicus, and its consequences.

6 De Facie in Orle Luntz, 6.

2G2 HISTORY OF FORMAL ASTRONOMY.

CHAPTER II.

..NDUCTIOX OF COPERNICUS. THE HELIOCENTRIC THEORY ASSERTED

OX FORMAL GROUNDS.

IT will be recollected that the formal are opposed to the
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 consider-
ations 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 uncer-
tainty 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 estab-
lished 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 feign-
ing 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 expla-
nations than the ancient ones, of the revolutions of the celestial orbs.

" Having then assumed the motions of the earth, which are here-
after explained, by laborious and long observation I at length found,
that if the motions of the other planets be compared with the revolu-
tion of the earth, not only their phenomena follow from the suppo-
sitions, 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

INDUCTION OF COPERNICUS. 263

grounds on which Copernicus adopted his theory ; as the craving foi
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 geo-
metrical 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 alsc
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 sup-
pose the earth to revolve and the heaven to be at rest, you will find,
he says, "si serio animadvcrtas" if you think steadily, that the appar-
ent diurnal motion will follow. And after alleging his reasons for his
system, he says, 1 " 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, iu the sequel, by God's favor, we will make clearer than
the sun, at least to those who are not ignorant of mathematics."

It will easily be understood, that since the ancient geocentric hypoth-
esis ascribed to the planets those motions which were apparent only,
and which really arose from the motion of theearth round the sun in
the new hypothesis, the latter scheme must much simplify the plan-
etary theory. Kepler 2 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 represent-
ing their inequalities ; and, accordingly, the ancient theory of eccen-
trics 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

1 Nicolai Copcrnici Torinensis de Rewlutionilus Orblum Ccukstiiun Lllri VI
Norimbergse, M.D.XLIII. p. 9.

2 Mi/st. Cosm. cap. 1.

264 HISTORY OF FORMAL ASTRONOMY.

great and small Epicycle ; or else by means of an Eccentric and Epicy-
cle, modified from Ptolemy's, for reasons which \ve shall shortly men-
tion. This mode of representing the motions of the planets continued
in use, until it was expelled by the discoveries of Kepler.

Besides the daily rotation of the earth on its axis, and its annual cir-
cuit about the sun, Copernicus attributed to the axis a " motion of dec-
lination," by which, during the whole annual revolution, the pole was
constantly directed towards the same jart of the heavens. This con-
stancy in the absolute direction of the axis, or its moving parallel to
itself, maybe 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 direc-
tion when the cup is carried round a room. And this was noticed by
Copernicus's adherent, Rothman, 3 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

O ' O

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 par-
allelism. 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.

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
Ihe facts.

The tendencies of our speculative nature, which cany us onwards in

3 Tycho. Epist. i. p. 184, A. D. 1500.

INDUCTION OF COPERNICUS. 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 pecu-
liar 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 Kep-
ler. 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 con-
ceived 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 excus-
able, 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 planet-
ary motions is fashioned upon it. His great desire was to apply it
more rigidly than Ptolemy had done. The time did not come for re-
jecting this axiom, till the observations of Tycho Brahe and the calcu-
lations 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* 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 epicy-
cles : 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 ec-
centric than that of the other planets, he makes suppositions which are
complex indeed, but which show his perception of the imperfection of

See B. iii. Chap. iii. Sect. 7.

266 HISTOEY OF FORMAL ASTRONOMY,

the common theory ; and he proposes a new theory of the moon, fof
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. 5

It is obvious, that, along with his mathematical clearness of view,
and his astronomical knowledge, Copernicus must have had great intel-
lectual boldness and vigor, to conceive and fully develop a theory so
different as his was from all received doctrines. His pupil and expos
itor, Ptheticus, 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, Aa 6' efavQipov dvaL TTJ yvupq rbv jueAAovTa
faXoaofietv. ' 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 lia-
bility to such a temper, which belongs either to youth, or to ardent
and light minds, or to those r&v piya (ppovovvruv im flecopm jut/cpr/,
'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 dis-
coverers.

Besides the intellectual energy which was requisite in'order to con
struct 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 Gali-

j}e Rev. iv. c. 2.

INDUCTION OF COPERNICUS. 267

co'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 there-
fore had not begun to look with alarm ou such movements. Still, the
claims of Scripture and of ecclesiastical authority were asserted as para-
mount on all subjects; and it was obvious that many persons would
be disquieted or offended with the new interpretation of many scrip-
tural 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 Fraueu-
burg, in the diocese of Ermeland. 6 lie had been a student at Bologna,
and had taught mathematics at Rome in the year 1500 ; and he after-
wards pursued his studies and observations at his residence near the
mouth of the Vistula. 7 His discovery of his system must have occurred
before 1507, for in 1543 he informs Pope Paulus the Third, in his dedi-
cation, 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 en-
treaty of his friend Cardinal Schomberg, whose letter is prefixed to
the work. "Though I know," he says, "that the thoughts of a phi-
losopher 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 Pytha-
goreans and others, who delivered their doctrines only by tradition
and to friends." It will be observed that he speaks here of the oppo-
sition of the established school of Astronomers, not of Divines. The
latter, indeed, he appears to consider as a less formidable danger. " II
perchance," he says at the end of his preface, "there be juarcuoAoyoi,
vain babblers, who knowing nothing of mathematics, yet assume the
light of judging pn 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 con-
temptible." lie 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 ou similar grounds by Lactautius, who,

6 Eheticusj 2iar. p. 94. ' Kiccioli.

268 HISTORY OF FORMAL ASTRONOMY.

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 te 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 consid-
ered so distinctly real as it necessarily was held to be in after times.

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 Coelestium 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 under-
stood 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 re-
mains immovable and fixed, and the Moon, along with the elements
included in her sphere, placed between the orbits (roslum) of Mars and
Venus, travels round the sun in a yearly revolution." 8 The writer goes
on to say that he has heard that Copernicus has written a book (Com-
mentaries), 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.

8 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 egregio
callere sed etiam novam mundi rationem constituisse : Qua doceas terrain nioveri :
solem imum mundi, atque medium locum obtinere : coelam octavum immotutn
atque fixnm perpetno manere : Lunam se una cum inclusis suse spherse elementis,
inter Martis et Veneris coelum sitam, anniversario cursu circum solem convertere.
Atque de hac tola astronomiae ratione commentarios a te confectos esse, ac errati-
carum stellarum motus calculis subductos tabulis te contulisse, maxima omnium
cum admiratione. Quamobrem vir doctissime, nisi tibi molestus sum, te etiam
atque etiam oro vehementcr ut hoc tuum inventum stuJiosis communices, et tuas
de mundi sphsera lucubrntiones, una cum Tabulis et si quid habes prseterea quod
ad eandem rein pertineat primo quoque tempore ad me mittas."

SEQUEL TO COPERNICUS. 26S

This letter is dated 1536, and implies that the work of Copernicus
tvas then written, and known to persons who studied astronomy. De-
lambre says that Achilles Gassarus of Lindau, in a letter dated 1540,
sends to his friend George Vogelin of Constance, the book De Rcvolu-
tionibus. But Mr. De Morgan 9 has pointed out that the printed work
which Gassarus sent to Vogelin was the Narratio by Rheticus of Fekl-
kirch, a eulogium of Copernicus and his system prefixed to the second
edition of the De Revolutionibus, which appeared in 15GC. In this
Narration, Rheticus speaks of the work of Copernicus as a Palingenesis,
or New Birth of astronomy. Rheticus, it appears, had gone to Coper-
nicus for the purpose of getting knowledge about triangles and trigo-
nometrical tables, and had had his attention called to the heliocentric
theory, of which he became an ardent admirer. lie speaks of his
" Preceptor" with strong admiration, as we have seen. " He appears
to me," says he, "more to resemble Ptolemy than any other astrono-
mers." This, it must be recollected, was selecting the highest known
subject of comparison.

CHAPTER III.

SEQUEL TO COPEKNICUS. THE RECEPTION AND DEVELOPMENT OF THE

COPERNICAN THEORY.

Sect. 1. First Reception of the Copernican Theory.

fTUIE theories of Copernicus made their way among astronomers, in
-L 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 Hippar-
chus 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

O

contains such Tables. In 1551 Reinhold improved and rcpublished
Tables founded on the principles of Copernicus. " We owe," he says
in his preface, "great obligations to Copernicus, both for his laborious

9 Ast. Mod. i. p. 138. I owe this and many other corrections to the personal kind-
ness of Mr. Pe Morgan.

270 HISTORY OF FORMAL ASTRONOMY.

observations, and for restoring the doctrine of the Motions. But though

o o

his geometry is perfect, the good old man appears to have been, at
times, careless in his numerical calculations. I have, therefore, recal-
culated the whole, from a comparison of his observations with those of
Ptolemy and others, following nothing but the general plan of Coper-
nicus's demonstrations." These " Prutenic Tables" were republished
in 1571 and 1585, and continued in repute for some time; till super-
seded 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 Borassice,
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 luith 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, aud 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 Wid-
manstadt, 1 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.

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

1 See Venturi, Essai sur les Outrages Physico-Mathematiques de Leonard da Vinci,
aiec des Fragmens tires de ses Manuscrits apportes d'ltalie. Paris, 1797 ; and, as
there quoted, Marini Arcltiatri Pontifaii, tom.ii. p. 251.

SEQUEL TO COPERXICUS. 271

straight line leading to tbe centre. He thus showed that he had

o o

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 ot
motions.

In like manner we find the question stirred by other eminent men.
Thus John Muller of Kouigsberg, a celebrated astronomer who died in

O O'

1476, better known by the name of Regiomontanus, wrote a disserta-
tion on the subject " Whether the earth be in motion or at rest," in
which he decides ex pro/bsso 2 against the motion. Yet such discus-
sions must have made generally known the arguments for the helio-
centric theory.

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 Mastlin, and his pupil, Kepler. Mastlin published in 1588
an Epitome Astronomice, in which the immobility of the earth is
asserted; but in 1596 he edited Kepler's Mysterium Cosmoyraphicum,
and the No.rra.lw 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 Tubingen, attending to Michael Majstlin, being dis-
turbed 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 consider-
ations, which were much more distinctly dealt with by Kepler, and
others of the followers of Copernicus, than they had been by the dis-

2 Schoneri Opera, part ii. p. 129.

272 HISTORY OF 'FORMAL ASTRONOMY.

coveixT 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, indepen-
dently 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 helio-
centric 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.
Amono- these was the unfortunate Giordano Bruno of Nola, who was

O

burnt as a heretic at Eorne 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 delta Beslia Trionfante, and which is under-
stood 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 con-
nected 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
innumeralilibus, immenso, et infiguraUli, seu de Universo et Mundis,
in which he maintains that eacli 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 ; 3 although other persons,
as Kecorde, 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

s See Burton's Anat. Mel. Pref. "Some prodigious tenet or paradox of the
earth's motion," &c. " Bruno," &c.

SEQUEL TO COPERNICUS. 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 irrespet-
tevole, incivile, rozza, rustica, selvatica, et male allevata, non cede ad
altra che pascer possa la terra nel suo seno." 4 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 " II 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 man-
ner 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 incivilita, che farebbe prevaricar
la pazienza di Giobbe," in his opponents, he refers to a public dispu-
tation which he had held at Oxford with these doctors of theology, in
presence of Prince Alasco, and many of the English nobility.*

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 Cceli 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 Intellcctualis he gives his reasons for not ac-
cepting 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

4 Opere dl Giordano Bruno, vol. i. p. 146. 5 Ib. vol. i. p. 179.

VOL. I. 18

274 HISTORY OF FORMAL ASTRONOMY.

other things which he assumes, are proceedings which mark a man
who thiuks 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 pre-
sented 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 Coperuican 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 super-
sede ; and that thus he, perhaps, did not see how much less harsh
were these fictions, as he called them, than those which Avere the in-
evitable alternatives. Perhaps he might even be liable to a little of
that indistinctness, with respect to strictly geometrical conceptions,
which we have remarked iu 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. 6 " 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 be-
hind to the east." Undoubtedly those who spoke of such a motion of
regression, were aware of this ; but they saw how the motion was sim-
plified 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.

Bacon's contemporary, Gilbert, whom he frequently praises as a
philosopher, was much more disposed to adopt the Copernican opin-
ions, 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. 7 He connects

Thema Oceli, p. 246. T Lib. vi. cap. 8. 4.

SEQUEL TO COPERXICUS. 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 1651 (De Mundo Nostro Sublunari
Philosopkia Nova), he appears to hesitate between the systems of
Tyrho and Copernicus. 8 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 arch-
angel 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. via.

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 Neiv 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 sup-

8 Lib. ii. cap. 20.

276 HISTORY OF FORMAL ASTRONOMY.

posed 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 1601, 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 solv-
ing 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 con-
triving 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 thor-
oughly roused again into activity, this was no longer the course of
events. Discoveries crowded on each other ; one wide field of specu-
lation was only just opened, when a richer promise tempted the labor-
ers away into another quarter. Hence the history of this period con-
tains 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

SEQUEL TO COPERNICUS. 2 77

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 Mechan-
ics implied a profounder genius than the novelties he detected in the
sky : but the latter naturally attracted the greater share of the atten-
tion of the world, and were matter of keener discussion.

It is not to our purpose to speak here of the details and of the occa-
sion 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 Nuntius 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 spec-
tacles, and offering them to the consideration of every one, but espe-
cially 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 wocderful celerity; which, hitherto not known to any one, the
author has decently 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 mat-
ters of science to newly observed facts, that several of the " paper-phi-
losophers," 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 HISTORY OF FORMAL ASTRONOMY.

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 sup-
ported the belief of such an arrangement of the planets, by an analogy
all but irresistible. It thus, as a writer 9 of our own times has said,
"gave the holding turn to the opinions of mankinc 1 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, 10
"the sun-following arrangement (solisequium) of Venus and Mercury ;
since it has been found by Galileo that Jupiter also has attendants."

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 abun-
dant quantity of reasons for the visible marks on her surface, all pro-
ceeding on these preconceived views. Others of his discoveries pro-
duced the same effect; for instance, the new stars invisible to the naked
eye, and those extraordinary appearances called Nebulae.

But before the end of the year, Galileo had new information to com-
municate, 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 :

Cynthia figuras semnlatur 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

Sir J. Ilerschel. 10 TJitma C<xli, ix. p. 233.,

SEQUEL TO COPERNICUS. 279

of that theory had endeavored to account for this, by supposing thai
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 adopt-
ing the system which, on the whole, appeared to agree best with the
phenomena, by meeting with some appearances which it did not en-
able him to explain. 11 Yet while the fate of the theory was yet un-
decided, this could not but be looked upon as a weak point in its
defences.

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 an-
swer it by saying, that luminous bodies were not governed by the
same laws of perspective as opake OIKS. But a more satisfactory an-
swer 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 tele-
scopes, 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 dis-
.,uvery 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.

11 Drinkwater-Bethune, Life of Galileo, p. 85.

230 HISTORY OF FORMAL ASTRONOMY.

Sect. 4. The Copernican Si/stem opposed on Theological Grounds.

THE doctrine of the Earth's motion round the Sun, when i,t 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 ecclesias-
tical 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 Galilaee et progredere.
Si bene conjecto, pauci de pnecipuis Europse Mathematicis a nobis
secedere volent; tanta vis est veritatis. Si tibi Italia minus est idonea
ad publicationem et si aliqua habitures es impedimenta, forsan Ger-
mania nobis hanc libertatem coucedet." Veuturi, 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 culti-
vated minds of Italy, and many of the most eminent of her ecclesiastics
among them, have always been the foremost in promoting and welcom-
ing the progress of science : and, as I have stated, there w r ere found
among the Italian ecclesiastics of Galileo's time many of the earliest
and most enlightened adherents of the Copernican system. The con-
demnation 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 adhe-

SEQUEL TO COPERNICUS. 281

*

rents of the Romish Church condemn the assumption o e 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 time?, as I have elsewhere remarked, 12 the Church of Authority
and the Church of Private Judgment have each its peculiar tempta-
tions and dangers, when there appears to be a discrepance between
Scripture and Philosophy.

But though we may acquit the popes and cardinals in Galileo's time
of stupidity and perverseuess 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 iuda'es,

J O

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

l - Phil. Lid. Sci. book x. clap. 4.

2S2 HISTORY OF FORMAL ASTBOXOMY.

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 sup-
plying a mechanical ground of belief, without which the mere astro-
nomical 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 sim-
plicity and symmetry. Galileo appears to have thought that now,
when these original recommendations of the system had been rein-
forced 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 main-
taining 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 mathe-
matical 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 pro-
hibited 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 Coperni-
sano :" 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 Sim-
plicius, in whose mouth was put the defence of all the ancient dogmas,
and who was represented as defeated at all points in the discussion ;

SEQUEL TO COPERNICUS. 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 w r as 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 abju-
ration 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 in-
quiry were deeply concerned. The general acceptance of the Coperni-
can 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 trou-
ble 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

O

favor of the system to pass unvisited : the notice which I have quoted,
in which the irony is quite transparent and the sarcasm glaringly ob-
vious, was deemed too flimsy a veil for the purpose of decency, and
: ndeed 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
.t 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 epi-

284 HISTORY OF FORMAL ASTRONOMY.

gram in the ear of a cardinal's secretary, with, a full knowledge tt \t it
would be immediately repeated to liis master.

[2cl Ed.] [Throughout the course of the proceedings against him,
Galileo was treated with great courtesy and indulgence. He was con-
demned to a formal imprisonment and a very light discipline. " Te
damnamus ad formalem carcerem hujus S. Officii ad tempus arbitrio
nostro limitandum ; et titulo posnitentise salutaris prsecipimus ut tribus
annis futuris recites semil in hebdomada 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 Pic-
colomini, one of his own warmest friends.

It has sometimes been asserted or insinuated that Galileo was sub-
jected to bodily torture. An argument has been drawn from the ex-
pressions used in his sentence : " Cum vero nobis videretur non esse a
te integram veritatem pronunciatam circa tuarn intentionern ; judica-
virntis necesse esse venire ad rigorosum examen tui, in quo respoudisti
catholice." It has been argued by M. Libri (Hist, des Sciences Ma-
thematiques en Italie, vol. iv. p. 259), and M. Quinet (L 1 Ultramonta-
nisme, iv. Lecon, 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 re-
jects the notion of Galileo's having been put to the torture, as incon-
sistent 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 im-
punity, if Galileo had been previously subjected to the rack. He adds,
very reasonably, " il ne faut noircir personne sans preuve, pas rnemc
ITnquisition ;" 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 heretica,, long ad-
hered in form to this declaration, and did not allow the Copernican
system to be taught in any other way than as an " hvoothesis." The

SEQUEL TO COPERNICUS. 285

Padua edition of Galileo's works, published in 1744, contains the Dia-
logue which now, the editors say, "Esce finalniente a pubblico libero
uso colle debite liceuze," is now at last freely published with the requi-
site license ; but they add, "quanto alia Quistione principale del moto
della terra, anche noi ci conformiamo alia ritrazione et protesta dell'
Autore, dichiarando nella piu solenne forma, che non puo, ne dee am-
metersi se non come pura Ipotesi Mathematice, che serve a spiegare
piu agevolamento certi fenomeni ;" " neither can nor ought to be ad-
mitted 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 Decla-
ratio, that though Newton assumes the hypothesis of the motion of the
earth, and therefore they had used similar language, they were, in do-
ing this, assuming a character which did not belong to them. " Hinc
alienam coacti sum us gerere persouam." They add, "Caeterum latis a
summis Pontificibus contra telluris motum Decretis, nos obsequi pro-
fitemur."

By thus making decrees against a doctrine which in the course of
time was established as an indisputable scientific truth, the See of
Pionie was guilty of an unwise and unfortunate stretch of ecclesiastical
authority. But though we do not hesitate to pronounce such a judg-
ment 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 contra-
dict the declarations of Revelation, according to our view of its mean-
ing ; 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 distinc-
tion between religious and physical tenets, which is necessary to re-
solve 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 religious import
of Revelation. But the establishment of this distinction was not accom-
plished without long and distressing controversies. Nor, if we wish t

286 HISTORY OF FORMAL ASTRONOMY.

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 interpre-
tation, which the new philosophy requires, and which appears to the
older school to be a fatal violence done to the authority of religion. '

J o /

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,
Avith 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 collat-
eral circumstance. At the present clay 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 tena-
ciously to the traditionary or arbitrary mode of understanding Scrip-
tural 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 con-
siderate and serious, who know how much sagacity and rightminded-
ness are requisite for the conduct of philosophers and religious men on
such occasions ; but who know also how weak and vain is the attempt

SEQUEL TO COPERNICUS. 287

.o get rid of the difficulty by merely denouncing the new tenets as
inconsistent with religious belief, and by visiting the promulgators of
them with seventy such as the state of opinions and institutions may
allow. The prosecutors of Galileo are still up to the scorn and aver-
sion of mankind : although, as we have seen, they did not act till it
seemed that their position compelled them to do so, and then pro-
ceeded with all the gentleness and moderation which were .compatible
with judicial forms.

Sect. 5. The Heliocentric Theory confirmed on Physical considera-
tions. (Prelude to Kei^le^s Astronomical Discoveries.)

Br physical .views, I mean, as I have already said, those which de-
pend' on the causes of the motions of matter, as, for instance, the con-
sideration 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 reason-
ing 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, Coper-
nicus 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 endeaver 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 Msestlin, " 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 im-
mensity 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 tc

288 HISTORY OF FORMAL ASTRONOMY'.

the centre of our earth, it is credible that the sun, the moon, and the
pther 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 re-
ceived from its tendency downwards was corn-pounded 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,
Moriu, Riccioli, and the defence of it by Galileo, Lansberg, Gassendi, 13
left on all candid reasoners a clear impression in favor of the system.
Morin attempted to stop the motion of the earth, which he called
breaking its wings; his Alee Terrce Fradce was published in 1643,
and answered by Gassendi. And Riccioli, as late as 1653, in his Al-
magestum Novum, enumerated fifty-seven Copernican arguments, and
pretended to refute them all : but such reasonings now made no con-
verts ; 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. lie applies to it the lines of Horace : u

Del. A. M. vol. i. p. 594. " Almag, Nov. p. 102.

SEQUEL TO COPERNICUS. 239

Per damna per caedes, ab ipso
Suinit opes animumque ferro.
Untamed its pride, unchecked its course,
From foes and wounds it gathers force.

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 connec-
tion among the parts of the universe was taken up by Kepler in an-
other 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 ex-
panse of human knowledge can show. I speak of the persuasion of
the existence of numerical and geometrical laws connecting the dis-
tances, 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 Mystcrium 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 sucii 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 writ-
ten 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 cir-
cle, 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
VOL. I. 19

290 HISTORY OF FORMAL ASTRONOMY.

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 knowl-
edge 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, per-
severance, 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.

QEVERAL persons, 1 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 fan-
tastical 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 rec-
oncile us to this result.

i Laplace, Precis de VHist. <PAst. p. 94. "II est affligeant pour 1'esprit humain
de voir ce grand liomme, meme dans ses dcrniers ouvrages, se coinplaire avec de-
lices dans ses chimeriques speculations, et les regarder comme 1'dme et la vie de
rastronomie."

Hist. ofAst., L. U. K., p. 53. " This success [of Kepler] may well inspire wilu
dismay those who are accustomed to consider experiment and rigorous induction
as the only means to interrogate nature with success."

Life of Kepler, L. IT. 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 purs-jit of truth."

INDUCTIVE EPOCH OF KEPLER. 291

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 knowl-
edge are not commonly made without the previous exercise of some
boldness and license in guessing. The discovery of new truths re-
quires, 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 neces-
sary to dwell on these discarded hypotheses, and on the process by
which they were condemned, as Kepler has done. But all who dis-
cover 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 excep-
tion. 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 HISTORY OF FORMAL ASTRO:S T OMY.

the sun on his axis, before the invention of the telescope, and his opin-
ion that the obliquity of the ecliptic was decreasing, but would, after
a long-continued diminution, stop, aud then increase again. 2 Nothing
can be mote just, as well as more poetically happy, than Kepler's pic-
ture 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 fugil 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.

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 rap-
idly testing false suppositions as they offer themselves. This talent
Kepler did not possess : he was not even a good arithmetical calcula-
tor, 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 con-
taining the genera] features of the character of a scientific discoverer

Bailly, A. M. iii. 175.

INDUCTIVE EPOCH OF KEPLEK. 29

o

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 erroneovs trains of thought which other persons con-
ceal from the world, and often themselves forget, because they find
means of stopping them at the outset. In the beginning of his book
(Argumenta Capituin) he says, " if Christopher Columbus, if Magel-
lan, 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 culti-
vated with abundant toil and vigor ; : but with great scantiness of agri-
cultural skill and implements. Weeds and the grain throve and flour-
ished 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. l.-^Kepler's Discovery of his Third Law.

I SHALL now'give some account of Kepler's speculations and discov-
eries. The first discovery which he attempted, the relation among the
successive distances of the planets from the sun, was a failure ; his doc-
trine being without any solid foundation, although propounded by him
with great triumph, in a work which he called Mysterium Cosmoyrapld-
cttm, and which was published in 1590. The account which he gives
of the train of his thoughts on this subject, namely, the various sup-
positions 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 doc-
trine which professed to give the true relation of the orbits of the dif-
ferent planets, was thus delivered : 3 " 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 tna Earth's orbit an
f.osahedron ; the circle inscribed in it will be the orbit of Venus. In-

L. U. K. Kepler, 0.

29-i HISTORY OF FORMAL ASTRONOMY.

scribe 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."

But though this part of the Mystcrium Cosmoyraphicum was a fail-
ure, the same researches continued to occupy Kepler's mind ; and twen-
ty-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 dis-
tances 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 Co-
pernican 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 1019, 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 Har-
monics 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 ex-
pectations."

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 pro-
portion 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

INDUCTIVE EPOCH OF KEPLER. 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 dis-
tance of the Earth."

When we now look back at the time and exertions which the estab-
lishment 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
poiver 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 pro-
portional ? 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 rea-
sonings ; and these, though vague or erroneous, determined the nature
of the mathematical connection which he assumed. Thus in the
Mystcrium 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
fo complex and laborious, that probably few modern readers have had
courage to go through it, Delambre acknowledged that his patience

296 HISTOEY OF FORMAL ASTRONOMY.

often failed him during the task; 4 and subscribes to the judgment o\
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 rela-
tion ; in a crowd of ideas there is not one truth : he becomes a mau
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. 5 The numerical rela-
tions of Concords are so peculiar that we can easily suppose them to
have other bearings than those which first offer themselves.

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 de-
duced from it, and which are found in the Epitome Astronomies Coper-
nicance, 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 NCAV ton'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 ot
these orbits, and the rule of motion of each planet in its own orbit.
Copernicus represented the motions in longitude by means of eccen-

4 A. M. a. 358. * Optics, b. ii. p. iv. Obs. 5.

INDUCTIVE EPOCH OF KEPLER. 297

tries and epicycles, as we have already said; and'the motions in lati-
tude by certain librations, or alternate elevations and depressions of
epicycles. If a mathematician had obtained a collection of true posi-
tions 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 posi-
tion, 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 ob-
served 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 ;" 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.

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 pub-
lished 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

6 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. "Duin
in hunc modum de Martis motibus triumpho, eique ut plane devicto tabularum
carceres et equationum compedes necto, diversis nuntiatur locis, futilem victorium
utbellum tota mole recrudescere. Nam domiquidem hostis ut captivus contemptus,
rupit omnia equationum vincula, carceresque tabularum eifregit. Foris specu-
jatores profligerunt meas cansarum physicarum arcessitas copias earumque ji-guin
sxcussernnt resumta libertate. Jamque parum abfuit quia hostis fugitivus sese
cum rebellibus suis conjungeret meque in desperationem adigeret: nisi raptkn,
nciva rationum physicarum subsidia, fusis et palantibus veteribus, submisissem, et
qua se captivus proripuisset, omni diligentia, edoctus vestigiis v-sius nulla mora
iuterposita inhsesisserem."

298 HISTORY OF FORMAL ASTRONOMY.

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 Mars
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 in-
troduced : and that, when so considered, it had none of the libratious
which Ptolemy and Copernicus had attributed to it. The four-
teenth chapter of the second part asserts, " Plana eccentricorum esse
drd^avra ;" 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, how-
ever, 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 in-
crease 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 there-
fore rejoice much that in this, as in others of my preconceived opin-
ions, the observations were found to be on my side." Kepler estab-
blished his point by a fair and laborious calculation of the results of
observations of Mars made by himself and Tycho Bralie ; and had a
I'if-ht to exult when the result of these calculations confirmed his views

o

of the symmetry and simplicity of nature.

We may judge of the difficulty of casting off the theory of eccen-
trics 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 pre-
pare the way to the natural form of the equations, of which I am now
to treat. 7 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,

7 De Stella Martis, iii. 40.

INDUCTIVE EPOCH OF KEPLER. 299

jn 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 \vas s
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

7 O 2

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
Ly 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 conse-
quence 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, 9
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. 10

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 Chap-
ter," six hypotheses, on which he calculated the longitude of Mars, in
order to see which best agreed with observation.

1. The simple eccentricity.

2. The bisection of the eccentricity, and the duplication of the
superior part of the equation.

De Stella Mortis, p. 194. Ib. iv. c. 47.

' L. U. K. Kepler, p. 30. u De Stella JfartU, p. 228.

300 HISTORY OF FORMAL ASTRONOMY.

3. The bisection of the eccentricity, and a stationary poirt of equa-
tions, after the maimer 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 ot

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' 2 that he might take another ellipsis, exactly in-
termediate 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 13 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 hypoth-
esis 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 con-
struction 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, accord-
ing 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 rny 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

De Stella Martls, c. 58. n Ibid. p. 235.

INDUCTIVE EPOCH OF KEPLER. 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 !"

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 insolu-
bility of this problem is a mere mathematical difficulty in the deduc-
tive 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 dis-
charged 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 iu the University of Paris. Kepler
quotes this passage, and adds, " it is well, Piamus, that you have run
from this pledge, by quitting life and your professorship ; 14 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 represen-
tation of the motions and distances as they were observed.

Ramus perished in the Massacre of St. Bartholomew.

302 HISTORY OF FORMAL ASTRONOMY.

CHAPTER V.

.SEQUEL TO THE EPOCH OF KEPLER. RECEPTION, VERIFICATION, AND
EXTENSION OF THE ELLIPTICAL THEORF.

Sect. 1. Application of the Elliptical Theory to the Planets.

fTIHE extension of Kepler's discoveries conceining the orbit of Mars to
-I- 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 circum-
stances of the elliptical motion. These and various other supplemen-
tary portions of the views to which Kepler's discoveries had led, ap-
peared in the latter part of his Epitome Astronomies Copernicance,
published in 1622.

The real verification of the new doctrine concerning the orbits and

o

motions of the heavenly bodies was, of course, to be found in the con-
struction 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' in 1627 pub-
lished 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 Tabulae. Perpetu&, 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 mag-
nificent 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 astrono-

Rhcticus, Narratio, p. 98.

SEQUEL TO THE EPOCH OF KEPLER. 303

mer, 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

O

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 Longomoutanus,
Kepler, and Lansberg ; and, in allusion to the story of ancient mythol-
ogy, his work was to have been called Paris Astronomicus ; we easily
see that he would have given the golden apple to the Keplerian god-
dess. Succeeding observations confirmed his judgment : and the Ru-
dolphine 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.

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 Eveclion, which Ptolemy had discovered),
Tycho proved that there was another inequality, which he termed the
Variation? 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.

These steps concerned the Longitude of the Moon ; Tycho also made
important advances in the knowledge of the Latitude. The Inclina-
tion of the Orbit had hitherto been assumed to be the same at all

2 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 befora
the time of Tycho, and has only recently been brought again into notice.

30-4 HISTORY OF FORMAL ASTRONOMY.

times; and the motion of the Node had been supposed uniform. jJe
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 some-
times go backwards.

Tycho's discoveries concerning the moon are given in his Progym-
nasmata, which was published iu 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 rnoon. Horrox succeeded in doing this; and in 1638 sent this
essay to his friend Crabtree. It was published in 1673, with the nu-
merical elements requisite for its application added by Flamsteed.
Flamsteed had also (in 1671-2) compared this theory with observa
tion, and found that it agreed far more nearly than the Philolaic Ta
lies of Bullialdus, or the Carolinian Tables of Street (Ejtilogus ad
Tabulas~). Moreover Horrox, by making the centre of the ellipse re-
volve in an epicycle, gave an explanation of the evection, as well as of
the equation of the centre. 3

Modern astronomers, by calculating the effects of the perturbing
forces of the solar system, and comparing their calculations with ob-
servation, 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 astron-
omers, and naturally gave rise to the question whether the motions ot
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 Hor-
rox, far more philosophically, argues against this opinion, though he

3 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 el-
lipseos in epicycle locavit." See Bully's Flamsteed, p. 683.

SEQUEL TO THE EPOCH OF KEPLER. 30>

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, 4 " these errors of the tables are
alternately in excess and defect ; how could this constant compensa-
tion happen if they were casual ? Moreover, the alternation from ex-
cess 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 impos-
sible, 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.

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 inev-
itably, 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 general-
izing from the astronomy already established, astronomers were ac-
cumulating 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

* Astron. Kepler. Prolog, p. 17.
Tot,. I. 20

806 HISTORY OF FORMAL ASTRONOMY.

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 dis-
turbed 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, 5 " the Divine Goodness has given us
in Tycho an observer so exact that this error of eight minutes is im-
possible, we must be thankful to God for this, and turn it to account.
And these eight minutes, which we must not neglect, will, of them-
selves, enable us to reconstruct the whole of astronomy." In addition
to other improvements, the art of numerical calculation made an in-
estimable 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.

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 dis-
covery 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

Z>( Stella Jfartis, c. 19.

SEQUEL TO THE EPOCH OF KEPLER. 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 compre-
hensive 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 Consti-
tution of material bodies, we have new fields of inquiry opened to us.
And when we find that in thes* fields, as well as in astronomy, there
are large and striking trains of unquestioned discovery to be nar-
rated, 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 impor-
tant questions, What is Truth ? and, How is it to be discovered ?

BOOK YI

THE MECHANICAL SCIENCES.

HISTORY OF MECHANICS,

INCLUDING

FLUID MECHANICS

K.PATOS BIA TE, v$$v ftiv ivro\ri
TfAoS Hi, K' ov&tv f'/<ffn5iiv In.

S. Prom. I'inct. 18.

You, FORCE and POWER, have done your destined task :
And naught impedes the -work of other hands.

INTRODUCTION.

"TTTE 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 agen-
cies, 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 ce-
lestial. 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 pro-
gress of Formal Astronomy, the creation of the science of Mechanics
now became necessary to the formation and progress of Physical As-
tronomy. 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 Kepler
might have anticipated Newton.

1 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 there-
fore at rest.

312 HISTORY OF MECHANICS.

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 ol
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 doc-
trine 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 doc-
trine of Archimedes, failed, in such a manner as to show that his fol-
lowers 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 laud.

This dimness and confusion, with respect to all subjects of me-
chanical reasoning, prevailed still, at the period we now have to
consider ; namely, the period of the first promulgation of the Coper-
nican opinions. This is so Jmportaut a point that I must illustrate it
further.

Certain o-eneral notions of the connection of cause and effect in mo-

o

lion, exist in the human mind at all periods of its development, and are
implied in the formation of language and in the most familiar employ-
ments of men's thoughts. But these do not constitute a science of Me-

PRELUDE TO THE EPOCH OF GALILEO. 313

-hanics, any more than the notions of square and round make a Geom-
etry, 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 menlion 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, no-
ticed 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 pro-
portion to their greater weight. These doctrines were still retained :
yet the views which they implied were essentially erroneous and un-
sound ; 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 Projiortionibus Numerorum, Motuum, Ponderum, &c., was pub-
lished 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, pub-
lished at Pesaro, in 1577, a work which he called Mechanicorum
Liber, in which he endeavors to prove that an acute wedge will pro-
duce a greater mechanical effect than an obtuse one, without deter-
mining in what proportion. There is, he observes, " a certain repug-
nance" between the direction in which the side of the wedge tends to

314 HISTORY OF MECHANICS.

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 W^edge 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 edi-
tions were published in the sixteenth century, and which treats this
matter in nearly the same way as Varro, and in favor of which a claim
has been made 1 (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 autiquo."
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 Velocites, 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 Ven-
ice, 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 add-
ed some others ; as, that " a body is heavier in proportion as it de-
scends 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" ot
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 ot
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,

i Mr. Drinkwater's Life of Galileo, in the Lib. Usef. Kn. p. S3.

PRELUDE TO THE EPOCH OF GALILEO. 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 pow-
ers of descent on the inclined planes ; whereas, in the previous part of
the reasoning, the weight was supposed to be proportional to the de-
scent 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 in-
clined 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 re-
quired to point out, with any exactness, the cases to which his reason-
ing 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 ge-
nius, who should give the subject a real scientific foundation, than
Aristotle's knowledge of the proportion of the weights on the lever su-
perseded the necessity of Archimedes' proof of it.

We are not, therefore, to wonder that, though this pretended theo-
rem was copied by other writers, as by Tartalea, in his Quesiti et In-
ventioni Diversi, published in 1554, no progress was made in the real
solution of any one mechanical problem by means of it. Guido Ubakli,
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 Jor-

316 HISTORY OF MECHANICS.

danus and Tartalea. 2 No progress was likely to occur, till the mathe-
maticians had distinctly recovered the genuine Idea of Pressure, as a
Force producing equilibrium, which Archimedes had possessed, an<?.
which was soon to reappear in Stevinus.

The properties of the Lever had always continued known to mathe-
maticians, 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 demon-
strate the theories of the Lever with apparent success. Writers on
Mechanics were, as we have seen, so vacillating in their mode of deal-
ing 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 Me-
chanics 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 mechan-
ical 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, pub-
lished De Centra 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 prin-
ciple, also, will enable us to determine the result of many simple me-
chanical 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 proba-
bly 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 an-

2 Ubaldi mentions and blames Jordanus's way of treating the Lever. (See his
Preface.)

PRELUDE TO THE EPOCH OF GALILEO. 317

ticipating any wider proofs 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 Bcghinsclen 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 fur-
ther ; and thus he would have reduced the impossibility of such a per-
petual motion, to the conception of gravity, as a force tending to pro-
duce equilibrium; a principle perfectly sound and correct.

Upon this principle thus applied, Stevinus did establish the funda-
mental property of the Inclined Plane. He supposed a loop of string,
loaded with fourteen equal balls at equal distances, to hang over a tri-
angular 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 him-
self in the title-page of his work, has lately become an object of gene-
ral interest in his own country, and it has been resolved to erect a

318 HISTORY OF MECHANICS.

statue in honor of him in one of the public places of his lative 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 worts, 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 re-
discovery 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 manu-
scripts have been published by Venturi, in his Essai sur les Ouvrayes
Physico-Mathematiques de Leonard da Vinci, avec des Fragmens tires
de ses Manuscrits apportes d' Italic. Paris, 1797: and by Libri, in
his Hist, des Sc. Math, en Italic, 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 suffi-
ciently promulgated in Italy to influence the speculations of Galileo

PRELUDE TO THE EPOCH OF GALILEO. 319

whose reasonings respecting the lever much resemble those of Leo-
nardo. 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
clown 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 tri-
angle ; 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 princi-
ples. In his Treatise Delle Sdenze Mecaniche (1592), he refers the
Inclined Plane to the Lever, in a sound and nearly satisfactory man-
ner ; 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, in-
cluding 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 hori-
zontal 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 HISTORY OF MECHANICS.

the smallness of the point of contact. 3 But the most common ruistab?
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

o

motion. Kepler's essays, which are in this respect so feeble and uu
meaning, 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; it
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 pull-
ing the body to the centre. Newton's Force is merely mutual attrac-
tion ; 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. 4 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 New-
ton's Dynamical Theory.

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

* In speaking of the force which would draw a body up an inclined plane he ob-
serves, that " per communem animi sententiam," when the plane becomes hori
zontal, the requisite force is nothing.

4 Epitome Astron. Copern. p. 176.

PKELUDE TO THE EPOCH OF GALILEO. S21

after the moving power had ceased to act ; and that lie 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 down-
wards. Benedetti, who has already been mentioned, must be con-
sidered 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 expres-
sions of respect, but in a very sweeping manner. His chapter xxiv. is
headed, "Whether this eminent man was right in his opinion con
cerning violent and natural motion." And after stating the Aristote-

o o

lian 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 5
" the motion of the body, separated from the mover, arises by a certain
natural impression from the impetuosity (ex impetuosiiate) 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.

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.

5 P. 1S4.
VOL. I. 21

322 HISTORY OF MECHANICS.

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 Lad begun to doubt or reject the authority
of Aristotle, they were still some time in coming to the conclu-
sion, that the distinction of Natural and Violent Motions was alto-
gether 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 disposi-
tion, 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 experi-
ence 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 Copemican System 1 (published in 1630), he asserts

i Dial. 1. p. 40.

DISCOVERY OF THE LAWS OF MOTION". 323

Circular Motion alone to be naturally uniform, and retains the distinc-
tion between Natural and Violent Motion. In the Dialogues on Me-
chanics, however, published in 1638, but written apparently at an
earlier period, in treating of Projectiles, 2 he asserts the true Law.
"Mobile super planum horizoutale projectum mente concipio orani
secluso impedimento ; jam constat ex his qiue fusius alibi dicta suut,
illius motum equabilem et perpetuum super ipso piano futurum esse,
si planum in infinitum extend atur." " 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 tin-
plane, if the plane be indefinitely extended." His pupil Borelli, in 166T
(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 P rincipia 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, 3
" the immutability and simplicity of the operation by which God pre-
serves 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 a
2iriori 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 a 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.

The induction by which the First Law of Motion is established, con-
sists, 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,

Dial. i. p. 40. 3 Princip. p. 34.

324 HISTORY OF MECHANICS.

Hooke and others showed that, by diminishing the obvious resistances,
the retardation also became less ; and men were gradually led to a dis-
tinct appreciation of the Resistance, Friction, &c., which, in all terres-
trial 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 exarnin-
ino- 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 ap-
pears 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 comment-
ing on Aristotle's question, why we obtain an advantage in throwing
by using a sling, he says, 4 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.

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

4

Corpus vellet recta iter peragcre." Speculutionum Liber, p. 160.

DISCOVERY OF THE LAWS OF MOTION. 32c

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 accel-
erate, retard, or deflect their motions. It was, however, only after
many attempts that they reached this point. They began by consid-
ering the u'hole motion with reference to certain ill-defined abstract
Notions, instead of considering, with a clear apprehension of the con-
ditions 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 projec-
tiles. Santbach, 5 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 assump-
tion. To this succeeded another doctrine, which, though not much
more philosophical than the former, agreed much better with the phe-
nomena. Nicolo Tartalea (Nuova Scienza, Venice, 1550; Quesiti et
Inventioni Diversi, 1554) and Gualtier Rivius (Architecture &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 down-
wards, 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 de-
scends 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, 6 makes Sim-
plicius come to the same conclusion. "Since," he says, " there is noth-
ing 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.

s Prollematum Astronomicorum el Geometricorum Sectiones vii. &c. &c. Auetorf
Daniele Santbach, Noviomago. Basilese, 1561. P. 147.

326 HISTORY OF MECHANICS.

The Force of Gravity which thus produces deflection and curvature
m the path of a body thrown olliquely, constantly increases the veloci-
ty 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 anal-
ysis 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, 7 " will fall in the most simple way, because Natural Motions arc
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.

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 Avas 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, Genevse, 1584), and
by Baliani, a gentleman of Genoa, who published it in 1638. It was,
however, soon rejected by Gal ; leo, though it was afterwards taken up
and defended by Casranis, 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 quits
possible in their own nature.

Dial. Sc. iv. p. 91.

DISCOVERY OF THE LAWS OF MOTION. 327

The Law of Velocity was hitherto, as we have seen, treated as a
of phenomena, without reference to the Causes of the law. "The
cause of the acceleration of the motions of falling bodies is not," Gali-
leo observes, " a necessary part of the investigation. Opinions are dif-
ferent. 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 accel-
eration 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 free-
ly by the action of gravity." 8

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 Casrseus 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 com-
pared 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 communi-
cate velocity to a body by the hand or by a spring, the effect we pro-
duce 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
appeal's that this is not so in the case of gravity ; the velocity added
in one second is the same, whatever downward motion the body al-
ready possesses. A body falling from rest acquires a velocity, in one
second, of thirty-two feet ; and if a cannon-ball were shot downwards
svith a velocity of 1000 feet a second, it would equally, at the end ot
one second, have received an accession of 32 feet to its velocity.

This conception of Gravity as a Uniform Force, as constantly and

Gal. Op. iii. 91, 92.

328 HISTORY OF MECHANICS.

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 anew
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 ac-
curately." 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 ve-
locity 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 velo-
city ; 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 infi-
nitely divisible, but not that t. falling body actually passes through all
these divisions."

The Principles of the Motion of Falling Bodies being thus establish-
ed by Galileo, the Deduction of the principal mathematical conse-
quences was, as is usual, effected with great rapidity, and is to be found

DISCOVERY OF THE LAWS OF MOTION". 329

in his works, and in those of his scholars and successors. The motioc
of bodies falling freely was, however, in such treatises, generally com-
bined 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 ; 9 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 10 that any falling body, however large and heavy, would
always have its velocity in some degree diminished by the air in which

V I/O

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 accel-
erating and retarding force.

O o

"When Uniform Accelerating Forces had once been mastered, there

o '

remained only mathematical difficulties in the treatment of Variable
Forces. A Variable Force was measured by the Limit of the incre-
ment 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 meth-
ods, 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, Enler, and since their time, many other mathemati-
cians, 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
Uieir Curvilinear Motion, to which we have now to proceed. But il

8 Galileo, iii. 43. 10 iii. 54.

330 HISTORY OF MECHANICS.

may be remarked that Newton, having established the laws of Curvi-
linear Motion independently, has, in a great part of his Seventh Sec-
tion, deduced the simpler case of the Rectilinear Motion from the more
complex problem, by reasonings of great ingenuity and beauty.

Sect. 3. Establishment of the Second Law of Motion. Curvilinear

Motions.

A SLIGHT dearee of distinctness in men's mechanical notions enabled

o

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 tc
describe a circle, as wheu 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, Avas 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," 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

Op. vol. iv. p. 490.

DISCOVERY OF THE LAWS OF MOTION. 831

from this theoretical result. For it may be observed, that the curvilinear
paths ascribed to military projectiles by Rivius and Tartalea, and bj
other writers who followed them, as Digges and Norton in our own
country, though utterly different from the theoretical form, the parab-
ola, do, in fact, approach nearer the true paths of a cannon or inuskei
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, 12 that the velocities of the projec-
tiles, 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 appli-
cations of the doctrine of projectiles no doubt had a share in estab-
lishing 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.

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 rela-
tion of inverse proportionality in a single word (avrnrtTrovOev), 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 conjec-
ture only, and had, therefore, no scientific value. This is the judg-
ment which we must pass on the book of Jordanus Nemorarius, which

11 Op. vol. iii. p. 147.

332 HISTORY OF MECHANICS.

tve have already mentioned. Its reasonings are professedly on Aris-
totelian 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 satis-
factorily proved, indeed, but much more distinctly conceived. This is
his first theorem : " Duarum virium connexarum quarurn (si moveantur)
motus erunt ipsis dvTtireTTOvdu)$ proportionales, neutra alteram move-
bit, 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

DISCOVERY OF THE LAWS OF MOTION. 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 pro-
duced, are called Virtual Velocities. And the general law of equilib-
rium 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 pro-
perty 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 pro-
portion of its greater magnitude. Accordingly, Aristotle, whose en-
tire 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 prin-
ciple 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 dis-
covery 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

38-i HISTORY OF MECHANICS.

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 pro-
duct 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

' O

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 pro-
gress of knowledge respecting the mode in which the Mass of the
body influences the effect of Force. This is a more difficult and com-
plex 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

DISCOVERY OF THE LAWS OF MOTIOX. 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 13
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 pusli ?" 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, poiocr, 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 himselt
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, 14 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 ^ohereness.

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 ex-
periment, 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 over-

13 avrtftlhiv. H Rod. cle Arriaga, Carsvs Philosopldcus. Paris, 1639.

336 HISTORY OF MECHANICS.

looked so obvious a fact. F. Piccolomini, in his Liber Sciential Je
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, Avould 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 dis-
covered 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 pro-
per 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 funda-
mental proposition on this subject, one much less evident than that
we have quoted, but one in which that is involved. His Postulate is, 13
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 assump-

is Opere, in. 96.

DISCOVERY OF THE LAWS OF AIOTIOX. 337

lion, but that, not having seen the proof, he will give his own. lu this
he refers us to the right principle, but appears not distinctly to con-
ceive 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 Avere self-evidently equal. Huyghens, in 1673,
expresses himself dissatisfied with, the proof by whicli Galileo's assump-
tion 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 ex-
perimental 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, 16
" that, in a movable body, the impetus, energy, momentum, or pvopm-
sion to motion, is as great as is the/o?-ce 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 am-
biguity of any one term, as appears to have happened to some mathe-
maticians. 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. 17 When Viviani was study-
ing 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 look-
ing at the proof, that the discoverer had had to struggle, not for inter-
mediate steps of reasoning between remote notions, as in a problem ot
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, be-
cause 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 com-
pare the forces of bodies at rest and in motion under the obscurity and
vacillation thus produced.

Galileo, Of. iii. 104. > : Drinkvater, Life of Galiko, p. 59.

VOL. I. 22

338 HISTORY OF MECHANICS.

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 slanno in su V Acqua, says, that
"Momentum is the force, efficacy, or virtue, with Avhich the motion
moves and the body moved resists, depending not upon weight onlv,
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 prede-
cessors and contemporaries, had speculated concerning the problem of
Percussion, he did not arrive at any satisfactory conclusion ; and the prob
lem remained for the mathematicians of the next generation to solve.

We may here notice Descartes and his Laws of Motion, the publica-
tion of which is sometimes spoken of as an important event in the his-
tory 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 sev-
eral 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 Gali-
leo, 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
aian 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, dcs Sciences Mathematiques en Italic, t. iii. p. 131) : "This short
analysis is sufficient to show that, at the period at which we are ar-
rived, 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 strug-

DISCOVERY OF THE LAWS OF MOTION. 309

gle was begun by Descartes, and they proclaim him the legislator of
modern philosophers. But when we examine the philosophical writ-
ings 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 es
teemed 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, estab-
lished truths inconsistent with the received Aristotelian doctrines. Gil-
bert in England, Kepler in Germany, as well as Benedetti and Galileo
in Italy, gave a powerful impulse to the cause of real knowledge, be-
fore 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. lie announced a
Xew 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 HISTORY OF MECHANICS.

CHAPTER III.

SEQUEL TO THE EPOCH OF GALILEO. PERIOD OF VERIFICATION AND

DEDUCTION.

TIIIE evidence ou which Galileo rested the truth of the Laws of Mo-
tion 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 Treat-
ises on Falling Bodies, Inclined Planes, Pendulums, Projectiles, Spout-
ing 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 Cas-
telli, 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 rep-
utation when we find Milton referring thus to his travels in Italy : l
"There it was that I found and visited the famous Galileo, grown old,
i prisoner in the Inquisition, for thinking in astronomy otherwise than
the Franciscan and Dominican licensers thought."

Besides the above writers, we may mention, as persons who pursued
and illustrated Galileo's doctrines, Borelli, who was professor at Flor-
ence and Pisa ; Merseune, the correspondent of Descartes, who was

i Speech for the Liberty of Unlicensed Printing.

SEQUEL TO THE EPOCH OF GALILEO. 3-il

professor at Paris ; Wai Us, who Avas appointed Saviliau professor at
Oxford in 1G49, his predecessor being ejected by the parliamentary
commissioners. It is not necessary for us to trace the progress ol
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 Co-
pernican 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 ele-
vated 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 be-
long to the history of Astronomy, and form part of the Sequel to the
Epoch of Copernicus, belong more peculiarly to the history of Mechan-
ics, 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 exper-
iment. Gassendi made many experiments on this subject publicly, of
which an account is given in his Epistolce ires de Motu Impresso a
Motore Translate? 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 mo-
tion were invalid. This restriction enabled Riccioli and other writers
on the geocentric side to involve the subject in metaphysical difficul-
ties'; but the conviction of men was not permanently shaken by these,
and the Second Law of Motion w 7 as soon assumed as unquestioned.

The Laws of the Motion of Falling Bodies, as assigned by Galileo, were
confirmed by the reasonings of Gassendi and Fermat, and the experi-
ments of Riccioli and Grimaldi ; and the effect of resistance was point-
ed out by Marsenne 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

Mont. ii. 109.

5-12 HISTOKY OF

is well adapted to attract notice, since the curve described, which is
transient and invisible in the case of a single projectile, becomes per-
manent 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, Delia Misura delV Acque Corrente (1G38),
is the first work on this subject, and Montucla with justice calls him
" the creator of a new branch of hydraulics ;" 3 although he mistakenly
supposed the velocity of efflux to be as the depth of the orifice from the
surface. Marsenue and Torricelli also pursued this subject, and after
them, many others.

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 fact so great as entirely to change the form and properties
of the curve. Notwithstanding this, the parabolic theory was employ-
ed, as in Anderson's Art of Gunnery (It374) ; and Blonde], in his
Art de jeter les Bomles (1C 83), not only calculated Tables on this sup-
position, 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 mathe-
maticians 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 trans-
lation. 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 thou-
sand pounds than a weight of a hundred ; another respecting space, as

Mont. ii. 201.

SEQUEL TO THE EPOCH OF GALILEO. 345

when we say that it requires more force to throw a stone one hundred
paces than fifty." 4 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 oi
percussion, however small." 5 lie 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 re-
moving the apparent incongruity of continuous and instantaneous force..
was a material step in the solution of the problem.

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 Iluyghens, who about the same time
(16G9) sent papers to the Royal Society of London on the subject. In
these solutions, we perceive that men were gradually coming to appre-
hend 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 dynam-
ical 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 Traile de In

Op. ill. 210. s iii. 211-

344 HISTORY OF MECHANICS.

Percussion (1084), had asserted this proposition for the case of direct
impact. But by the reasoners of Newton's time, the dynamical prop-
osition, 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 ot
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 iu 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 Mecanigue, in which the whole of statics should be
founded on the composition offerees. This project was published in
1C87; 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 oi
the mechanics of fluids to the corresponding point.

MECHANICAL PRINCIPLES OF FLUIL'*. 345

CHAPTER IV.

DISCOVERY OF THE MECHANICAL PRINCIPLES OF FLUIDS.

Sect. 1. Rediscover)/ of the Laius 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 impo
sible for men to retain such clear views as Archimedes had disclosed.
Stevinus must be considered as the earliest of the authors of this re-
discovery; 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 arti-
fices 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 Hydro-
statics 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 Aris-
totelians, 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 iu 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 HISTORY OF MECHANICS.

of ebony sinks in water, while aflat 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 Co-
lombe ; 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 equi-
librium 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, 1 talks of the
"gravity of the air," and of its power of diffusing itself when con-
densed, as the causes of wind ; but we can hardly consider such pro-
priety 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 hardlv attach

O 1 "

much value to such a recognition of the gravity and elasticity of
the air.

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

1 (Jti<xst. Sat. \. 5.

MECHANICAL PRINCIPLES OF FLUIDS. 347

action of a pair of bellows, its drawing water if immersed in water,
its refusing to open when the vent 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 ihefuya vacui.
Indeed, we must contend that the principle was a very good one, inas-
much as it brought together all these facts which are really of the
same kind, and referred them to a common cause. But when uro-ed

' O

as an ultimate principle, it was not only unphilosopliical, but imper-
fect 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 point-
ing out any physical cause ; and it was torong, because it gave an un-
limited 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
1043, 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 Baliaui, writing to him in 1630, says, 5 "I{
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 1G31, he explains the suspension of
mercury in a tube, closed at top, by the pressure of the column of air
reaching to the clouds.

Drinkvvatei-'s GallUo, p. 00.

348 HISTORY OF MECHANICS.

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 goino- to
a high place, we alter the weight which it will support. This cele-
brated 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 Dome 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 can-
not 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 diffi-
culties in the progress of the theory of Hydrostatics. When mathe-
maticians 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 differ-
ent conception of the fundamental nature of fluid equilibrium.

Sect. 2. Discovery of the Laws of Motion of Fluids.

THE art of conductiug 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.

Wh^n a fluid spouls from an orifice in a vessel, Castelli saw that
the velocity of efflux depends on the depth of the orifice below the

MECHANICAL PRINCIPLES OF FLUIDS. 34.S

surface : but he erroneously judged the velocity to be exactly propor-
tional to the depth. Torricelli found that the fluid, under the inevit-
able causes of defect which occur in the experiment, would spout
nearly to the height of the surface : he therefore inferred, that the

/ O

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
Accelerate, printed in 1G43.

Newton treated the subject theoretically in the Principia (1687) ;
but we must allow, as Lagrauge savs, that this is the least satisfactory

O O J ' v

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 Principiaf Newton gave a train of reason-
ing 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 repeti-
tion : how was this discrepancy to be explained?

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 clue 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 (1*714), 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 cat-
aract ; and supposes that while this part descends, the surrounding

3 B. ii. Prop, x.xxvii.

350 HISTORY OF MECHANICS.

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 prob-
lems 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 (ffydraulify, 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. 4 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 engi-
neers are able tc obtain, between their calculated and observed results,

Eennie, Report to Brit.

MECHANICAL PRINCIPLES OF FLUIDS. 351

is very groat: but these calculations are performed by means of
empirical formulae, which do not connect the facts with their causes,
and still leave a wide space to be traversed, in order to complete the
science.

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 pro-
gress we must relate.

[2d Ed.] [The hydroclynamical 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 Princ'qria, an explanation of the waves
of water (Lib. ii. Prop. 44), which appears to proceed upon an erro-
neous 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 sub-
ject, 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 Ondcs, 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
Encyclopedia 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 conse-
quences more simple than they are in most other problems of Hydro-
dynamics.

352 HISTORY OF MECHANICS.

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 vary-
ing in magnitude and direction. This was the task of the generaliza-
tion of the laws of motion.

Galileo had convinced himself that the velocity of projection, and
that which gravity alone would produce, are "both maintained, with-
out being altered, perturbed, or impeded in their mixture." It is to be
observed, however, that the truth of this result depends upon -a par-
ticular 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 Avhich are heterogeneous. Descartes had noticed this difficulty,
but without giving any satisfactory solution of it. 1 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 fells towards the earth's centre, and is, at the same time, carried

Princip. P. iii. 59.

GENERALIZATION OF PRINCIPLES. 353

rouud by the motion of the earth ; and obtained an erroneous result.
Kepler and Fermat attempted the same problem, and obtained solu-
tions different from that of Galileo, but not more correct.

Even Newton, at an early period of his speculations, had an erro-
neous opinion respecting this curve, which he imagined to be a kind
of spiral. Ilooke animadverted upon this opinion when it was laid
before the Royal Society of London in 1679, and stated, more truly,
that, supposing n<3 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 prob
lem occurs, so far as I know, in the Theorems of Huyghens concern-
ing Circular Motion, which were published, without demonstration, at
the end of his Horologium Oscillatorium, in 1673. It was there as-
serted that when equal bodies describe circles, if the times are equal,
the centrifugal forces will be as the diameters of the circles; if the
volocities 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 limit-
ing 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 gur 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 dis-
tinction 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 ivhat ivas the truth with regard to the mechanism of
the universe remained to be determined by other means. Physical As-
tronomy, at the period of which we speak, eclipsed and overlaid theo-
VOL. I. 23

354 HISTORY OF MECHANICS.

retical Mechanics, a?, 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 ex-
ercises 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 1660, 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 pro-
mulgator 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, beganto perceive the
real nature of the question. As early as 1666, we read, in the Jour-
nals 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 super-
vening attractive principle ;" and before the publication of the Prin-
cipia 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, 2 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 16S4, 3
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

- Newt. Princlp. Scliol. to Prop. iv. 8 Sir D. Brcwster's Life of Neicton, p. 154

GENERALIZATION OF PRINCIPLES. 355

force, and, on the 10th of December, 4 announced to the Royal Society
that he had seen Mr. Newton's book, De Molu Corporum. The feel-
iu^ that mathematicians were on the brink of discoveries such as are

O

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
Pldlosophicc NaturaUs 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,
li that the method was so much the more to be prized as it was both
invented and perfected at the same time."

The reader will recollect that we are here speaking of the Principiu
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 w r hich 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 Laics of Mo-
tion, which stand at the beginning of the book, are a much clearer and

7 O O

more general statement of the grounds of Mechanics than had yet ap-
peared, they do not involve any doctrines which had not been pre-
viously stated or taken for granted by other mathematicians.

The work, however, besides its unrivalled mathematical skill, em-
ployed 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,

O '

philosophers have pursued their researches in vain. And I hope

* Id. p. 1S4.

356 HISTORY OF MECHANICS.

that the principles expounded iu 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.

t, 9. Generalization of the Third Law of Motion. Centre of
Oscillation. Huyghens.

THE Third Law of Motion, whether expressed according to New-
ton's formula (by the equality of Action and Reaction), or in any
other of the ways employed about the same time, easily gave the solu-
tion of mechanical problems in all cases of direct action ; that is, when
each body acted directly on others. But there still remained the prob-
lems 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, " inotus," will not be altered by
beiuo; communicated. This principle is true, if, by motion, we under-
stand 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, con-
sidered the velocity only; thus making 'motion, in this case, identical
with the momentum which he introduces iu treating of the simpler case

GENERALIZATION OF PRINCIPLES. 357

of the third law of motion, when the action is direct. This error was
retained even in the later editions of the Pi-ina'pia*

The question of the centre of oscillation had been proposed by M<-r-
senne somewhat earlier, 6 in 1G46. 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 Per-
cussion. The Centre of Percussion is the point about which the mo-
menta 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 ; Des-
cartes 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.

Huyghens was hardly advanced beyond boyhood when Mersenne
first proposed this problem ; and, as he says, 7 could see no principle
which even offered an opening to the solution, and had thus been re-
pelled at the threshold. When, however, he published his Horologium
Oscillatorium in 16V3, 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 ori-
ginal position ; and this consideration leads to a determination of the
oscillation of a compound pendulum. We may observe, in the prin-
ciple thus selected, a conviction that, in all mechanical action, the cen-
tre 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, 8 that he assumes only this, that a heavy body
cannot, of itself, move upwards.

5 B. iii. Lemma iii. to Prop, xxxix. < Mont. ii. 423.

i Hor. Osc. Pref. * Ifor. Osc. p. 121.

358 HISTuKY OF MECHANICS.

Clear as Huyghen's principle appeared to himself, it \Vas, after some
time, attacked by the Abbe Catelan, a zealous Cartesian. Catelau
also put forth principles which he conceived were evident, and deduced
from them conclusions contradictory to those of Huygheus. His prin-
ciples, now that we know them to be false, appear to us very gratu-
itous. 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 pen-
dulum 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 Huygheus. As the discussion thus proceeded, it began
to be seen that the question really was, in what manner the Third
Law of Motion Avas 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 mathe-
maticians," 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 communi-
cated from the one body to the other to be distributed in the same
proportion in which a load supported on the lever would be distrib-
uted ?" 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 Ber-
noulli 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 1'IIopital ; 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 mathema-
ticians, &c."

We may, from this time, consider as known, but not as fully estab-
lished, the principle that " When bodies in motion affect each other,
the action and reaction are distributed according to the laws of Sta-
tics ;" although there were still found occasional difficulties in the

' O

GENERALIZATION OF PRINCIPLES. 359

generalization and application of the rule. James Bernoulli, in 1703,
gave "a General Demonstration of the Centre of Oscillation, drawn
from the nature of the Lever." In this demonstration 9 he takes as a
fundamental principle, that bodies in motion, connected by level's,
balance, when the products of their momenta and the lengths of the
levers are equal in opposite directions. For the proof of this proposi-
tion, he refers to Marriotte, who had asserted it of weights acting by
percussion, 10 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. 11 Moreover, says Bernoulli, there is no one who
denies it. Still, this kind of proof was hardly satisfactory or elemen-
tary enough. John Bernoulli took up the subject after the death ot
his brother James, which happened in 1705. The former published
in 1714 his Meditalio de Naturct 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

o

lever. 12 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 be-
tween the English mathematicians and those of the Continent. Her-
mann 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 oj
gravity" and the "-vicarious solicitations" which conespond 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.

It was shown by John Bernoulli and Hermann, and was indeed
easily proved, that the proposition assumed by Huyghens as the foun-
dation, of his solution, was, in fact, a consequence of the elementary
principles which belong to this branch of mechanics. But this as-
sumption of Huyghens was an example of a more general propositiun,
which by some mathematicians at this time had been put forward as
in 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

9 Op. ii. 000. 10 Choq. d(s CVw, p. 236.

Ib. Prop. xi. '- P. 172.

360 HISTORY OF MECHANICS.

make this cliano-e was the commencement of one of the most obstinate

O

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 1680, he published, in the Leipsic Acts, "A short
Demonstration of a memorable Error of Descartes and others, concern-
ing 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 qx;antity 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 mo-
menta in this case are as one to two. This was answered by the Abbe
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 1095 laid down the dis-
tinction between vires mortuce, or pressures, and vires vivce, 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, 13 made him think for him-
self, which ended in his proving directly that which Leibnitz had de-
fended 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 conve-
niently 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 tiuicc 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 conve-
niently use similar methods..

But it was not till a later period that the question excited any
general notice. The Academy of Sciences of Paris in 1724 proposed

is Op. iii. 40.

GENERALIZATION OF PRINCIPLES. 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.' 4 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 New-
tonian system. It was, howevec, 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 par-
ticular 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
Leibuitzian memoirs by Hermann, Bullfinger, and Wolff. In England,
Clarke was an angry assailant of the German opinion, which S'Grave-
sande maintained. In France, Mairan attacked the vis viva in 172S ;
"with strong and victorious reasons," as the Marquise du Chatelet
declared, in the first edition of her Treatise on Fire. 1 * 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 Moviny
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.

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

14 Discours sur Us Loix de la Communication da Mbuvemcnt. > 5 ilout. iii.

362 HISTORY OF MECHANICS.

had taken place somewhat earlier; and that law which is more par
ticularly 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. Iluygheus,
Marriotte, the two Bernoullis, L'Hopital, 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 prin-
ciple 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.

E have now finished the history of the discovery of Mechanical
Principles, strictly so called. The three Laws of Motion, gen-
eralized 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
pel-formed by means cf the reasonings of mathematics ; and the science

SEQUEL TO THE GENERALIZATION. 863

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 mod-
ifications of this kind.

1. Geometrical Mechanics, Newton, ct-c. The first great systematical
Treatise on Mechanics, in the most general sense, is the two first Books
of the Prindpia of Newton. In this work, the method employed is
predominantly geometrical : not only space is not represented symbol-
ically, 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. Eulsr. 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 geom-
etry, had great attractions for minds to which they became familiar.
The person who did most to give to analysis the generality and syru-

364 HISTORY OF MECHANICS.

metry which are now its pride, was also the person w no made Mechanics
analytical ; I mean Euler. He began his execution of this task iu
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 Trans-
actions of the Imperial Academy of Sciences. In the preface to this
work, lie 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, happen-
ing to think of the line of Virgil,

Anehora de prora 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 cal-
culate 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 en-
rich 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 Prin-

SEQUEL TO THE GENERALIZATION. 365

*

ciple in 1*743, 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 mo-
tions of several bodies, with or without weight, which pull or push
each other by menus 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, respect-
ing 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
or 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'Alcmbert's Principle. D'Alembert's Principle is only the ex-
pression, 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 par-
ticle 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 distinc-
tion 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 re-
duces 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

tt

determining the laws of equilibrium, in the application of this prin-
ciple 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 HISTORY OF MEgHAXICS.

real or imagined blemishes in the work. Against the validity oi
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 seri-
ously 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, 17 12, when the impres-
sion of the second edition of the Principia was just drawing to a,
close, under the care of Cotes at Cambridge ; and Newton immedi-
ately cancelled the leaf and corrected the error. 1

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 New-
ton 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 procrastina-
tion, 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 Avhom 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

MS. Correspondence in Triii. Coll. Library.

SEQUEL TO THE GENERALIZATION. 367

higher or brighter. The gieat discoveries of Copernicus, Galileo,
Newton, had fixed all eyes on those portions of human knowledge on
which their successors employed their labors. The certainty belong-
ing to this line of speculation seemed to elevate mathematicians above
the students of other subjects ; and the beauty of mathematical rela-
tions, 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. Thai 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 Mau-
pertuis visited John Bernoulli, at that time the. Nestor of mathemati-
cians, 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 bril-
liant 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 ma-
thematical works of the century.

7. The Problem of Three Bodies. In 1747, Clairaut and D'Alem-
bert 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 gen-
erally, 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 HISTORY OF MECHANICS.

One consequence of the synthetical form adopted by Newton in the
Principia, was, that his successors had the problem of the solar sys-
tem to begin entirely anew. Those who would not do this, made nc
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 ac-
curacy.

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
Theoriede 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, pub-
lished 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 cer-
tain algebraical equations, which express the mechanical conditions of
the motion. The operation, by which the result is to be obtained, in-
volves 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 re-
quire us to know the very thing which we have to determine by the
operation. The result must be got at, therefore, by successive approx-
imations : 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

SEQUEL TO THE GENERALIZATION. 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 eccen-
tricities 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 con-
tinue 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 complex-
ity 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 rapidiy does : *
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 suc-
ceeded 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 re-
duces the solution, 5 adds, " Integrate them who can" (Integre main-
tenant qui pourra). New methods of approximation were devised for
this case.

The problem of three bodies was not prosecuted in consequence ot
its analytical beauty, or its intrinsic attraction ; but its great difficul-
ties 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 mathemat-
ical 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 approxima-

Journal des Sevang, Aug. 1753.
VOL. I. 24

370 HISTORY OF MECHANICS.

tions 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 1*748 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 neces-
sary to consider each satellite as disturbed by the other three at once ;
zmd thus there occurred the Problem of Five Bodies. This problem
was resolved by Lagrange. 3

Again, the newly-discovered small Planets, Juno, Ceres, Vesta,
Pallas, whose orbits almost coincide with each other, and are more in-
clined 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 4 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 El-
liptical orbit which the planet describes. 5 Taking this view, he deter-

3 Bailly, Ast. Mod. iii. 178. 4 Gautier, Prol. de Trois Corps, p. 155.

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 New-
ton, whose mode of representing the paths of bodies by means of a Revolving Orlit,
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 Mecanique Celeste, livre
xv. p. 305, is an abstract of Euler's paper of 1749 ; where Laplace adds, " C'est le
premier essai de la methode de la variation des constantes arbitrages." And in
page 810 is an abstract of the paper of 1756 : and speaking of the method, Laplace

SEQUEL TO THE GENERALIZATION. oTl

mines the secular changes of each of the elements or determining quan-
tities of the orbit. lu 1773, Laplace also attacked this subject of
secular changes, and obtained expressions for them. Ou 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 re-
versed ; no increase, which is not, after some period, changed into de-
crease ; 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 conse-
quence of the laws of universal attraction. In 1774 and 1776, La-
grange 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, 7
was true, however far the approximation was carried, so long as the
squares of the disturbing masses were neglected. He afterwards im-
proved his methods ; 8 and, in 1783, he endeavored to extend the calcu-
lation of the changes of the elements to the periodical equations, as
well as the secular.

8. Mecanique Celeste, &c. Laplace also resumed the consideration
of the secular changes; and, finally, undertook his vast work, the
Mecanique Celeste, 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 ao-e. the enthusiasm which had been ex-

o o *

cited 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
Mecanique Celeste ; the object of which was to improve still further

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 ; C, 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 Mcc. Cil. vol. v. p. 812. But Euler's conception and treatment of the method
nre complete, so that he must be looked upon as the author of it.
* Gautier, p. 104. 7 Ib. p. 1S1. 6 Ib p. VS

372 HISTORY OF MECHANICS.

the mode of obtaining the secular variations of the elements. Poisson

o

and Lag-range 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, ex-
tended the perturbing function as far as the sixth order of the eccen-
tricities. Gauss, Hauseu, and Bessel, Ivory, MM. Lubbock, Plana,
Pontecoulant, 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 sub-
ject 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 mathe-
maticians of the last century had determined, in a demonstrative man-
ner, 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 ap-
proximation employed in Physical Astronomy rested on arbitrary pro-
cesses, 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, an:l thus made the result conceivable
more distinctly than as a mere result of calculation. And it appears

SEQUEL TO THE GENERALIZATION. 373

to me that Professor Airy's treatise entitled Gravitation, published at
Cambridge in 1834, is of great value in supplying similar modes ol
conception with regard to the mechanical origin of many of the prin-
cipal inequalities of the solar system.

Bessel iu 1824, and Hansen in 1828, published works which are
considered as belonging along with those of Gauss, to a new era in

O O ' O

physical astronomy. 9 Gauss's Thcoria Motuuin Corpomm Cclestium,
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 Plan-
ets was recognized by the Astronomical Society of London, which
awarded to them its gold medal.

The investigations of M. Damoiseau, and of MM. Plana and Carliui,
on the Problem of the Lunar Theory, followed nearly the same course
as those of their predecessors. In these, as in the Mecanique Celeste,
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 re-
version 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. Pontecoulant have made the mean longitude
of the moon, that is, the time, the independent variable, and have ex-
pressed 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 Pontecoulant
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.
Pontecoulant conceives that the method of variation or arbitrary con-

9 AlKand. der Akad. d. Wissfnsch. zu Berlin. 1824 ; and Dixquisitiones circa Theo
riam Perturbation/urn, See Jalm. Gesch. der Astron. p. 84.

374 HISTORY OF MECHANICS.

stants may most conveniently be reserved for secular inequalities and
inequalities of long periods.

MM. Lubbock and Pontecoulant Lave 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 Fundamental, Nova Investiyaiionis Orbitce
ver<% quam Luna fwlustrat (Gothce, 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 Mechan-
ical 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 mutually attracting bodies, given by
Sir W. K. 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 formula supply a means
of successive approximation without limit.]

9. Precession. Motion of Rigid Bodies. The series of investiga-
tions 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, 10 in the mean time, had published, in 1751, a solution of the

Ac. Bed. 1745, 1750.

SEQUEL TO THE GENERALIZATION. 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" about 17GO, and published in 1765.
The formulae in this work were much simplified by the use of a dis-
covery of Seguer, 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 Trans-
actions for 1785 ; but I think it is impossible to consider this criticism
otherwise than as an example of the inability of the English mathe-
maticians of that period to take a steady hold of the analytical general-
izations 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 Libra-
don and by which he showed that the Nodes of the Moon's Equator
and those of her Orbit must always coincide.

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, pub-
lished 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

11 See the preface to the book.

376 HISTORY OF MECHANICS.

1*748, Euler not only assented to the generalization of D'Alembert,
but held that it was not necessary tbat the curves so introduced should
be defined by any algebraical condition whatever. From this extreme
indeterminateness D'AJembert 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 com-
plex 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 iu 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 accord-
ingly was done, by the founders of mechanics, both for the cases of
the equilibrium and of motion. Newton's attempt to solve the prob-
lem 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

SEQUEL TO THE GENERALIZATION. 371

weight of columns of the fluid reaching to the centre ;

O <J

took, as his basis, the prepeudicularity of the resulting force at each
point to the surface of the fluid ; Bouguer conceived that both prin-
ciples were necessary ; and Clairaut showed that the equilibrium ol
all canals is requisite. He also was the first mathematician who de-
duced from this principle the Equations of Partial Differentials by
which these laws are expressed ; a step which, as Lagrange says, 12
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.

The explanation of the Tides, in the way in which Newton at-
tempted 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 Firjure of the Earth, by Clairaut, in 1743, ex-
tended 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 eccen-
tricity, which is, as Professor Airy has said, 13 " a calculus the most
singular in its nature, and the most powerful in its effects, of any
which has yet appeared."

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, u in 1738, states that he
passes over the subject, because he could not reduce the facts to gen-
eral laws : but Clairaut was more successful, and Laplace and Poisson
have since given great analytical completeness to his theory. At pres-
ent our business is, not so much with the sufficiency of the theory tc
explain phenomena, as with the mechanical problem of which this is
an example, which is one of a very remarkable and important char-
acter; namely, to determine the effect of attractions which are exer-
cised by all the particles of bodies, on the hypothesis that the attrac-

12 Mic. Anal'jt. ii. p. ISO. 1S Enc. lid. Fig. of Earth, p. 192.

14 Hydrodyn. Tref. p. 5.

378 HISTORY OF MECHANICS.

tion of each particle, though sensible when it acts upon another par-
ticle 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 ob-
tained under conditions so general and so peculiar, is curious and
abstract ; the problem has been resolved in some very extensive cases.
13. Motion of Fluids. The only branch of mathematical mechan-
ics which remains to be considered, is that which is, we may venture
to say, hitherto incomparably the most incomplete of all, Hydro-
dynamics. It may easily be imagined that the mere hypothesis oi
absolute relative mobility in the parts, combined with the laws of mo-
tion 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 acknowl
edged 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 sutlers 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 Hydro-
Jynamica was published in 1738. This work rests upon the Huy-
gheuiau 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 j or, in other words, the con-
servation of vis viva. This was the first analytical treatise ; and the
analysis is declared by Lagrange to be as elegant in its steps RS it is
simple in its results. Maclaurin also treated the subject ; but is ac-
cused 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 Res istance of Fluids in. 1753. His JRe-
fiexions sur la Cause Generale 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

SEQUEL TO THE GENERALIZATION. 379

have been mentioned, lie and Lag-range 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 ab-
struse considerations concerning the significations of the integrals of

o o o

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 me-
chanical proposition, unproved, and only conjectured to be true-;
namely, 15 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.

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 condi-
eions 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 a 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 Ave 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, inter-
mediate 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.

i 5 Mec. &l. t. ii. p. 21S.

380 HISTORY OF MECHANICS.

The reason of this peculiarity in the science of Hydrodynamics appears
to be, that its general principles were not discovered with reference tc
the science itself, but by extension from the sister science of the Me-
chanics of Solids; they were not obtained by ascending gradually
from particulars to truths more and more general, respecting the mo-
tions 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 trav-
ersing 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 mo-
tion ; 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 par-
ticular results.

14. Various General Mechanical Principles. The generalized laws
of motion, the points to which I have endeavored to conduct my his-
tory, include in them all other laws by which the motions of bodies
can be regulated; and among such, several laws which had been dis
covered 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 mathema-
ticians 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 demon-
strated, 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 pub-
lished 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. Man-

SEQUEL TO THE GENERALIZATION. 381

pertuis conceived that he could establish a priori, by theological argu-
ments, 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 char-
acter which the science of Mechanics has now assumed, in consequence
of the extreme analytical generality which has been given it. Sym-
bols, 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 Mccanique Analytique of Lagrange, of which the first
edition appeared in 1T8S, 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 the-
ory of this science, and the art of resolving the problems which it in-
cludes, to general formula?, 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 Anal-
ysis ; instead of making, as had previously been done, Analysis an
implement of Mechanics. 15 The transcendent generalizing 1 genius of

o o o

Lag-range, and his matchless analytical skill and elegance, have made
this undertaking as successful as it is striking.

The mathematical reader is aware that the language of mathemat-

o o

ical 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 Me-
chanics. 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 acknowl-

lc Lagrange himself terms Mechanics, " An Analytical Geometry of four dimen-
sions." Besides the three co-ordinates which determine the place of a body in
-he time enters ns y. fourth co-ordinate. [Note by Littrow.]

382 HISTORY OF MECHANICS.

edge 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 Ve-
locities 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 be-
fore ; and those persons, therefore, who are willing to assent to such a
use of words, can thus obtain an additional generalization of dynamical
principles ; and this, as I have stated, has been adopted in several re-
cent 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 Attrac-
tion in the abstract, we return to the attempt to interpret the phenom-
ena 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 pro-
posed 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 es-
pecially in our own time, to curious and valuable results. Some of
these will be noticed in the Additions to this volume.

BOOK VII.

THE MECHANICAL SCIENCES*
(CONTINUED.)

HISTORY

OF

PHYSICAL ASTRONOMY,

DESCEND from heaven, Urania, by that name

IT 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.

CHAPTER I.

PRELUDE TO THE INDUCTIVE EPOCH OF NEWTON.

"\T7"E have now to' contemplate the last and most splendid period of
'" the progress of Astronomy; the grand completion of the his-
tory 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 assem-
blage 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 com-
plete disclosure of the new truths by the principal discoverer, was pro
ceded 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 Astron-
omy, 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 rniud of
Bacon, who, looking at the progress of knowledge with a more com-
prehensive 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 "Descrip-
tion 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 ; Philos-
ophy neglecting facts, and Astronomy claiming assent to her mathe-
VOL. I. 25

386 HISTORY OF PHYSICAL ASTRONOMY.

matical hypotheses, which ought to be considered as mere steps o (
calculation. " Since, therefore," he continues, 1 " eacli 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 pro-
fessors have been so long dissevered, are, in fact, one and the same
thing, and compose one body of science." It mnst be allowed that,
however erroneous might be the points of Bacon's positive astronomi-
cal creed, these general views of the nature and position of the science
are most sound and philosophical.

(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 re-
duce 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 the nature of this Virtue in various ways, com-
paring 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 athioart 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, suggest-
ed 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

1 Vol. ix. 221. 2 He Stella Ma/'tis, T. 3. c. xxxiv.

PRELUDE TO THE EPOCH OF XEIVTOX. 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 whirl-
pool (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 inter-
preted 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 revo-
lution, as a whirlpool carries straws, could be readily understood ; and
though it appears to have been held by Kepler that this current and
Cortex 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. Kep-
ler'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 spe-
cies," and by the fickleness and variety of his phraseology on the sub-
ject, 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 ven-
ture 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.

(Descartes.} But if Kepler might be excused, or indeed admired,
for propounding the theory of Vortices at his time, the case was differ-
ent 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 shallowucss, that he should have
proclaimed with much pomp this crude invention of the ante-mechan-
ical period, at the time when the best mathematicians of Europe, as
Borelli in Italy, Hooke and Wallis in England, Huyghens in Holland

388 HISTORY OF PHYSICAL ASTRONOMY.

were patiently laboring to bring the mechanical problem of the uni-
verse 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 sugges-
tions rather in the casual examples offered to the sense than in the
exact laws of motion. Nor would it be reasonable to rob this philos-
opher of that credit, of the plausible deduction of a vast system from
apparently simple principles, which, at Jhe 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. Des-
cartes said that he should think it little to show how the world is con-
structed, 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 a priori philosopher has,
however, always a strong feeling in his favor among men. The deduc-
tive 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 ob-
servations, 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 wit-
ness 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 Philosophies) in
1644. In order to arrive at this theory, he begins, as might be ex-
pected 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. Con-
ceiving himseff 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

PRELUDE TO THE EPOCH OF NEWTON. 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. 8
This matter being in motion, the parts are necessarily ground into
a spherical form ; and the corners thus rubbed off (like filings or saw-
dust) form a second and more subtle matter. 4 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 mate-
rial of opakc bodies, as the earth, planets, and cornets. "NVe may suppose,
also, 5 that the motions of these parts take the form of revolving circular
currents, 6 or vortices. By this means, the first matter will be collected
to the centre of each vortex, while the second, or subtle matter, sur-
rounds it, and, by its centrifugal effort, constitutes light. The planets
are carried round the sun by the motion of his vortex, 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 trav-
elling 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 ob-
servation. in details and measures. Its general reception and tempo-
rary 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

/ O J v

and .a soldier; an inoffensive philosopher, attacked and persecuted

Prin. p. 53. * Ib. p. 59. 5 Ib. p. 5'"..

Ib. p. 61. ' Ib. c. 140, p. 114.

390 HISTOEY OF PHYSICAL ASTEOXO.MY.

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 dauo-hter

' / o

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 ple-
num. Undoubtedly he tried to avoid promulgating opinions which
might bring him into trouble. He, on all occasions, endeavored to ex-
plain 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 stat-
ing the theory of vortices, he says, 8 " 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 phy-
sical speculations Bacon applies this description. 9

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 but the system was
soon embraced by the younger professors, Avho were eager to dispute
in its favor. It is said" that the University of Paris was on the point
of publishing an edict against these new doctrines, and w ? as only pre-
vented 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 Parnas-

* Prin. p. 56. 9 Bacon, Descriplio Gldbi Intellectmdis

Del. A. M. ii. 193. u Enc. Brit. art. Cartfsianism.

PRELUDE TO THE EPOCH OF NEWTOX. 301

BUS in consequence. It is obvious that, at this time, the cause of Car
tesianisra Avas looked upon as the cause of free inquiry and moderr.
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 -Art-,
Professors and Regents of the University of Paris, humbly showeth.
that it is of public notoriety that the sublime and incomparable Aris-
totle 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 Rea-
son and Experience, have leagued themselves together to dispute his
claim to the rank Avhich 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 td shako
off the yoke of their master, Aristotle ; and, contemning his authority,
with unexampled temerity, would dispute the right which he had ac-
quired 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 foot-
ing in the University of Paris, under the cover of this assault on his
adversaries. The Physics of Rohatilt, a zealous disciple of Descartes,
was published at Paris about 1G70, 12 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.

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' country-
men could no longer refuse their assent and admiration to the New-
tonian theory, it came to be the fashion among them to say that Des-
cartes had been the necessary precursor of Newton ; and to adopt a
favorite saying of Leibnitz, that the Cartesian philosophy was the ante-
chamber of Truth. Yet this comparison is far from being happy : it
appeared' rather as if these suitors had mistaken the door; for those

12 And n second edition in 1GT'2.

392 HISTORY OF PHYSICAL ASTRONOMY.

who first came into the presence of Truth herself, were those who never
entered this imagined antechamber, and those who were in the ante-
chamber 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 Italiau
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.' 3

(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 philoso-
phy, he was far from admiring his work. Gassendi's own views of the
causes of the motions of the heavenly bodies arc not very clear, noi
even very clearly referable 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 " Quse sit rnotrix 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 ot
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
lo describe their orbits.

(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, iy which the causes of most phenomena are deduced
from a certain single universal motion sup2)oscd in our globe ; not tc
be despised either bij the Tychonians or the tyiernicans. He 'supposes

3 Cartesianism, Enc. Phil. H Gassendi, Opera, vol. i. p. C39

PRELUDE TO THE EPOCH OF XEWTOX. 393

.he particles of tli earth to have separate motions, which produce
collisions, and thus propagate 15 an "agitation of the ether," ladiating
in all directions; and, 16 "by the rotation of the sun ou its axis, con-
curring with its rectilinear action on the earth, arises the motion of
the earth about the sun." The other motions of the solar system arc,
as we might expect, accounted for in a s.milar manner ; but it appears
difficult to invest such an hypothesis with any mechanical consistency.

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, be-
longs to a later period of our history ; to the reception, not to the prel-
ude, 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 Mcdicean 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 trans-
verse 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 " that
every planet and satellite revolves round some principal globe of the
universe as a fountain of virtue, which so draw's 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 the nature of the action, as a matter of
conjecture indeed, but with remarkable correctness. 19 " We shall ac-
count 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 in-
stance, 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 acquires, by the circular motion, a
force to recede from the same central body, it comes to pass, that wher,

15 Art. 5. is ib. S. 17 Cap. 2. > ? Ih. 11. '" P. 47.

39-i HISTORY OF PHYSICAL ASTROXOMY.

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."

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 be-
ginning 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
Eno-lish mathematicians : and this we can do with tolerable distinct-

O 7

ness. Gilbert, in his work, De Maynete, printed in 1GOO, has ouly
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 rota-
tion, and that of the revolution of the moon about it. 20 He died iu
1603, and, iu his posthumous work, already mentioned (De Mundo
nostro Sullunari Philosophia nova, 1651), we have already a more
distinct statement of the attraction of one body by another. 21 " 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, ac-
cording 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 prob.-xl^' say the
emne 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.

Lib. vi. cap. 6, 7. 51 Ib. ii. c. 19.

PRELUDE TO THE EPOCH OF XETCTOX. 395

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 inan-
imate,*"' the contrivance is very' rarely so exquisite but that the various
motions and occurrences of their parts may, without much improb-
ability, be suspected capable, after many essays, to cast one another into
several of those circumvolutions called by Epicurus ovorpofias, 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, Wilkius,
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 Eng-
land ; 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 knowl-
edge 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 Lans-
berg's astronomical tables, left papers on this subject, which were lost
by the coming of the Scotch army into England in 1C39; 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. Wilkius
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

52 Shaw's Boyle's Works, ii. 160.

396 HISTORY 'OF PHYSICAL ASTRONOMST.

royal sway. Setli Ward, who was a Fellow of Sidney College, Cam-
bridge, 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, arid 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 pecu-
liar 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 iu
London, and sometimes iu Oxford, according to the changes of fortune
and residence of the members. Hooke went to Christ Church, Oxford,
in 1653, 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
iu the promotion of science.

The connection of the persons of whom, we have been speaking has
a bearing on our subject, for it led, historically speaking, to the pub-
lication 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 pre-
viously to Newton ; and though this pretension could not be main-
tained, 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 166G. Hooke had also spoken more clearly on this subject

PK ELUDE TO THE EPOCH OF NEWTON. 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 under-
taking, 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 attrac-
tive 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 appeal-
that Huyghens made this application of his principles. Newton, how-
ever, had already made this step some years before this time. Accord-
ingly, he says in a letter to Halley, on Hooke's claim to this discovery, 23
" When Huygeuius put out his Iloroloyium 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 Comcta, 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 emana-
tion, 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 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

23 Bioy. Brit., art. Hooke.

'" Bulliakltis, iu 1045, had nsserted that the force by which the sun " prehendit
et harpagat,'' take? hold of and grapples the planets, nui^t be as the inverse square
of the distance.

398 HISTORY OF PHYSICAL ASTRONOMY.

easily conceive, must have appeared of very formidable complexity
while i't was unsolved, and the first of its kind. Accordingly Halley,
as lus '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 Cam-
bridge in August (1684), to Mr. Newton, who supplied him fully with
what he had so ardently sought."

A paper of Halley's in the Philosophical Transactions for January,
1086, 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 Eng-
lish 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, Renault's Physics was used as a class-
.book 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 ot
the sun follows the inverse duplicate proportion of the distances, we
oee that several other persons were on the verge of it at the same time
with Newton ; though he alone possessed that combination of distinct-
ness 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 reason-
ing that brought the conclusion to men's minds with irresistible force.

3 o

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
history of Newton's great discovery properly begins.

INDUCTIVE EPOCH OF XEWTOX. 391)

CHAPTER II.

THE INDUCTIVE EPOCH OF NEWTON. DISCOVERY OF THE UNIVER-
SAL GRAVITATION OF MATTER, ACCORDING TO THE LAW OF THE
INVERSE SQUARE OF THE DISTANCE.

TX order that we may the more clearly consider the bearing of this,
J- the greatest scientific discovery ever made, we shall resolve it into
the partial propositions of which it consists. Of these we may enumer-
ate 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
(he 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 discover-
ed 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 al

iOO HISTORY OF PHYSICAL ASTRONOMY.

least nearly true, before lie 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 in-
formed Newton (in a letter dated June 29, 1686), that Hooke's con-
duct " 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." 1 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," New-
ton 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 Horoloyio Oscil-
latorio, compares the force of gravity with the centrifugal forces of re-
volving bodies."

o

The two steps requisite for this discovery were, to propose the mo-
tions 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 conse-
quence 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 dif-
ficult ; 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, 2 or a curve like
an ellipse. 3 But it does not appear that this was auy thing more than

1 Blog. Brit, folio, art. Hooke. - Kewton's Letter, Biog. Brit., Ilooke, p. 2C60.

s Birch's Hist. E. S., VTallis's Life.

INDUCTIVE EPOCH OF NEWTON. 401

.'i conjecture. Hal ley says" that "Hooke, in 1683, told him he had
demonstrated all the laws of the celestial motions by the recipro-
cally duplicate proportion of the force of gravity ; but that, being
offered forty shillings by Sir Christopher Wren to produce such a de-
monstration, 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 Prmcipia, 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."

Newton allows that Hooke's assertions in 1679 gave occasion to his
investigation on this point of the theory. His demonstration is con-
tained in the second and third Sections of the Principia. He first
treats of the general law of central forces in any curve ; and then, ou
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 solu-
tion 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 in-
ability ; 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

4 Enc, Brit. Hooke, p. 2660.
VOL. I. 26

102 HISTORY OF PHYSICAL ASTRONOMY.

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 proposi-
tion now under notice. We may add, that in the sequel of the third
Section of the Princi-pia, he has traced its consequences, and solved
various problems flowing from it with his usual fertility and beauty ot
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
eosmical 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 occurreBce ; and
by the antithesis which makes a profound theory appear the result ot
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 Pembertou (who had it from Newton himself) in his pre-
face to his View of Newton's Philosophy, and by Voltaire, who had it
from Mrs. Conduit, Newton's niece. 5 " The first thoughts," we are
told, " which gave rise to his Principle*., he had when he retired from
Cambridge, in 1G6G, on account of the plague (he was then twenty-
four years of age). As he sat alone in a garden, he fell into a specu-
lation on the power of gravity; that as this power is not found sensi-
bly 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 him-
self; and if so, her motion must be influenced by it; perhaps she is
retained in her orbit thereby."

.The thought of eosmical gravitation was thus distinctly brought
into being ; and Newton's superiority here was, that he conceived the

6 EUmens de Phil, de Newton, Sme partie, chap. iii.

INDUCTIVE EPOCH OF NEWTON. 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 calcu-
lating 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 in-
verse 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 prob-
able cause of this difference. But Newlon acquiesced in it as a dis-
proof 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 1079, contradicted Newton on the subject of the curve
described by a falling body, and asserted it to be an ellipse, Newton

10-i HISTORY OF PHYSICAL ASTRONOMY.

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 ex-
planation at once. He had been mistaken in the magnitude of the
earth, and consequently in the distance of the moon, which is deter-
mined by measurements of which the earth's radius is the base. lie
had taken the common estimate, current among geographers and sea-
men, 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 me-
chanical calculation for the solar system, gave a stamp from that
moment to his opinions, aud through him to those of the whole philo-
sophical 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 1G66.
And M. Biot, in his Life of Newton, published in the Biographic Uni-
verselle, 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

INDUCTIVE EPOCH OF NEWTON". 405

inversely as the square of the distance, in 1679, upon occasion of hi a
correspondence with Hooke. la 1684, at Halley's request, he returned
to the subject, and in February, 1685, there was inserted in the Regis-
ter of the Royal Society a paper of Newton's (Isaaci Neiotoni Proposi-
tiones 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 " Lunarn gravitare in terrain," nor any of the
other propositions of the third Book. The Princijiia was printed in
1686 and 7, apparently at the expense of Hal ley. On the 6th of April.
168Y, the third Book was presented to the Royal Society.]

It does not appear. I think, that before Newton, philosophers in gen-
eral 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 grav-
ity : 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 sug-
gestion ; but we should err if we inferred from this coincidence of ex-
pression that the notion was commonly entertained before him. Thus
Huyghens appears to use language which may be mistaken, when he
says, 6 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. 7 But Horrox, as early as 1635,
appears to have entertained the true view on this subject, although vi-
tiated 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, 8 that the emanation of the earth carries a pro-
jected 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.

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 de-

6 CosmotJieros, I. 2. p. 720.

7 I have found no instance in which the word is so used by him.

8 Astronomia Kepleriana, defensa tt promote, cap. 2. See further on this subject in
the Additions to this volume.

i06 HISTORY OF PHYSICAL ASTEOX03IY.

fleeted 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 ob-
tained these elements, and ^udgment in selecting among them, were
necessary : thus, the mean distance of the moon had been made as lit-
tle 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 con-
jecture, 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 math-
ematical 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 ver-
ified, 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 diffi-
culties 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 wc - .ald disturb the motions of these bodies. Thus he says
(cap. 14), "How can we believe that the Medicean globes are not,
.ike other planets, impelled with a greater velocity when they approach
the sun : and thus they are acted upon by two moving forces, one o

INDUCTIVE EPOCH OF NEWTOX. 407

which produces their proper revolution about Jupiter, the other regu-
lates their motion round the sun." And in another place (cap. 20),
he attempts to show an effect of this principle upon the inclination ot
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 pri-
mary ones, might seem to be our own moon ; for the great inequalities
which had hitherto been discovered, had all, except the first, or ellip-
tical 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 dis-
turbing 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 infer-
ence 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 satel-
lite 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

iOS HISTORY OF PHYSICAL ASTRONOMY.

any impression on this problem, or course of problems. No one fol
sixty years after the publication of the Principia,, and, with Newton's
methods, no cue up to the present day, had added any thing of any
value to his deductions. AVe know that he calculated all the prin-
cipal 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 calcu-
lations 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 effica-
cious artifices. But Newton's inventive faculty was exercised to au
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 eccen-
tricity of the moon's orbit upon the motion of the apogee, he says, 9
"The computations, as too intricate and embarrassed with approxima-
tions, I do not choose to introduce."

The computations of the theoretical motion of the moon being thus
difficult, and its irregularities numerous and complex, we may ask

9 Schol. to Prop. 35, first edit.

INDUCTIVE EPOCH OF XEWTOX. 409

whether Newton's reasoning was sufficient to establish this part of hi*
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 Inequal-
ity, 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

' O

instances w r as striking. The Variation agreed with Halley's recent
observations within a minute of a degree. 10 The Mean Motion of the

O

Nodes in a year agreed within less than one-hundredth of the whole."
The Equation of the Motion of the Nodes also agreed well. 12 The
Inclination of the Plane of the Orbit to the ecliptic, and its changes,
according to the different situations of the nodes, likewise agreed. 13
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 Quad-
ratures, is, Newton says, " 4|- minutes by the Tables, 6| by our calcu-
lation." 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 obser-
vations 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.

The same theory which gave these Inequalities in the motion of the
Moon produced by the disturbing force of the sun, gave also corres

B. Hi. Prop. 20. " Prop. 32. Prop. C3. 13 Prop. 35.

410 HISTORY OF PHYSICAL ASTRONOMY.

ponding 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

o o

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 ; 14 and it was shown that the motions of their nodes
would .be slow by theory, as Flamsteed had found it to be by observa-
tion. 15 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 ;'"
and he notices in the second edition," that it follows from the theory
of gravity, that the aphelia of Mercury, Venus, the Earth, and Mars,
slightly progress.

In one celebrated instance, indeed, the deviation of the theory of
the Principia from observation was wider, and more difficult to ex-
plain ; 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 1*750,
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 ot
the same amount as that which the sun exerts on the moon, he simply
says, 18 " the apse of the moon moves about twice as fast."

The difficulty of doing what Newton did in this branch of the sub-
ject, 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

14 B. i. Prop. 66. 15 B. iii. Prop. 23. 16 B. iii. Prop. 13.

17 Scholium to Prop. 14. B. iii.

18 B. i. Prop. 44, second edit. There is reason to believe, however, that Kewtor
\iad, in his unpublished calculations, rectified this discrepancy.

INDUCTIVE EPOCH OF NEWTON. 41 i

into many elements, such as can be separated ; to invent artifices for
dealing \vith each of these ; and then to recompound the laws thus ob-
tained 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 com-
ponent 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 re-
lations of space and the laws of force, however complicated be the con-
ditions 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, 19 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.

But we have not yet done with his achievements on this subject ;
for some of the most remarkable and beautiful of the reasouino-s which

O

he connected with this problem, belong to the next step of his geuer
alizatiou.

5. Mutual Attraction of all Particles of Mutter. 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 dog-
~nas have generally nothing accurate or substantial, either in their con-
ception 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 at-

10 See the history of the Problem of Three Hodies, ante, in Book vi. Chop. TU
Sect. 7.

112 HISTORY OF PHYSICAL ASTRONOMY.

traction of matter, we cannot help noticing Francis Bacon ; for his
notions were so far from being chargeable with the looseness and indis-
tinctness to which we have alluded, that he proposed an experiment 20
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 Causa
Gravitatis, published in 1G90, 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 attrac-
tion 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.

That all such forces, cosmical and terrestrial, were the same single
force, and that this was nothing more than the insensible attraction

' O

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

! JYbi>. Org. Lib. ii. Aph. 36.

INDUCTIVE EPOCH OF NEWTON. 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 parti-
cles ? We may reason, as Newton does, 21 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 in-
quiry ; and this he did.

These solutions are no less remarkable for the mathematical power
which they exhibit, than the other parts of the Principia. The prop-
ositions 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 consid-
ered only as a rude approximation. In one (the Precession) he com-
mitted an error, and in all, his means of calculation were insufficient.
Indeed these are much more difficult investigations than the Problem

O

of Three Bodies, in which three points act on each other by explicit
laws. Up to this clay, the resources of modern analysis have been em-
ployed upon some of them with very partial success ; and the facts, in
all of them, required to be accurately ascertained and measured, a pro-
cess 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 explaii:

31 Prinrip. B. iii. Prop. 7.

11-i HISTORY OF PHYSICAL ASTRONOMY.

till such phenomena as have been spoken of. "We shall afterwards
have to speak of the labors, undertaken in order to examine the phe-
nomena 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 re-
sults 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 doc-
trine. For the same reasoning which explained the erection, 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 astrono-
mers 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, 22 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 re-
ferred to the prosthaphseresis of< the moon, and confounded with it."

Reflections on the Discovery. Such, then, is the great Newtonian
Induction of Universal Gravitation, and such its history. It is indis-
putably 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 con-
sidered as an important advance ; would have conferred distinctio*
on the persons who made it, and the time to which it belonged. All

E. iii. Prop. 22.

INDUCTIVE EPOCH OF NEWTON. 415

the five steps made at once, formed not a leap, but a flight,- not ai.
improvement merely, but a metamorphosis, not an epoch, but a ter-
mination. Astronomy passed at once from its boyhood to mature man-
hood. 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. Kep-
ler's laws were merely formal rules, governing the celestial motions ac-
cording to the relations of space, time, and number ; Newton's was a
casual 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 oper-
ates ; questions with which Newton himself struggled. But, in the
mean time, few persons will dispute, that both in generality and pro-
fundity, both in width and depth, Xewton's theory is altogether with-
out a rival or neighbor. 23

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

23 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 Newtoirs
discoveries. "Kepler," says a celebrated German metaphysician,* " discovered the
laws ot fv^e 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 hap-
pened 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 concep-
tion 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 Newtorfs Principia. Cambridge Transactions, 1849.

* Hegel, Encyclopedia, 270.

416 HISTORY OF PHYSICAL ASTRONOMY.

force as the cause of the celestial motions, had, as \ve have seen, beer,
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 iu generality and distinct-
ness ; and in the inventiveness and sagacity with which he traced the
consequences of this conception, he was, as we have sliown, without a
rival, and almost without a second. As to the facts Avhich 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 laivs which his predecessors had estab-
lished. What Kepler and Horrox had put forth as "theories," were
now established truths, fit to be used in the construction of other theo-
ries. 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 Neioton. It is not easy to anatomize the constitution
and the operations of the mind which makes such an advance in knowl-
edge. 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
blocks and mills, carts and dials, as well as the facility with which he

INDUCTIVE EPOCH OF NEWTOX. 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 ; 24 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 invent-
ive faculty in the only way in which it appears possible to conceiye 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 K
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 requi-
site 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.

The hidden fountain of our unbidden thoughts is for us a mystery ;
and we have, in our consciousness, no standard by which we can meas-
ure 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 men-
tioned, 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 discover-

24 As in Galileo, Hooke, Huygliens, and others.
VOL. I. 27

ilS HISTORY OF PHYSICAL ASTRONOMY.

ies, 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 im
pressions and common impulses. The stories which are told of his ex-
treme absence of mind, probably refer to the two years during which
he was composing his Princi-pia, and thus following out a train of rea-
soning 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 cal-
culate and to think." 25 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 fre-
quently 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 steadi-
ness of will the strongest character, as well as the highest endow-
ments, which belong to man.

' o

Newton has been so universally considered as the greatest example
of a natural philosopher, that his moral qualities, as well as his intel-
lect, have been referred to as models of the philosophical character ;
nud those who love to think that great talents are naturally associated
with virtue, have always dwelt with pleasure upon the views given ot
Newton by his contemporaries ; for they have uniformly represented
him as candid and humble, mild and good. We may take as an ex-
ample of the impressions prevalent about him in his own time, the ex-
pressions of Thomson, in the Poem on his Death. 26

Biot.

se 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 . . Matliematieo,
Physico, Chymico consummatisshno ; nee minus suavitate inornin et candore
auimi . . . 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 ever,
Flamsteed speaks well of his general disposition. "Whiston was himself so weak
iud prejudiced that his testimony is worth very little.

INDUCTIVE EPOCH OF NEWTON. 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 uuborrowed 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.

[2d Ed.] [In the first edition of the Principia, published in 1GS7,
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 ob-
s-rvatious. Such observations as he needed for this purpose had been
made by Flarnsteed, and for these he applied, representing how much
value their use would add to the observations. "If," he says, in 1094,
" 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 Astronomies Elemental
He also obtained from Flamsteed the diameters of the planets as ob-
served at various times, and the greatest elongation of Jupiter's Satel-
lites, both of which, Flamsteed says, he made use of in his Principia.

Newton, in his letters to Flamsteed in 1694 and 5, acknowledges
this service. 53

aT In the Preface to a Treatise on Dynamics, Parti., published in 1S36, I have
endeavored to show that Newton's modes of determining several of the lunar in-
equalities admitted of an accuracy not very inferior to the modern analytical methods.

38 The quarrel on the subject of the publication of Flamsteed's Observations took

420 HISTORY OF PHYSICAL ASTRONOMY.

CHAPTER III.

SEQUEL TO THE EPOCH OF NEWTON*. RECEPTION OF THE

N THEORY.

Sect. 1. General Remarks.

THE doctrine of universal gravitation, like other great steps in sci-
ence, 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, eacli 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 discover-
ies, only so far as it illustrates their philosophy. And though the

place at a later period. Flauisteed wished to have his Observations printed com-
plete and entire. Halley, who, under the authority of Newton and others, had the
management of the printing, made many alterations and omissions, which Flam-
steed considered as deforming and spoiling the work. The advantages of publish-
ing 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 print-
ed by Halley might be removed out of the Bodieian Library, where it exists, ns be-
ing "nothing more than an erroneous abridgment of Mr. Flamsteed's works," and
unfit to see the light.

SEQUEL TO THE EPOCH OF NEWTOX.

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 Ave 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 in-
stance it is most important ; both from, the weight and dignity of the
theory concerned, and the ingenuity and extent of the methods em-
ployed : and, of course, so long as the Newtonian theory still required
verification, the question of the truth or falsehood of such a grand sys-
tem 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 cer-
tainly 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 lead/nt.

422 HISTORY OF PHYSICAL ASTRONOMY.

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 riot 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 Priii-
cipia, 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 men-
tioned except in terms of profound admiration ; as, for instance, when
he is called by Dr. Bentley, in his sermon, 1 " That very excellent and
divine theorist, Mr. Isaac Newton." It appears to have been soon sug-
gested, that the Government ought to provide in some way for a per-
son 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 calam-
ity, 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.
It cannot be superfluous to say a word or two on the reception oi

1 Scrm. vii. 21.

SEQUEL TO THE EPOCH OF NEWTON. 423

his philosophy in the universities of England. These are often repre-
sented 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 ot
Edinburgh, so far possessed by them, as to be incapable of seeing, or
interpreting, in any other way, any facts respecting Oxford and Cam-
bridge. 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 estab-
lished ; 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 doc-
trines, and adopt a novel and strange set of principles as soon as pre-
sented; 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
follows of Trinity College in general are ; by his college he was relieved
from all offices which might interfere, however slightly, with his stu-
dious employments, though he resided within the walls of the society
thirty-five years, almost without the interruption of a month. 2 By the
University he was elected their representative in parliament in 1GS8,

2 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 iu rotation. This might
be owing in part, however, to his being Lucasian Professor. The constancy of hi

HISTORY OF PHYSICAL ASTRONOMY.

and again iu 1701 ; and though lie was rejected in the dissolution of
1705, those who opposed him acknowledged him 3 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 bad for him." Instruments and other memo-
rials, valued because they belonged to him, are still preserved in his
college, along with the tradition of the chambers which he occupied.

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 philos-
ophy, as early as 1694 ; and in 1697 published an edition of Renault's
Physics, with notes, in which Newton is frequently referred to with
expressions of profound respect, though the leading doctrines of thy
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 mathe-
matics. 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 Univer-
sity disputations, in order to promote the diffusion of the new mathe-
matical doctrines. By this time the first edition of the Principia was
become rare, and fetched a great price. Beutley 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, Lit-
trow, 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

residence in college appears from the exit and redlt book of that time, which is
still preserved.
3 A pamphlet by Styan Thurlby.

SEQUEL TO THE EPOCH OF XEWTOX. 425

openlv. I am quite sure that any one who looks into this uuttcr will
see that this supposition of any unwillingness at Cambridge to receive
Xexvton'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. AVhiston, 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 Philosophic^
2\'aturalis Princlpia 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 Renault's Physics, it really did contain the best me-
chanical philosophy of the time; the doctrines which were held by
Descartes in common with Galileo, and with all the sound mathema-
ticians who succeeded them. Nor does it look like' any great antip-
athy to novelty in the University of Cambridge, that this book, which
was quite as novel in its doctrines as Newton's Princijria, and which
had only been published at Paris in 1C71, 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 Undu-
latory Theory of Light of Young and Fresnel.

IG Newton's College, we possess, besides the memorials of him men-
tioned 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 Pnnclp'm in the original Latin (184G).

Bentley, who had expressed his admiration for Newton in his Boyle's
Lectures in 1G92, 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 ol

i26 HISTORY OF PHYSICAL ASTRONOMY.

the College, erected a statue of Newton in the College Chapel (a ncble
work of Roubiliuc), with the inscription, Qui genus humanum interne
superavit.]

At Oxford, David Gregory and Hal ley, both zealous and distinguish-
ed disciples of Newton, obtained the Savilian professorships of astron-
omy and geometry in 1091 and 1703.

David Gregory's Astronomice Physicce et Geometricce Element a is-
sued 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 Coelestis), which Isaac Newton, the Prince of Geom-
eters, has carried to a point of elevation which all look up to with ad-
miration. And this design is executed by a full exposition of the
Newtonian 'doctrines and their results. Keill, a pupil of Gregory, fol-
lowed 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 Prin-
cipia 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 Ox-
ford, and was succeeded there by his brother James. The latter had,
as early as 1690, printed a thesis, containing in twenty-two proposi-
tions, a compend of Newton's Principia* Probably these were in-
tended as theses for academical disputatious ; as Laughton at Cam-
bridge introduced the Newtonian philosophy into these exercises. The
formula at Cambridge, in use till very recently in these disputations,
was " Recte statuit Newtonus de Motu Lunce ;" or the like.

The general diffusion of those opinions in England took place, not
only by means of books, but through the labors of various experimen-
tal lecturers, like Desaguliers, who removed from Oxford to London in
1713 ; when he informs us, 5 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."

4 See Hutton's Math. Diet., art. James Gregory. If it fell in with my plan to no-
tice derivative works, I might speak of Maclaurin's admirable Account of Sir Isaa:
Fewtoii's Discoveries, published in 1748. This is still one of the best books on the
subject. The late Professor Eigaud's Historical Essay on the First Publication of
Sir Isaac Neictori's " Pnncipia" (Oxf. 1SCS) contains a careful and candid view of
.lie circumstances of that event.

5 De?ag. Pref.

SEQUEL TO THE EPOCH OF NEWTON. 427

"\Ve might easily trace in our literature indications of the gradual
progress of the Newtonian doctrines. For instance, in the earlier edi-
tions of Pope's Dunciad, this couplet occurred, in the description of
the effects of the reign of Duluess :

o

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 oc-
cult 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. 6 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 ; 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.

To the cordial reception of the Newtonian theory by the English
astronomers, there is only one conspicuous exception ; which is, how-
ever, one of some note, being no other than Flamsteed, the Astron-
omer 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 inter-
est in it. He then declared to one of his correspondents, 8 " 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 un-
derstood 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 tc
satisfy the conditions of Mechanics as well as of Geometry.

6 I presume Bolingbroke is here meant. 7 See Cotes's Pref. to the
* Baily's Account of Flamsteed, <kc., p. 509.

428 HISTORY OF PHYSICAL ASTRONOMY.

[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 New-
ton's suggestions with great deference, and had regulated his own ob-
servations 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 er-
rors. One of the equations was at first published (in Gregory's Astro-
nomice Elemental) 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 consider-
ably later that this amount of exactness was attained.

The late Mr. Baily, to whom astronomy and astronomical literature
are so deeply indebted, in his Siqiplement to the Account of Flamstecd,
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 luuar tables, than a phys-
ical Theory in the modern acceptation of the term. He shows, too,
that Flamsteed had read the Principla, with attention. 9 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 formulae, but also a magnificent phys-
ical discovery, we are obliged, I think, to make Flamsteed, in this re-
spect, an exception to the first class of astronomers of his own time.

Mr. Baily's suggestion that the annual equations for the corrections
rf the lunar apogee and node were collected from Flamsteed's tables

3 Sit pp. p. 691.

SEQUEL TO THE EPOCH OF NEWTOX. 429

and observations independently of their suggestion by Newton as the
results of Theory (Supp. p. 692, Note, and p. G98), 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 ; wh; all clung to one
modification or other of the system of vortices. In France, the Car-
tesian system had obtained a wide and popular reception, having been
recommended by Fontenelle with the graces of his style ; and its em-
pire 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

* O

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 ap 1 -
peared. 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 di-
rectly 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 HISTORY OF PHYSICAL ASTRONOMY.

easy to leave out of sight all other effects of the vortex, and to con-
sider 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 decree,

*f O *

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 in-
crease 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 otheis, as John Ber-
noulli, contrived ways of having elliptical motion in a circular vortex.

The mathematical prize-questions proposed by the French Academy,
naturally brought the tw r o sets of opinions into conflict. The Carte-
sian memoir o-f John Bernoulli, to which we have just referred, was
the one which gained the prize in 1730. It not unfrequently hap-
pened that the Academy, as if desirous to show its impartiality, di-
vided 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 Me-
moir 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 Carte-
sian 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.

SEQUEL TO THE EPOCH OF NEWTON. -iol

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 W.IF
selected by Peter the Great :>f Russia, to found the Academy of St
Petersburg who visited England in 1724, and to whom Newton then

O * O '

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 grav-
itates 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 instru-
mental 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
Tulles of the Sun. In this, however, the mode of explaining the
motions of the planets by means of an original impulse and an attrac-
tive force is attributed to Kepler, not to Newton. The first Memoir
which refers to the universal gravitation of matter is by Maupertuis, in

432 HISTORY OF PHYSICAL ASTRONOMY.

173G. 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 Fonte-
nelle, 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 secre-
tary, he says, 10 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."

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 con-
sequence of the controversy between the rival parties ; and thus the
prevalence of the Cartesian system did not seriously impede the prog-
ress of sound knowledge. In some cases, no doubt, it made men un-
willing to receive the truth, as in the instance of the deviation of the

O '

comets from the zodiacal motion ; and again, when Romer 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.

> Hint. Ac. &. 1708. p. 103.

SEQUEL TO THE EPOCH OF NEWTOX. 433

CHAPTER IV.

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

Sect. 1. Division of the Subject.

verification of the Law of Universal Gravitation as the govern-
J- ing 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 con-
sider 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 con-
firmation 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 ex-
emplification 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, sc
affected, we now proceed.

VOL. I. 28

434: HISTORY OF PHYSICAL ASTRONOMY.

Sec i. 2. Application of the Newtonian Theory to the Moon.

THE Motions of the Moon may be first spoken of, as the most ob
vious 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, iu the construction of Tables derived from the theory,
and the comparison of these with observation. The advancement ot
astronomy would alone have been a sufficient motive for this labor;
but there were other reasons which urged it on with