History of the inductive sciences

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I

000

r

000.

HISTORY

V . . OP THE

»

INDUCTIVE SCIENCES

VOL. I.

\<

HISTORY

OF THE

INDUCTIVE SCIENCES,

FROM THE EARLIEST TO THE PRESENT TIMES.

BY THE

REV. WILLIAM WHEWELL, M.A.,

FELLOW AND TUTOR OT TRINITY OOU<BOK, GAMRRIDOB ; PRUIOSNT OW THE OBOLOOICAL

SOCIBTY or LONDON.

IN THREE VOLUMES.

AofiTrdbia ^xopt€S dtabwrovaiv dXXrjXois.

VOLUME THE FIRST.

LONDON :

JOHN W. PARKER, WEST STRAND.
CAMBRIDGE : J. awd J. J. DEIGHTON.

M.DCCc.xxxyn

I OOO,

TO

SIR JOHN FREDERICK WILLIAM HERSCHEL,

K. G. H.

Mt DEAR HeRSCHEL,

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

VI DEDICATION.

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 admira-
tion of your moral and social, as well as intellectual excel-
lencies, which springs up in the hearts of yonr friends,
whenever you are thought of. They are much delighted
to look upon the halo of deserved fame which plays round
your head ; but still more, to recollect, as one of them said,
that your head is far from being the best part about you.

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

Ever, my dear Herschel,

Yours,

W. Whkwell.

6, Hyde Pabk Street,
22 March, 1837.

PREFACE.

At the present day, any endeavour to improve and
extend the Philosophy of Science may hope to
excite some interest. All persons of cultivated
minds will agree> that a very important advan-
tage would be gained, if any light could be
thrown upon the modes of discovering truth, the
powers that we possess for this end, and the points
to which these may most profitably be applied.
Most men, too, will allow, that in these respects
much .renuiins to be done. The attempts of this
kind, made from time to time, are far from ren-
dering future efforts superfluous. For example, the
Great Reform of Philosophy and Method, in which
Bacon so eloquently called upon men to unite their
ezertioiui in his day, has, even in ours, been very
imperfectly carried into effect. And, even if his plan
had been fully executed, it would now require to be
pursued and extended. If Bacon had weighed well

all that Science had achieved in his time, and had

a 2

«••

Vlll PREFACE.

laid down a complete scheme of rules for scientific
research, so far as they could be collected from the
lights of that age, it would still be incumbent upon
the philosophical world to augment as well as pre-
serve the inheritance which he left ; by combining
with his doctrines such new views as the advances
of later times cannot fail to produce or suggest;
and by endeavouring to provide, for every kind of
truth, methods of research as effective as those to
which we owe the clearest and surest portions of
our knowledge. Such a renovation and extension
of the reform of philosophy appears to belong pecu-
liarly to our own time. We may discern no few or
doubtful presages of its approach ; and an attempt
to give form and connexion to the elements of such
a scheme cannot now be considered premature.

The Novum Organon of Bacon was suitably
ushered into the world by his Advancement of
Learning ; and any attempt to continue and extend
his Reform of the Methods and Philosophy of
Science may, like his, be most fitly preceded by,
and founded upon, a comprehensive Survey of the
existing state of human knowledge. The wish to
contribute something, however little it may be, to
such a Reform, gave rise to that study of the His-

PREFACE. ix

tory of Science of which the present Work is the
fruit. And the effect of these researches has been,
a persuasion, that we need not despair of seeing,
even in our own time, a renovation of sound
philosophy, directed by the light which the History
of Science sheds. Such a reform, when its Epoch
shall arrive, will not be the work of any single
writer, but the result of the intellectual tendencies
of the age. He who is most forward in the work
will wisely repeat the confession of his sagacious
predecessor: Ipse certe (ut ingenue fatear) soleo
sestimare hoc opus magis pro partu Temporis quam
Ingenii.

To such a work, whensoever and by whomso-
ever executed, I venture to hope that the present
Volumes may be usefully subservient. But I trust,
also, that in its independent character, as a History,
this book may be found not altogether unworthy of
the aim which its title implies.

It is impossible not to see that the writer of such
a history imposes upon himself a task of no ordinary
difficulty and delicacy ; since it is necessary for him
to pronoimce a judgment upon the characters and
achievements of all the great physical philosophers
of all ages, and in all sciences. But the assumption

X PREFACE.

of this judicial position is so inevitably involved in
the functions of the historian (whatever be his sub-*
ject), that he cannot justly be deemed presumptuous
on that account. It is true, that the historian of
the progress of science is required by his undei^
taking to judge of the merits of men, in reference
to subjects which demand a far intenser and more
methodical study than the historian of practical life
gives to the actions of which he treats; and the
general voice of mankind, — ^which may often serve as
a guide, because it rarely errs widely or permanently
in its estimate of those who are prominent in public
life, — ^is of little value when it speaks of things
belonging to the region of exact science. But to
balance these disadvantages, and to enable us to
judge of the characters who must figure in our
history, we may recollect that we have before us,
not the record only of their actions, but the actions
themselves; for the acts of a philosopher are his
writings. We do not receive his exploits on tradi-
tion, but by sight ; we do not read of him, we read
him. And if I may speak of my own grounds of
trust and encouragement in venturing on such a
task, I knew that my life had been principally spent
in those studies which were most requisite to enable

PBSFAGE. Xi

me to understand what had thus been done; and
I had been in habits of intercourse with several
of tiie most eminent men of science of our time,
both in our own and in other countries* Having
thus lived with some of the great intellects of the
past and the present, I had found myself capable of
rejoicing in their beauties, of admiring their endow-
ments, and, I trusted, also, of understanding their
discoveries and views, their hopes and aims. I did
not, therefore, turn aside from the responsibility
which the character of the Historian of Science
imposed upon me. I have not even shrunk from
it when it led me into the circle of those who are
now alive, and among whom we move. For it
seemed to me that to omit such portions of the
history as I must have omitted to avoid thus speak-
ing of my contemporaries, would have left my work
mutilated and incomplete ; and would have prevented
its forming a platform on which we might stand
and look forward into the future. I trusted,
moreover, that my study of the philosophers of
former times had enabled me to appreciate the dis-
coveries of the present, and that I should be able to
speak of persons now alive, with the same impar-
tiality and in the same spirit as if they were already

211 PREFACE.

numbered with the great men of the past. Seeking
encouragement in these reflections, and in the
labour and thought which I was conscious of having
bestowed upon my task, I have conducted my history
from the earliest ages of the speculative world up to
our own days.

To some persons it may iappear that I am not
justified in calling thai a History of the Inductive
Sciences, which contains an account of the progress
of the physical sciences only. But it would have
conveyed a false impression of my purpose, had I
described my history in any manner which implied
that the sciences which it embraces are partially
selected or arbitrarily limited. Those of which the
progress is exhibited in the present volumes, appear
to me to form a connected and systematic body of
knowledge. And if there be branches of knowledge
which regard Morals, or Politics, or the Fine Arts,
and which may properly be called Inductive (an
opinion which I by no means gainsay) ; still it must
be allowed, I think, that the processes of collectiug
general truths from assemblages of special £EU3ts, and
of ascending from propositions of a limited to those
of a larger generality, which the term Indiu^tion
peculiarly implies, have hitherto been far more

PREFACE. Xiii

dearly exhibited in the phjrsical sciences which form
the subject of the present work, than in those hyper-
physical sciences to which I have not extended my
history. I will further add, that if I should be
enabled hereafter to lay before the world a view of
the Philosophy of Inductive Science in its general
bearings, it will be requisite, in order to exhibit, in
its due light the state of the philosophy of morals,
or art, or any similar subject, to give a view of
the steps by which it has reached its present
position; and thus such a work will supply that
which some may judge wanting to fill up the outline
of this historical undertaking.

As will easily be supposed, I have borrowed
largely from other writers, both of the histories of
special sciences and of philosophy in general*. I
have done this without scruple, since the novelty of
my work was intended to consist, not in its supe-

* Among these, I may mention as works to which I have
peculiar obligations, Tennemann's Geschichte der Philosophic,
Degerando's Histoire Comparee des Systemes de Philosophic,
Montucla's Histoire des Mathematiques, with Delambre's con-
tinuation of it, Delambre's Astronomic Ancienne, Astronomic
du Mojen ^ge, Astronomic Modeme, and Astronomic du Dix-
huitiime Siecle ; Bailly's Histoire d' Astronomic Ancienne, and
Histoire d' Astronomic Modeme, Voiron's Histoire d' Astronomic

Xiv PRBFAOE.

riority as a collection of &ct0» 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 authors. According to the plan
which I have pursued, the history of each science
forms a whole in itself, divided into distinct but
connected members, by the Epochs of its successive
advances. If I have satisfied the competent Judges
in each science by my selection of such epochs, the
scheme of the work must be of permanent value,
however imperfect may be the execution of any of
its portions.

With all these grounds of hope, it is still impos-
sible not to see that such an undertaking is, in no
small degree, arduous, and its event obscure. But
all who venture upon such tasks must gather
trust and encouragement from reflections like those

(published as a continuation of Baillj), Fischer's Geschichte
der Physik, Gmelin's Geschichte der Chemie, Thomson's History
of Chemistry, Sprengel's History of Medicine, his History of
Botany, and in aU branches of Natural History and Physiology,
Cuviei^s works, in their historical, as in all other portions, most
admirable and iostructire.

PREFACE. XT

by Mrhich their gr^at forerunner prepared himself
for his endeavours; — ^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 labours.

"Concerning ourselves we speak not; but as
touching the matter which we have in hand, this we
ask ; — ^that men deem it not to be the setting up of
an Opinion, but the performing of a Work; and
that they receive this as a certainty ; that we are
not laying the foundations of any sect or doctrine,
but of the profit and dignity of mankiud : — Further-
more, 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 impedi-
ments, they may lend their hands also to the labours
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 infi-
nite dimension and beyond the grasp of mortal man,
when, in truth, it is, of infinite errour, the end and
true limit ; and is by no means unmindful of the

XVI PREFACE.

condition of mortality and humanity, not confiding
that such a thing can be carried to its perfect close
in the space of one single age, but assigning it as a
task to a succession of generations."

Instaur. Mag. Prcef. ad fin.

CONTENTS

or

THE FIRST VOLUME.

Page
Imtroduction . •••••• 3

BOOK I.

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

Chapter I. — ^Prelude to the Qreek School Philobophy.

Sect. 1. First Attempts of the Speculatire Faculty in Phy-
sical Inquiries • * . • . . 23
Sect. 2. Primitiye Mistake in Greek Physical Philosophy . 32

Chapter II. — The Greek School Philosophy.

Sect. 1. The general Foundation of the Greek School Phi-
losophy 37

Sect. 2. The Aristotelian Physical Philosophy . . 41

Sect. 3. Technical Forms of the Greek Schools . . 55

1. . of the Aristotelian Philosophy . 55

2. ■ of the Platonists ... 59

3. — __ of the Pythagoreans . • 62

4. — — — — of the Atomists and others . 63

Chapter III. — ^Failure of the Greek School Philosophy.

Sect. 1. Result of the Greek School Philosophy . • 67
Sect. 2. Cause of the Failure of the Greek Physical Phi-

losophy . . • . . • 72

XViii CONTENTS OP THE FIRST VOLUME.

BOOK 11.

HISTORY OF THE PHYSICAL SaENCES IN ANCIENT

OREECE.

Page

Introduction ^ • 89

Chapter I. — Earliest Stages of Mechanics and

Hydrostatics.

Sect 1. Mechanics ...... 91

Sect, 2. Hydrostatics 95

Chapter II. — Earliest Stages of Optics. . . 98
Chapter III. — Earliest Stages of Harmonics. . 102

BOOK III.
HISTORY OF GREEK ASTRONOMY.

Introduction 109

Chapter I. — Earliest Stages of Astronomy.

S'tfc/. 1. Formation of the Notion of a Year . . .111
Sect. 2, Fixation of the Civil Year . . . . 114

Sect. 3. Correction of the Civil Year. (Julian Calendar) 120
iS'ec^ 4. Attempts at the Fixation of the Month . .123
Sect, 5. Invention of Lunisolar Years . . . 126
Sect, 6. The Constellations ....«• 132

Sect, 7. The Planets . ... . . . 137

Sect, 8. The Circles of the Sphere » . • . 140
Sect. 9. The Glohular Form of the Earth . . . 147
Sect, 10. The Phases of the Moon . . . .150

Sect, 11. Eclipses « 151

Sect, 12. Sequel to the Early Stages of Astronomy . 154

Chapter II. — Prelude to the Inductive Epoch op

HiPPARCHUS. . . .157

Chapter III. — lNDuc?rivE Epoch of Hipparchus.

Sect, Ik Estahlishment of the Theory of Epicycles and

Eccentrics 169

CfONTRNTS OF THE FIRST VOLUICE. XIZ

Page
Sect. 2. Estimate of the Value of the Theory of Eooentiics

and Epicycles . . . . • 179

Sect 3. Discoyerj of the Precession of the Equinoxes . ]86

Chapter IY. — Sequel to the Inductive Epoch of

HiPPARCHUS.

SecL 1. Researches which yerified the Theory *• .190

Sect. 2. Researches which did not rerify the Theory « 194
Sect. 3. Methods of Observation of the Greek Astronomers 197

Sect, 4. Period from Hipparchus to Ptolemy . . • 205

Sect. 5. Measures of the Earth . . . . 211

Sect. 6. Ptolemy's Discovery of Evection . . .213

Sect. 7. Conclusion of the History of Greek Astronomy . 220

Sect. 8. Arabian Astronomy ..... 222

BOOK IV.

HISTORY OP PHYSICAL SCIENCE IN THE

MIDDLE AGES.

Introduction . . 235

Chapter I.— On the Indistinctness op Ideas op the

Middle Ages. . . . 237

1. Collections of Opinions 239

2. Indistinctness of Ideas in Mechanics . . . 241

3. shown in Architecture . 246

4. _— — in Astronomy . . . 248

6. shown by Sceptics . . 249

6. Neglect of Physical Reasoning in Christendom . . 252

7* ' Question of Antipodes ..... 253

8. Intellectual Condition of the Religious Orders • • 257

9. Popular Opinions . • . . . . 260

Chapter II. — ^The Commentatorial Spirit of the

Middle Ages. • • . 264 *

1 . Natural Bias to Authority 266

2. Character of Commentators . • . « • 268
3» Qreek Commentators on Aristotle • . . 271

XX CONTENTS OF THE FDUST VOLUME.

Page

4. Greek Commentators on Plato and others • . 275

5. Arabian Commentators on Aristotle . . . 276

Chapter III. — Op the Mysticism op the Middle

Ages 281

1. Neoplatonic Theosophy 283

2. Mystical Arithmetic 289

3. Astrology 293

4. Alchemy 303

5. Magic 306

Chapter IV. — Op the Dogmatism op the Middle

Ages.

1. Origin of the Scholastic Philosophy . . . .311

2. Scholastic Dogmas .^. . . . . 316

3. Scholastic Physics 324

4. Authority of Aristotle among the Schoolmen . 325

5. Subjects omitted. Civil Law. Medicine . . . 329

Chapter V. — Progress op the Arts in the Middle

Ages.

1. Art and Science ....... 331

2. Arabian Science ...... 336

3. Experimental Philosophy of the Arabians . . . 338

4. Roger Bacon ....... 341

5. Architecture of the Middle Ages .... 343

6. Treatises on Architecture 347

BOOK V.

HISTORY OP FORMAL ASTRONOMY AFTER THE

STATIONARY PERIOD.
Introduction . . . . . . . .355

Chapter I.-p-Prelude to the Inductive Epoch op

Copernicus. . . . 359

Chapter II. — Induction of Copernicus. The Helio-
centric Theory asser^fj) on formj^l Grounds. . 368

CONTENTS OF THE FIRST VOLUME, XXI

Page
Chapter III. — SEauEL to Copernicus. The Reception

AND DeVELOPEMENT OF THE CoPERNICAN ThEOBY.

Sect 1. First Reception of the Copemican Theory . . 381
Sect 2. Diffusion of the Copemican Theory . . 384
Sect. 3. The Heliocentric Theory confirmed by Facts.

Galileo's Astronomical DiscoYeries . . 392
Sect. 4. The Copemican System opposed on Theological

Grounds ...... 397

Sect. 5. The Heliocentric Theory confirmed on Physical
Considerations. (Prelude to Kepler's Astro-
nomical Discoveries.) .... 404

Chapter IV. — Inductive Epoch op Kepler.

Sect^ 1 , Intellectual Character of Kepler , . . 410
Sect. 2. Kepler's Discovery of his Third Law . .415

Sect. 3. Kepler's Discovery of his First and Second Laws.

Elliptical Theory of the Planets . . 421

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 ...... 430

Sect. 2. Application of the Elliptical Theory to the

Moon 432

Sect. 3. Causes of further Progress of Astronomy . 435

VOL. I.

ADDITIONAL NOTE IN VOL. X.

« Page 69 line 7* I lutve attempted to lUustrate Bomewhat haHkew the
nature of Inductive reasoning, in a stmall work entitled the Mechanical
Euclid, and in the Remarks annexed thereto.

Pa^ 42, line 16^ for inscribed, read iatented.

INDEX OP PROPER NAMES.

Abdollatif, 0. 891

Aboazen, a. 900

Aboul Wef% ct. 228

Achard, b. 516

Achillini, c. 394

Adam Marsh, a, 258

Adanson, e», 338

Adelbold, a. 258

Adelhard Groth, a, 258

Adet, 0. 134

Achilles Tatius, a. 188

^pinus, 0. 17, 24, 34

Agassiz, 0. 373, 514, 544

Agatharohus, 6. 842

Airy, b. 107, 228^ 277, 364, 446

AlbaJbe^ius, a. 224

Albertus Magnus^ a. 308^ 826; d

270
Albmnazar, a. 300
Alexander Aphrodisiensis, a, 272
Alexander the Great, a. 167
Alfarabi, a. 279
Alfred, a. 257
Algazel, a. 251
Alhazen, a. 339 ; b, 345
Alis-ben-Isa, a. 212
Alkindi, a. 879
Almansor, a. 224
Almeric, a. 326
Alpetragius, a. 225
Alphonso X., a. 180
Amauri^ a, 326
Ammonius Bacoas, a. 273, 264
Ampere, 6. 528 ; c. 75, 78, 81, 142
Anaxagoras, a. 43 ; b, 848
Anaximander, a. 143, 147, 151
Anaximenes, a. 26
Anderson, b, 56
Anna Coninen% a* 274
Anselm, a. 314

Arago, b, 871, 884, 416, 435 ; e. 91
Aratus, a. 208

Archimedes, a. 91, 95 ; 6. 844
Arduino, o. 506
Aristarchus, a. 156, 363
Aristillus, a. 167

AristophaiMS, a. 135

AristoUe, m. 41; b. 44, 896, 844,

349 ; 0. 261, 344, 358, 357, 383,

387» 883, 412, 001
Arnold de Villa Nora, a. 898
Arriaga, 6. 45
Artedi, e. 362
Artephius, a. 308
Aryabatta^ a. 364
Arzachel, a. 225
Asclepiades, o, 384
Asdepigenia, a. 288
AseUi, 0. 407
Aredbron, a. 318
Averroes, a. 280
Avicenna^ a. 251, 879
Avienus, a. 209
Aubriet, o. 303
Audouin, o. 458
Augustine, a. 256, 296, 318
AutolycuB, a. 148, 140
Auzout, b, 273

Babbage, Professor, e. 98, 580

Bachman, 0. 301

Bacon,FhuiC]s, a.886) b, 187, Udy

296, 310, 501
Bacon, Roger, b. 845
BaUly, a. 259 ; b. 229, 247
BaliaJii, 6. 30, 65
Banister, c. 291
Barlow, b, 364; c. 56, 80, 02
Bartholin, b. 366
Barton^ 6« 453
Bauhin, John, 0, 292
Bauhin, Gaspard, c. 294
Beaumont, Elie de, o» 586, 534,

542, 600
Beccaria, 0. 18
Beccher, 0. 116
Bede, a, 257, 317
Bell, Sir Charles, e. 485
B^lon, 0. 359, 446
B^edetti, b. 10, 20, 26, 46
Bentley, b. 191, 195
Berard, 6» 493

b2

XXIV

INDEX OF PBOPEB NAMES.

Bergman, 0. 114, 138, 200
Bernard of Chartres, a. 314
BemouUi, Daniel, b. 109, 113, 116,

119, 201, 308, 318, 322
Bemonlli, James, 6. 83, 23
Bernoulli, James, the yonnger, 6.

327
Bernoulli, John, h. 84, 87, 93, 98,

99, 110, 141, 201, 308
Bernoulli, John, the younger, 6.

310
Berthollet, c, 115, 132, 138
BerzetiuB, c. 142, 151, 175, 222,

241
Bessel, b. 107
Betancourt, b. 516
Beudant, e. 243
Bichat, 0. 425
Bidone, 6. 70
Biela, b. .239
Biker, 6. 516
Biot, b, 375, 386, 425, 476 ; e. 55,

56,87
Black, b. 500; c 124, 138
Blair, b. 364
Bloch, c, 368
Blondel, 6. 56
Bock, e. 276
Boethius, a. 257, 273
Boileao, b, 137
Bonaparte, e, 73, 162
Bonaventura, a. 320
Bontius, 0. 310

Borelli, b. 24, 132, 141, 162, 164
Bossut, b, 70
Bou^, Ami, 0. 520
Bouguer, 6. 112 .
Bouillet, b. 503
Bourdon, c. 421
Boumon, e. 208
Bonvard, b. 224
Boyle, b, 144, 383, 501 ; e. 109
Boze, c. 14

Bradley, 6. 214, 220, 244, 254, 258
Brander, c. 495, 509
Brasavola, c. 272
Brewster, Sir David, b, 360, 376,

385, 434, 449; 0. 217
BriggB,a.391

Brisbane, Sir Thomas, b. 278
Brocchi, 0. 514, 6 11
Brochant de Villiers, c. 525, 534
Broderip, e, 572
Brongniart, Alexandre, c, 508, 531

Brongniart, Adolphe, e, 543

Brook Taylor, b. 85, 110, 307

Brooke, c. 207

Brougham, Lord, 6. 382, 431

Brown, Robert, c. 339, 442

Brunfels, e. 273

Bruno, Giordano, a. 384

Buat, b, 70

Buch, Leopold von, c. 520, 525,

542, 563
Buckland, Dr., c. 536
Budseus, a. 57
Buffon, c. 192, 419, 445
BuMnger, b. 88
Bullialdus, a. 216; b, 149
Burckhardt, b, 222, 233
Burg, b, 224
Burkard, c. 418
Burnet, c. 566, 602

Cabanis, c. 467
Csesalpinus, c. 192, 277? 280
Calceolarius, 0. 495
Calippus, a. 130, 161
Callisthenes, a. 167
Gamerarius, Joachim, c. 278
Camerarius, Rudolph Jacob, c. 416,

418
Gampanella, a. 303, 326
Campani, 6. 273
Camper, c. 445
Canton, e^ 17, 49
Capelli, b. 209
CappeUer, c. 194
Cardan, b. 9, 17, 37, 45
Carlini, b. 246
Came, c. 540
Caroline, Queen, b, 192
Carpa, c. 394
Casrseus, b. 30
Cafisini, Dominic, b. 217, 241, 255,

280, 311
Castelli, b, 52, 55, 62, 67
Catelan, 5. 82
Cavallieri, b. 201

Cavendish, 6. 246 ; c. 26, 125, 133
Cauchy, b, 117, 328, 455
Cans, Solomon de, b. 40
Cesare Cesariano, a. 349
Chalid ben Abdolmalic, a. 212
Chatelet, Marquise du, b, 88
Chaussier, c, 425
Chladni, b. 324, 326
Christie, c. 92 :

INDEX OF PROPER NAMES.

Christina, b. 136

Chrompr^, c. 176

Cicero, a. 124

Cigna, 6. Ill; e. 22

Clairaut, 6. 100, 103, 113, 171, 213,

238, 243, 363
Clarke, b. 88, 194
Cleomedes, a, 198, 207
Clusins, e. 288
Cobo, c, 290

Colombe, Lndovico delle, b, 62
Colnmbus, Realdus, o. 396, 403
Columna, Fabius, o. 292
Commandinus, b, 14
Comparetti, b. 382
Condamine, b. 241
Constantine of Africa, c. 270
Conti, Abb^ de, b. 86
Conybeare, o. 613, 623
Copernicus, a. 368
Cosmas Indicoplenstes, a, 266
Cotes, b. 97, 196
Coulomb, c. 26, 30, 34, 63
Crabtree, a, 391, 431 ; b. 146
Cramer, b. 316
Cronstedt, 0. 230
Craicksbaiiks, 0, 70
Cumming, Prof., c, 90
Cunsaus, 0. 14
Cnvier, c. 366, 429, 448, 463, 466,

472, 610, 617, 608

D*Alembert, b. 89, 96, 101, 108,
110, 116,228,308,318

D*Alibard, c. 18

Dalton, Dr. John, b, 497, 609, 616,
621; e. 147, 152

DanieU, b. 621 ; 0. 669

Dante, a. 362

D'Arcy, b, 119

Davy, c. 141, 167, 162, I70

Daubenton, c, 446

Daubeny, Dr., e. 666

Danssy, b. 261

De CandoUe, Prof. c. 339, 441

Deohen, M. von., c. 636

Defrance, e. 608, 612

Degerando, a. 261, 311

De la Beche, 0. 613

Delambre, b. 222, 232

De la Rive, Professor, 6. 633

De Lisle, b, 202

De Lnc, b, 606, 620

D^meste^c. 197

Democritns, a. 64 ; c. 268

Derham, 6. 602

Desaguliers, ell

Descartes, b. 24, 32, 60, 56, 66, 76|

131, 199, 347, 360; 0. 51.
Des Hayes, e. 614
Desmarest,'c. 602, 606
Dexippns, a. 275
Digges, b. 37
DiUenius, c. 329
Diogenes Laertins, a. 239
Dioscorides, 0. 266, 270
DoUond, b. 273, 363
Dominis, Antonio de, b, 847
Dubois, 0. 394
Dufay, e. 10, 13, 21
Du Four, b. 382
Dufr^noy, 0. 626, 634
Dulong, 6. 485, 633
Duns Scotus, a. 321, 327
Dunthome, b. 209
Dupuis, a. 134
Durret, a. 406
Dutens, a. 71
Duvemay, e, 444

Ebn lonnis, a, 224

Encke, b. 239, 263, 287

Eratosthenes, a. 193

Ericsen, 6. 606

Eristratus, 0. 407

Etienne, 0, 394]

Evelyn, 6. 191

Euclid, a. 98, 146

Eudoxus, a. 161, 166

Euler, 6. 93, 101, 104, 109, 113, 119,

213, 308, 323
Eusebius, a. 263
Eustachius, e. 396, 408
Eustratus, a. 274

Fabricius, «. 276

Fabricius of Acquapendentc, e,

396, 412
Fabricius, David, a. 427
Fallopius, 0, 396
Faraday, Dr., e, 80, 91, 163, 170
Format, b. 66, 73
Fitton, Dr., 0. 621
Flacourt, c, 291
Flamsteed, a. 434 ; b, 170, 179, 197,

210
Fleischer, b, 347
Fontaine, 6. 108

XXVl

INDEX OF PEOPEE NAKES,

FonteneBe, b. 219, 217; o. 112, 407
Forbes, Professor, 6. 494
Forster, Rev. Charles, a. 388
Fouroroy, 0. 138, 188
Fourier, b, 470, 482, 489, 523
Fowler, 0. 73
Fracastoro, 0. 494
Francis I. (king of France) a. 827
Franklin, 0. 12, 15, 29, 33
Fraunhofer, b. 274, 365, 411, 456
Frederic II., Emperor, a, 326
Fresnel, 6. 371, 402, 400, 420, 485,

522
Fries, 0.354
Frondnus, a. 350
Fuchs, 0. 221, 274
Faohsel,0. 503

Gartner, 0. 333

Galen, 0. 885, 381, 893, 493, 496

GaUleo, a. 393; k I7, 98, 96, 28,

47,56,69
Gall, 0. 425, 427
GalYani, 0. 66, 72
Gambart, b, 239
Gascoigne, 5. 354
Gassendi, a. 406; &. 54, 187, 140,

311
Gauss, b. 107, 238
Gay-Lnasac, 6. 49f, 508, «99( c.

141, 153
Geher, a. 996, 304
CreUiloand, 0. 48
Geminns, a. 129, 165, X>7
GenerelH, CiilBo, «w 607
Gaoffiroj (botaaisl), c 417
Geoffiroy (chemiii), c^ 119
Geoffiroy Saint-Hdair% c 448, 4tt,

457
Geoige PSMhymeraa, «. 974

Gerberi, «. 957

I, Mile. St^pbio!, A. 898

Gessaer, e. 199, 978, 4M

Ghim, 0.908

Gibbon, «• 336

Gabari, «. 39; 5. 143; 0u f, 45^ 48,

51,58
Giordano l^nuio^ a 384
Giiard,*. 78
GirtaniMr, It. 588
CHseke, 0. 393
Glisson, r, 437
Gm^in, r. dl3

Godefroy of St. Victor, a. 816

Groldfiiss, 0. 514

Goppert, c. 693

Gothe, 6. 357; 0.434,440

Gongh, b. 512

Graham, b. 268 ; 0. 49

Gramatici, b. 209

Grazia, Yincenzio de, b, 62

Greenough, 0. 525

Gregory, David, 6. 195, 909

Gregory VII., Pope, a. 308

Gregory IX., Pope, «. 326

Gren, b. 516

Grew, 0. 414, 444

Grey, 0. 10

Grignon, 0. 196

Grimaldi, b, 55, 362, 381

Grotthus, 0. 175

Guericke, Otto, 6. 310; 0. 9

Gnettard, 0. 498

Gnliefanini, 0. 194

Guyton de Morvean, 0. 139, 188

Hachetie, b, 70

Hadley, b. 2^

Haidinger, 0. 216

Halicon, a. 178

Haller, 0. 327, 429

Halley, a. 434 ; 6. 77t 147, 158, 190,

196, 910, 995, 937, 248, 982;

0.47
Haly, a. 301
Hamilton, Sir W. (matbom.), 5.

451,460
Hampden, Dr., a. 311
Hansftit, A. 107
Hansteen, 0. 48
Harding, 5.984
Hairis, Snow, 0. 35
Harrison, 5. 971
Hart8oe^i»r, 5.973
Harvey, e. 397, 488, 419
Haosmann, 0* 914
Hauy, c. 199^ 205, 988
HawkttBba^ 0. % 19
Hegel, iu 181
He^moait, c^ 187
Henckel, 0. 194
H^mIow, IVotenr, «» 448
H^raefitusi, «. 96
HeanMB. FiBl» 0. 988
Hennamk, Contractaib m. 888
Hamann, JanM% A. 89^ 88» 8B; «.

301

IHDBX OF PBOPSE NAMM

••

XXTU

Hermolaufl BarbanUi «• 67

Hernandez, o, 200

Herodotus, a. 27; o. 260, 401

Herophilus, o. 387

Herrenschneider, b. 478

Herschel, Sir John, 6. 208, 864,
386; c. 92, 218, d61, 566

Herschel, Sir William, b. 280

Hevelius, 6. 236, 267, 281

Higgins, e. 148

Hill, c. 196, 330

Hipparchus, a. 168

Hippasus, a. 104

Hippocrates, o, 383

Hof, K. E. A. von, c. 561

Hofifinann, o. 626
Home, 0. 613
Homer, c. 383

Hooke, A. 26, 73, 76, 132, 148, 168,
165, 164, 304, 386, 366, 378,
381, 391 ; 0. 607
Hopkins, b. 323; o. 664
Horroz, a. 391, 431 $ b. 146
Hoskins, 6. 77
Howard, Mr. Luke, b, 623
Hudson, c. 330
Hugo of St. Victor, a. 316
Humboldt, Alexander von, e, 48,

620, 641, 664
Humboldt, Wilhdm von, 0. 71
Hunter, John, 0, 445
Hutton (fossOist), c. 514
Button (geqbgist), b, 246; 0. 506,

603
Huyghens, b. 48, 67, 74, 81, 112,
132, 149, 174, 311, 855, 367,
392
Hyginus, a. 209

lamblichus, a. 287

Ideler, a. 118

Ivory, b. 107

Jacob of Edessa, a, 278

Jameson, Professor, a. 226, 505

Job, a. 133

John of Damascus, a. 274

John Philoponus, a. 273

John of Salisbury, a. 318, 822

John Scot Erigena, a. 814

Jordanus Nemorarius, 5. 10, 89

Joseph, a. 309

Julian, a. 288

Jung, Joaofaim, c. 897

Adrian de,0.8M
Jussieu, Antoine l4Mirent da, e.

335
Jussieu, Bernard de, 0. 835

Ksdmpfer, r. 291

Kant, c. 469

Kazwiri, 0. 600

Keckerman, a, 324

Keill, b. 98, 196; 0. ll(|

Kelland, Mr. Philip, ^. 454^ 400

Kempelen, b, 385

Kepler, a. 371, 388, 410; 6. 78» 128,

181, 266, 347
Key, 0. 130
Kircher, a. 293
Kirwan, 0. 127, 138
Klaproth, 0. 134
Klingenstiema, b. 273, 863
Knaut, Christopher, 0. 801
Knaut, Christian, p. 801
Konig, 0. 613
Krafft, b. 473; 0. 60
Kratzenstein, b, 604
Kriege, 0. 291

Lacaille, b. 222, 242

Lactantius, a. 263

Lagrange, b. 100, 108, 104, 105,

106, 107, 110, 120, 229, 8U,

318, 322
L*Ain^, b. 469
La Hire, b, 216, 255
Lalande, b, 218, 231
Lamarck, 0. 339, 448, 51^
Lambert, b. 328, 473; c, 58
Landen, b. 109
Lansberg, a. 406, 481
Laplace, b. 104, 105, 106, 826, 947»

816, 470, 482, 580, 559
Lasus, a. 104
LatreUle, 0. 460
Lavoisier, 0. 128, 136
Laughton, 6. 196
Launoy, a, 326
Laurenoett 0. 469
Lawrence, 0. 575
Lecchi, b, 70

Leeuwenhoek, 0. 414, 419
Legendre, 0. 55
L*Hopital, b. 84
Leibnitz, b. 86, 140
Le Monnier, b. 210, 813, 256

XXVlll

INDEX OF PBOPEE NAMES.

Leonardo 6a Ymd, a. 351 ; b. 122 ;

e. 493, e06
Leonicenus, c. 272
Le Boi, b. 604, 521
LesUe, b, 478, 489, 525
Levy, c. 217
Leucippus, a. 64, 75
Lexell, b. 231, 239
Lhwyd, c, 495

Libri, ft. 487
Lindenau, 6. 219
Lindley, c. 442, 514
Liimseus, c, 195, 304, 364
Linus, b. 354
Lister, c. 497> 500
Littrow, b. 277
Lloyd, Professor, ft. 451, 460
Lobeck, ft. 461
Lobel, c. 292, 338
Locke, ft. 191

Longomontanus, a, 422, 431
Lonville, ft. 203, 217
Lubbock, ft. 107, 250
Lucan, a. 245
Lucas, ft. 355

Lyell, e. 483, 530, 552, 556, 567,
570, 612

Macleay, c, 353

Msestlin, a. 383, 405

Magin, a. 382

Mairan, ft. 88

Malpighi, c. 413, 414

Malus, ft. 369,374

Manilius, a, 209

Maraldi, ft. 216, 382

Marcet, ft. 533

Margrave, o. 360

Marinus (anatomist), o. 423

Marinus (Neoplatonist), a, 288

Mariotte, ft. 59

Marsilius Ficinus, a. 328

Martianus Capella, a. 363

Martyn,T. 0.329

Matthioli, c. 293

Maupertuis, ft. 99, 203, 242

Mayer, Tobias, ft. 214, 480 ; o. 29, 53

Mayo, Herbert, e. 425

Mayow, c. 130

Mazeas, ft. 383; c. 18

M'Cullagh, Professor, ft. 448, 460

Meckel, c. 463

Melloni, ft. 493

Menelans, a, 208

Mersenne, ft. 32, 53, 55, 65, 13G,

302,317
Messa, c. 394
Meton, a. 128
Meyranx, c. 459
Michael Scot, a, 308
Michell, c. 501
Michelotti, ft. 70
Miller, Professor, c. 217
Milton, a. 262, 389; ft. 53
Mitscherlich, c, 220
Mohs, c. 207, 213, 237
Mondino, c, 394
Monge, c. 127
Monnet, e. 498
Monnier, c. 16
Monteiro, c, 217
Montfau9on, a. 255
Morin, a. 406
Morison, c, 295
More, Lazzaro, e. 607
Morveau, Guyton de, c, 132, 138
Mosotti, c. 39
Munro, c. 445
Murchison, c. 530
Muschenbroek, ft. 503

Napier, a. 391, 437

NaudsBus, a. 308

Naumann, c. 249

Newton, ft. 58, 68, 73,77, 92, 153,
155, 158. 165, 175, 183, 203,
256, 311, 321, 352, 368, 373,
379, 395, 472 ; c. 429

Nicephorus Blemmydes, a. 274

Nicholas de Cusa, a. 367

Nicomachus, a. 102

Nigidius Figolus, a. 296

Nobili, ft. 493

Nollet, c. 13

Nordenskiold, c. 246

Norman, c. 47

Norton, ft. 37

Numa, a. 122, 365

Odoardi, c. 503, 507
Oersted, Professor, c. 77
(Eyenhausen, e. 535
Oken, Professor, c, 447
Olbers, ft. 232
Orpheus, a. 287
Osiander, a. 378

INDEX OF PROPER NAMES.

Ott, b. 478

Otto Gaericke, 0. 9, 13

Ovid, c, 491

Pabst von Ohain, c, 231

Packe, c. 498

Pallas, 0. 445, 503

Papin, b, 515

Pappus, a. 241

Paracelsus, a. 308 ; 0. 10?

Pardies, b. 354

Pascal, b. 63

Paulus III., Pope> a, 377

Pecquet, e. 408

Pepys, b. 191

Perrier, b. 66

Peter of Apono, a, 308

Peter Bungo, a. 293

Peter Damien, a. 316

Peter the Lombard, a. 317

Peter de Vineis, a, 326

Petit, b. 485, 533

Petrarch, a. 328

PhUip, Dr. Wilson, e. 410

Phillips, William, c. 207, 234, 523

Philolaus, a» 362

Photius, a. 276

Piazzi, b. 232

Picard, 6. 161, 256, 267, 311

Piccolomini, b, 46

Pictet, b. 507

Picus of Mirandula, a. 308, 328

Plana, b. 107

Playfair, 6. 192

Pliny, a. 178,239,295; c. 191,258,

264
Plotinus, a, 275, 284
Plumier, c. 29]
Plutarch, a. 61, 366
Poisson, 6. 107, 117, 323, 328, 527;

c. 32, 55, 562
Polemarchus, a. 161
Poncelet, b, 70
Pond, b, 277

Pontanus, Jovianus, 0. 416
Pont^coulant, 6. 107
Pope, b. 196
Porphyry, a. 272, 275
Posidonius, a. 212
Potter, Mn Richard, 6. 453, 460
Powell, Prof., b. 455, 460, 493
Prevost, Pierre, 6. 474
Prevost, Constant, c. 611
Prichardy Dr., 0. 483, 575

Priestley, e. 123, 126, 134
Proclus, a. 269, 275, 988, 291, 298
Prony, 6. 70.516
Proust, r. 115
Prout, Dr., 0. 152, 410
Psellus, a. 275
Ptolemy, a. 214; 6. 299
Ptolemy Euei^tes, a. 200
Purbach, a. 426
Pythagoras, «. 24, 63, 137, 291
Pytheas, a. 199

Quetelet, b. 460

Raleigh, c. 289

Ramsden, b. 268

Ramus, a. 327, 429

Raspe, c. 506, 509

Ray, c. 297, 360

Raymund Lully,'a. 308

Reaumur, e. 497

Recchi, 0. 290

Redi, 0, 444

Reinhold, a. 381

Rennie, Mr. Oeorgc, b. 71

Rheede, 0. 290

Rheticus, a. 375, 380

Riccioli, a, 406 ; b. 55,

Richman, 6. 473 ; o. 19

Richter, 0. 146

Riffault, c. 175

Riolan, 0. 399

Rivinus, 0. 301 1

Rivius, a. 350 ; 6. 28

Robert GrostSte, a. 258, 308

Robert of Lorraine, a. 258

Robert Mai^h, a. 258

Roberval, 6. 311

Robins, 6. 56

Robinson, Dr., b. 277

Robison, 6. 508, 515; c. 29

Roger Bacon, a. 258, 308, 339, 241

Rohault, 6. 138

Romd de lisle, c. 195, 108, 205

Romer, 6. 257, 281,311

Rondelet, c. 359

Roscoe, c. 339, 340

Ross, Sir John, 0, 48

Rothman, a. 372

Rouelle, c. 502, 507

Rousseau, c. 328

Rudberg, b, 456

Ruellius, 0. 272

Rufus, 0. 387

INDBX OF PBOPBR NAHSS.

Bumphe> 0. 290

SalnceSyi. Ill

Salusbury, a. 391

Salviani, c, 359

Santbach, b, 27

Santorini, e, 424

Saron, b, 231

Savart, 6. 323, 330; c. 80

Savile, a. 270

Saussure, 6. 620 ; c. 603

Sauveur, b, 304, 317

Scheele, c. 123

Schelling, 6. 367

Schlottheim, c. 606, 614

Schmidt, c. 616, 664

Schomberg, Cardinal, a. 377

Schweigger, c. 89

Schwerd, b. 462

Scilla, c. 494

Scot, Michael, e. 270

Scrope, Mr. Poulett, 0. 666

Sedgwick, Professor, a, 635, 640

Sedillot, M., a. 228

Seebeck, Dr., b, 376,386; 0. 90

Segner, b. 109

Seneca, a. 210, 363; 6. 63, 66

Sergius, a. 278

Servetus, 0, 395

Sextns Empiriens, a. 261

S'Gravesande, b. 88

Shaipe, b, 61 7

Sherard, c. 291

Simon of Genoa, 0. 270

Simplicius, a, 269, 273

Sloane, 0. 291, 829

Smith, Mr. Archibald, b. 460

Smith, Sir James Edward, 0, 330

Smith, William, c. 607, 516

Snell, b. 347

Socrates, c. 390

Solomon, a. 309; c. 260

Sorge, b. 319

Sofl^fenes, a. 122, 210

Sonthem, d. 617

Sowerby, c. 614

SpaUanzani, c. 410

Spix, c. 447

Sprengel, 0. 440

Stahl, c. 116

Stancari, 5. 304

Steno, c. 193, 494, 502

Stephanus, c, 394

Stevinns, b. 16, 46, 61

Stillingfleet, c. 330

Stobseus, a. 276

Stokes, c 693

Strabo, a. 268 ; c. 263, 607

Strachey, c. 501

Stukeley, c. 601

Svanberg, b, 484

Sarian, 0. 291

Sylvester II. (Pope), a. 257, 808

Sylvius, c. 108, 394, 396

Symmer, c, 22

Syncellus, a. 121

Synesius, a. 206

Tacitus, a. 294

Tartalea, b. 13, 20, 27

Tartini, b. 319

Taylor, Brook, b. 85, 110, 307

Tchong-Kang, a. 162, 199 .

Telauge, a. 291

Tennemann, a. 311

Thales,a.24,26,37, 143

Thebit, a. 308

Thenard, 0. 141

Theodore Metochjrtes, a. 274

Theodosius, a. 207

Theophrastus, a, 271 ; 0. 258, 261,

276
Thomas Aqninas, a. 308, 318,

326
Thomson, Dr., 0. 149, 162
Tiberius, a. 297
Timocharis, a. 167
Torricelli, b. 48, 62, 65, 67
Toomefort, 0. 301, 417
Tostatus, a. 266
Totaril, Cardinal, a. 327
Tragus, 0. 276
Trithemius, a. 308
Troughton, 6. 268
Turner, 0. 162
Tycho Brahe, a. 422, 432 ; h. 346

Vaillant, Sebastian, 0. 417

VallisnCTi, 0. 494

Van Helmont, 0. 107

Varignon, b. 69; 0. 409

Varolius, 0. 424

Yarro, Michael, b. 10, 17, 30, 89

Vesalins, 0. 392, 394, 423

Vicq d*Azyr, a. 424, 445

Vieussens, 0. 425

Vincent, b, 77

Ymcent of Beanvais, 0. 270

INDEX OF PROPER NAMES.

XXXI

Yinciy Leonardo da, 6. 122; o. 493,

606
Virgil (bishop of Salzburg), a. 3^ *
Vii^l (a necromancer), a. 809
YiteUio, b. 346
YitruviuB, a. 348, 360 ; b. 296
Viviani, b. 49, 63
Voet, b. 136
Voigt, c. 441
Volta, c. 68, 72
Voltaire, & 80, 203
Voltz, 0. 634
Von Kleist, o. 14

Ubaldi, 5. 10
Ulugh Beigh, a, 226
Ungem-Stemberg, Count, o« 664
Uranus, a. 278
Ure, Dr., *. 617
Usteri, 0. 440

Wallerius, b. 606 ; o. 197

Wallis, a. 391; 6. 63, 67, 182, 146,

317
Walmesley, b. 218
Warburton, b, 196
Ward, Seth, a. 391 ; b. 146
Wargentin, 6. 220
Watson, 0. 12, 16, 22
Weber, Ernest and William, 6. 820
Weiss, Prof, 0. 210, 213
Wel]s,6. 610, 619; 0. 73
Wenzel, c, 146

Werner, e. 197, 224, 231, 604, 616,

619,603
Whaatstone, 6. 329
Wheler. c. 291
Whewell, 6.260; <;.216
Whistou, b, 195
Wilke, 6. 600; c. 18,26
Wilkins (Bishop), a. 390; 6. 40, 146
William of llirsangen, a. 268
Willis, Rev. Robert, «. 848; «. 884,

336
Willis, Thomas, e. 428, 427
Willoughby, 0. 360, 362
Wolf, Caspar Frederick, «. 488
Wolff, b. 88, 602
Wollaston, 6. 366, 887, 869, 386;

c. 149, 207
Woodward, c, 496, 600, 002
Wren, a. 391 ; b. 67, 146, 190
Wright, 6. 209

Xanthus, 0, 268

Yates, 0. 48

Young, Thomas, b. 71, 829, 402,
426, 431

Zabaxella, a. 324
Zach, b. 233
Zeiddler, b, 616
Ziegler, b. 616
Zinunerman, 0. 664

INDEX OF TECHNICAL TERMS.

Abeb&atiok, b. 258

Absolute and relative^ a. 48

Accelerating force, b. 32

Achromatism, b, 363

Acid, c. 109

Acoustics, b. 304

Acronycal rising and setting, a. 146,

and erreUa
Action and reaction, 6. 58
Acuation, c. 107
Acumination, c. 197
Acute harmonics, 5. 317
iEtiology, c. 482
Affinity (in Chemistry), c. 113
Affinity (in Natural iffistory), c. 353
Agitation, centre of, b, 81
Alidad, a. 231
Alineations, a. 192
Alkali, c. 109
Almacantars, a. 231
Almagest, a. 214
Almanac, a. 231
Alphonsine tables, a. 225
Alternation (of formations), o, 541
Amphoteric sUicides, c. 250
Anflogy (in Natural History), o.

353, 355
Analysis (chemical), c. 107

^olar, of light), b. 384, 385

Angle of cleavage, c, 202
■ incidence, b, 342

reflection, b. 342

Animal electricity, c. 66
Anion, c, 166
Annus, a. 113
Anode, e. 166
Anomaly, a. 151, 171
Antarctic circle, a. 144
Antichthon, a. 70
Anticlinal line, c. 539
Antipodes, a, 253
Apogee, a. 172

Apotelesmatic astrology, a. 301
Apothecee, o. 268
Appropriate ideas, a. 80
Arctic circle, a. 144

Armed magnets, c. 49

Armil, a. 200

Art and science, a. 331

Articulata, c, 449

Artificial magnets, c. 50

Ascendant, a. 300

Astrolabe, a. 203

Atmology, b, 466, 581

Atom, a. 64

Atomic theory, c. 145

Axes of symmetry (of crystals), c.

211
Axis (of a mountain cliain), c, 539
Azimuth, a. 231
Azot, c. 129

Ballistics, b, 97
Bases (of salts), c. HI
Basset (of strata), o. 502
Beats, 6. 304

Calippic period, a. 130

Caloric, b, 474

Canicular period, a. 122

Canon, a. 172

Capillary action, b, 113

Carbonic acid gas, c. 129

Carolinian tables, a. 434

Catasterisms, a. 193

Categories, a. 272

Cathion, c. 166

Cathode, c, 166

Cation, c. 166

Causes, material, formal, efficient,

final, a, 53
Centrifugal forces, b. 36
Cerebral system, 0. 425
Chemical attraction, <;. Ill
Chyle, e. 407
Chyme, c, 409

Circles of the sphere, a. 140
Circular polarization, 6. 388, 444
Circular progression (in Natural

History), c. 353
Civil year, a. 120
Climate, b, 479

INDEX OF TECHNICAL TERMS«

xxxni

Coexistence of vibrations, b. 318

Coexistent vibrations, 6. Ill

Colures, a. 145

Conditions of existence (of ani-
mals), e. 467, 472

ConducibUity, b, 475

Conductibility, b, 475

Conduction, b. 468

Conductivity, b, 475

Conductors, c. 11

Conical refraction, 6. 451

Conservation of areas, 6. 110

Consistence (in Thermotics), b, 499

Constellations, a. 132

Constituent temperature, 6. 513

Contact-theory of the Voltaic pile,
c. 160

Cor (of plants), c. 283

Cosmical rising and setting, a, 146

Cotidal lines, 6. 252

Craters of elevation, c. 463

DsBmon, a. 286

D*Alembert*s principle, b. 96

Day, a. Ill

Decussation of nerves, c. 424

Deduction, a. 15

Definite proportions (in Chemis-
try), 0, 145

Delta, e. 553

Dephlogisticated air, 0. 126

Depolanzation, b, 384

Depolarization of heat, b. 495

Depolarizing axes, b, 385

Descriptive phrase (in Botany), c.
313

Dew, 6. 519

Dichotomized, a. 155

Difiraction, b. 387

Dimorphism, c* 223

Dioptra, a. 204

Dipolarization, 6. 384, 424

Direct motion of planets, a, 150

Discontinuous functions, 6. 316

Dispensatoria, c. 268

Dispersion (of light), b, 453

Doctrine of the sphere, a. 144

Dogmatic school (of medicine),o.384

Double refraction, b, 366, 403, 413

Eoeentric, a. 170
fichineis, a, 245
Eclipses, a. 151
Eocene, a. 529

Effective forces, b, 85
Elective attraction, 0. 112
Electrical current, c 74
Electricity, c. 7
Electrics, c. 11
Electric tension, e. 74
Electro-dynamical, 0. 81
Electrodes, c. 166
Electrolytes, c. 166
Electro-magnetism, e, 77
Electro-magnetic induction, c. 95
Elements (chemical), c. 183
Elliptical polarization, 6. 447
Empiric school (of medicine), c. 384
Empyrean, a. 70
Enneads, a. 285
Entelechy, a. 57
Epicycles, a. 160, I70
Epochs, a. 12
Equation of time, a. 193
Equator, a. 144
Equinoctial points, a. 145
Escarpment, c. 539
Evection, a. 215
Exchanges of heat, theory of, b, 474

Facts and ideas, a. 6

Faults (in strata), o. 539

Final causes, 0. 389, 472

Finite intervals (hypothesis of), b,

454
First law of motion, 6. 22
Fits of easy transmission, b, 396
Fixed air, c. 125
Fixity of the stars, a. 191
Formal optics, b. 340
Franklinism, c. 22
Fresnel's rhomb, 6. 424
Fringes of shadows, 6. 382, 451
Fuga vacui, b. 64
Full months, a. 128
Function (in Physiology), c. 377

Galvanism, c. 69
Galvanometer, c. 89
Ganglionic system, c. 425
Ganglions, c. 424
Generalisation, a. 11
Greocentric theory, a. 360
Gnomon, a. 119
Gnomonick, a, 155
Golden number, a, 130
Grave harmonics, 6. 319
Gravitate, b. 163

XXXIT

mDEX OF TECHNICAL TEBMS.

Habitations (of plants), e, 671
Hsecceity, a. 321
Hakemite tables, a. 2i6
Halogenes, c. 183
Haloide, c. 249
Harmonics, acute, 6. 317

gravO) ** 81^

Heat, h. 468

latent, 6. 429

Heccsedecaeteris, a. 127
Height of a homogenous atmo-
sphere, 6. 314
Heliacal rising and setting, a. 145
Heliocentric theory, a* 860
Hemisphere of Berosus, a. 200
Hollow months, a. 128
Homoiomeria, a. 64
Horizon, a, 146
Horoscope, a. 300
Horror of a vacuum, b, 64
Houses (in Astrology), a. 300
Hydracids, c. 142
Hygrometer, b, 620
Hygrometry, 5. 467
Hypostatical principles, e, 107

latro-chemists, 0. 108
Ideas of the Platonists, tu 69
Ilchanic tables, a. 226
Impressed forces, b, 85
Inclined plane, b, 9
Induction (electric), c. 17
Induction (logical), a. 6
Inductive, a. 6
Inductive charts, a. 13
Inductive epochs, a. 12
Inflammable air, c. 125
Influences, a. 294
Intercalation, a. 121
Interferences, 6. 391, 403
Ionic school, cu 24
Isomorphism, c 220
Isothermal lines, 6. 480 ; e. 641
Italic school, a. 24

Joints (in rocks), c, 640
Judicial astrology, a. 301
Julian calendar, a. 123

Lacteals, c. 407
Latent Heat, 5. 499
Laws of motion, first, b, 22

second, ft. 36

third, 6. 44

Leap year, a. 121
Leyden phial, e, 14
Librations (of planets), a, 421
Idmb of an instrument, a. 199
Longitudinal vibrations^ 0. 880
Lunisolar year, a. 126
Lymphatics, 0. 408

Magnetic elements, e» 64

equator, c. 48

Magnetism, c. 46

Matter and form, a, 66

Mean temperature, b. 479

Mechanidd mixture of gases, 6. 613

Mechanico-chemieal sciences, 0. 6

Meiocene, 0. 629

Meridian line, a, 202

Metals, 0. 180

Meteorology, 6* 466

Meteors, a. 78

Methodic school (of medicine), 0.
385

Metonic cycle, a. 128

Mineral aUcali, 0. 110

Mineralogical axis, 0. 639

Minutes, a. 201

Miocene, 0. 629

Mollusca, 0» 449

Moment of inertia, 6. 80

Momentum, 6. 49

I^Ioon*s libration, b, 100

Morphology, 0. 433, 436

Moveable polarization, 6» 486

Multiple proportions (in Chemis-
try), 0. 146

Music of the spheres, a. 71

Mysticism, a. 281

Nadir, a. 231

Nebular hypothesis, 0. 486

Neoplatonists, a, 276

Neutral axes, ft. 386

Neutralisation (in Chemistry), 0.

109
Newton's rings, b, 879, 460
■ scale of colour, ft. 879

Nitrous air, 0. 126
Nomenclature, 0. 307
Nominalists, a. 389
Non-electrics, 0. 11
Numbers of the Pythagoi^eans, s. 6fi!
Nutation, ft. 260
Nycthemer, a. 194

INtlfiX Cnf TECHNICAL T&RMS.

XXXV

Octaeteris, a. 126
Octants, a, 228
Oolite, c, 530
Optics, 6. 340
Orgonical scicttices, e, 377
Organic molecules, e. 419
Organization, o. 377
Oscillation, centre of, b. 79
Outcrop (of strata), e. 502
Oxide, e. 138
Oxyd, c, 138
Oxygen, c, 129

Palaeontology, o. 0l3
PalaBtiological sdences, c, 481
Parallactic instrument, a, 204
Parallax, a. 195
Percussion, eentre of, 6, 81
Perfectihabia, a, 58
Perigee, a, 170
Perijove, 6. 229
Periodical colours, b. 403
Phases of the moon, a. 150
Philolaic tables, a, 434
Phlogisticated air, c. 126
Phlogiston, c. 118
Phthongometer, b. 336
PhjBictd optics, 6. 340
Piston, 6. 63
Pla^edral faces, b, 388
Plane of maximum areas, 6. 119
Pleiocene, c. 529
Flesiomorphous, c, 222
Pliocene, c. 529
Plumb line, a. 202
Pneumatic trough, c. 125
Poikilite, c. 530
Polar decompositions, c. 158
Polarization, 6. 375, 403, 415, 535

circular, b, 388, 444

elliptical, b. 447

movable, b. 425

plane, b, 444

of heat, b. 463

Poles (voltaic), c 165

-^— of maximum cold, b. 480

Potential levers, b, 122

Power and act, a, 56

Precession of the equinoxes, a, 186

Predicables, a. 272

Predicaments, a. 272

Preludes of epochs, a. 12

Primary rocks, o. 503

Primitive rocks, c, 503

Primum calidum, a, 61
Principal plane (of a rhomb), b. 373
Principle of least action, 5. 119
Prosthaphseresis, a. 171
Provinces (of plants and animals),

0.571
Prutenic tables, a. 38S
Pulses, 5. 312
Pyrites, c. 249

Quadrant, a. 202
Quadrivium, a. 260
Quiddity, a. 321

Quinary division (in Natural His-
tory), e. 853
Quintessence, a, 54

Radiata, c, 449
Badiation, b. 468
Rays, b. 342
Realists, a. 329
Refraction, b, 344

of heat, b, 495

Remora, tf. 245
Resinous electricity, c. 12
Rete mirabile, c. 424
Retrograde motion of planets, a. 159
Roman calendar, a. 131
Rotatory vibrations, 6. 3S(0
Rudolphine tables, a, 382, 431

Saros, a. 154

Scholastic philosophy, a. 315

School philosophy, a, 19

Science, a.

Secondary rocks, c. 509

meclianical science<:i, b,

293
Second law of motion, b. 36
Seconds, a. 201
Secular inequalities, b. l05
Segregation, c. 565
Seminal contagion, c. 419

proportions, a. 65

Sequels of epochs, a, 12
Silicides, c. 250
Silurian rocks, c, 530
Sunples, c. 269
Sine, a. 230
Solar heat, b, 477
Solstitial points, a. 145
Solution of water in air, 5. 504
Sothic period, a. 122
Spaglric art, c. 107

*

XXXVl

INDEX OF TECHNICAL TERMS.

Specific heat, b. 498
Sphere, a. 144

Spontaneous generation, c. 414
Statical electricity, c. 33
Stationary periods, a. 15

planets, a, 159

Stations (of plants), c. 571
Sympathetic sounds, 6. 317
Systematic Botany, c, 254

Zoology, c, 343

Systems of crystsdUzation, c. 212

Tahles, Solar (of Ptolemy), a. 172

Hakemite, a. 226

Toletan, a. 225

Uchanic, a. 225

Alphonsine, a. 225

Prutenic, a. 382

Rudolphine, a. 431

Perpetual (of Lansberg),

a. 431

Philolaic, a. 434

Carolinian, a, 434

Tangential vibrations, b, 332
Tautochronous curves, b. 108
Technical terms, c. 307
Temperament, 6. 335
Temperature, b. 469
Terminology, c. 307
Tertiary rocks, c. 503
Tetractys, a. 62
Theqry of analogues, c. 457
Thermomultiplier, 6. 493
Tliermotics, b, 465
Thick plates, colours of, b, 383
Thin plates, colours of, b. 378
Third law of motion, b, 44
Three principles (in Chemistry), c.

106
Toletan tahles, a. 225
Transition rocks, o. 530

Transverse vibrations, b. 330, 403,

419
Travertin, e. 553

Trepidation of the fixed stars, a. 227
Trigonometry, a. 207
Trivial names, c. 312
Trivium, a. 260
Tropics, a. 144

Truncation (of crystals), c. 196
Type (in Comparative Anatomy),

0.446

Variation of the moon, a. 221
Vegetable alkali, c. 110
Vertebrata, e. 449
Vibrations, b. 330
Vicarious elements, e. 221

solicitations, b. 85

Virtual velocities, 6. 41
Vitreous electricity, c. 12
Volatile alkali, c. 110
Volta-electrometer, c, 166
Voltaic electricity, c. 69

pile, c. 70

Volumes, theory of, c. 153
Voluntary, violent, and natural

motion, b, 18
Vortices, b. 134

Uniform force, b.3l

Unity of composition (in Compa-
rative Anatomy), c. 457

Unity of plan (in Comparative
Anatomy), e. 457

Week, a. 139

Year, a. 112

Zenith, a. 231
Zodiac, a. 145
Zones, a, 154

HISTORY

OP

INDUCTIVE SCIENCES,

INTRODUCTION.

VOL. 1. B

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

^^ The use and end of which work I do not so much design for
curiosity, or satisfaction of those that are the lovers of learning : but
chiefly for a more serioaB and grave purpose; which is this, in few
words, that it vill make learned men more wise in the use and
administration of learning.'*

Bacok, Advancement of Learning, book ii.

INTRODUCTION.

It is my purpose to write the history of some of
the most important of the physical sciences, from
the earliest to the most recent periods. I shall
thus have to trace some of the most remarkable
branches of human knowledge, from their first
germ to their growth into a vast and varied assem-
blage of undisputed truths; from the acute, but
fruitless, essays of the early Greek philosophy, to
the comprehensive systems, and demonstrated gene-
ralizations, which compose such sciences as the
Mechanics, Astronomy, and Chemistry, of modem
times.

The completeness of historical view which belongs
to such a design, consists, not in accumulating aU
the details of the cultivation of each science, but
in marking clearly the larger features of its forma-
tion. The historian must endeavour to point out
how each of the important advances was made, by
which the sciences have reached their present posi-
tion; and when and by whom each of the valuable
truthi^ was obtained, of which the aggregate now
constitutes a costly treasure.

B 2

4 HISTORY OF INDUCmVE SCIENCES.

Such a task, if fitly executed, must have a well-
founded interest for all those who look at the exist*
ing condition of human knowledge with complacency
and jidmiration. 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 for ever.
Our species, from the time of its creation, has been
travelling onwards in pursuit of truth; and now
that we have reached a lofty and commanding posi-
tion, with the broad light of day around us, it must
be grateful to look back on the line of our past
progress; — to review the journey, begun in early
twilight amid primeval wilds; for a long time con*
tinned with slow advance and obscure prospects;
and graduaUy 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 favour on the
score of the mere subject of his narrative, and in
virtue of the curiosity which the men 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 presait
form and extent, the future hopes and proifiects of
science, as well as its past progress. The eminence
on which we stand may enable us to see the land

INTRODUCTION. 5

of promise as well as the wilderness through which
we have passed. The examination of the steps by
which our ancestors acquired our intellectual estate,
may make us acquainted with our expectations as
well as our possesions ; — may not only remind us
of what we have, but may teach us bow to improve
and increase our store. It will be universally ex-
pected that a history of Inductive Science should
point out to us a philosophical distribution of the
existing body of knowledge, and afford us some
indication of the most promising mode of directing
our future efforts to add to its extent and complete-
ness.

To deduce such lessons from the past history of
human knowledge, was the intention which originally
gave rise to the pretent work. Nor is this portion
of the design in any measure abandoned ; but its
execution, if it take place, must be attempted in a
separate and future treatise. On the PhUmophy of
Inductive Science. 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.

Though, therefore, many of the principles and
maxims of such a work will disclose themselves
with more or less of distinctness in the course of
the history on which we are about to enter, the
systematic and complete exposition of such prin-
ciples must be reserved for this other treatise. My
attempts and reflections have led me to the opinion

6 HISTORY OF INDUCTIVE SCIENCES.

that justice cannot be done to the subject without
such a diidslon of it.

To this Aiture 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 whicb
is Inductivb differs from that which is not so ; or
why some portions of knowledge may properly be
seled^ed from the general nuuss and termed Science.
It will be sufficient at present to say, that the
sciences of which we have here to treat, are those
which are commonly known as the Physical Sciences;
and that by IndmHon is to be understood that pro-
cess of collecting general truths fit>m the examination
of particular fects, 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. — In the first place, then, I re-
mark, 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

, INTKODUCnON. 7

end in a practical acquaintance with indiTidoal
olgects ; the operations of the rational fiu^nhies, on
the other hand, if alloiiFBd to go on without a con-
stant reference to external thiB^ can lead only to
empty abstraction and barren ingenuity. Real
specuhtive knowledge demands the combination of
the two ingredients ;-^right reason, and feets to
reason upon. It has been well said, that true know«
ledge is the interpretation of nature; and thus 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
connexion of thought, arc necessary on the one
hand, for the progress of philosophical knowledge;
and on the other hand, the precise and steady
application of these feculties to facts well known
and clearly conceived. It is easy to point out
instances in which science has fiedled to advance, in
consequence of the absence of one or other of these
requisites; indeed, by &r the greats part of the
course of the woorld, the history of most times and
most countries, exhibits a condition thus stationary
with respect to knowledge. The jGstcts, the im-
pressions 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
fi^niiliflr to man before the rise of the Greek astro-
nomy and mechanics : but the '' diviner mind" was

8 HISTORY (HP INDUCmVK SCIENCES.

sMU absent; the act of thoiiglit had not be^i ex**
ertedy by which these facts were bound together
under the fonn of hiws and principles. And ereti
at this day, the tribes of uncivilized and half-civilized
man over Uie whole face of the earth, have before
their eyes a vast body of Acts, of exactly the same
nature as those with whidi Europe ha« built the
stately fitbric of her physical philosophy; but, in
almost every other part of the earth, the process ci
the intellect by which these facts beooma sci^ice, is
unknown. The scientific ftcuity does not work.
The scattered stones are indeed there, but the
builder^s hand is wanting. And again, we have no
lack of proof that the 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 philoso-
phers; shows us that we may have extreme ingenuity
and subtlety, invention and connexion, demonstrar
tion 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 mate-
rials we shall never form mechanics and optics,
chemistry and physiology. How impossible is the
formation of these sciences without a constant and
careful reference to observation and experiment ; —
how rapid and prosperous may be their progress
when they draw from such sources the materials on

IMTRODUOnOI^. 9

vMck the mind of the philosopher employs itsdf ^^
the history of those branches of knowledge for the
last three hundred yeaxs abundantly teaches us.

Accordingly, the existence of clear ideas applied
to distinct &cts will be discernible in the History of
Science^ whenever any marked advance takes place.
And, in tracing the progress of the various provinces
of knowledge which oome under our survey, it will
be important for us to see, that, at all such epochs,
such a combination has ooourred; that whenever
any material step in general knowledge has been
made,-«~wh6never any philosophical discovery arrests
our attrition ; — ^some man or men come before us,
who have possessed, in an eminent degree, a clear*
ness of the ideas which belong to the subject in
question* and who have applied such ideas in a
vigorous and. distinct manner to ascertained fects
and exact observations. We shall never proceed
liirough any considerable range of our narrative,
without having occasion to remind the reader of
this reflection.

Successive steps m Science. — ^But there is another
remark which we must also make. Such sciences
as we have here to do with, are, commonly, not
formed by one single act ; — ^they are not completed
by the discovery of one great principle. On the
contrary, they consist in a long^continued advance ;
a series of changes ; a repeated progress from one
principle to another, different and often apparently
contradictory. Now, it is important to remember

10 HISTORY OP INDUCTTVK SCIENCES.

that this eontradiction is apparent only. The prm^
ciples which constituted the trimnph of the pre-
ceding stages of the science, may appear to be sub-
verted and ejected by the later discoveries, but in
fiict they are, (so £ur as they were true,) taken up
into the subsequent doctrines and included in ihem*
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 succes-
sion of revolutions, is, in reality, a series of deve*
lopements. In the intdleetual, as in the matmal
worid,—

Omnia mutantur nil interit

Nee manet ut fuerat nee formas senrat easdem,
Sed tamen ipsa eadem est.

All ehanges, nought is lost ; the forms are changed,
And that whidi has be^i is not ^at it was,
Yet that whidi has heen is.

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

Thus the final fonn 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 develope-
ment of its proper branch of knowledge. Such
previous doctrines may require to be made precise
and definite, to have their superfluous and arbitraiy
portions expunged, to be expressed in new language,
to be taken up into the body of science by various

INTRODUCTION* 11

processes ; — ^but they do not on audi aoeonnts cease
to be true dootrines, or to form a portion of the
essential constituents of our knowledge.

Terms record Discaveries. — ^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 ahnost self-evident axioms. They are
recorded by some familiar maxim, or perhaps by some
new word or phi«e. which forms paTofTe e«n«nt
language of the philosophical world; and thus asserts
a principle, while it appears merely to indicate a tran*
sient 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 man-
ner in which great discoveries thus stamp their im-
press upon the terms of a science; and, like great
political revolutions, are recorded by the change of
the current coin which has accompanied them.

Generalizaiion. — The great changes which thus
take place in the history of science, the revolutions
of the intellectual world, have, as a usual and lead-
ing character, this, that they are steps of ffeneraUzor
turn /-^transitions firom particular truths to others of
a wider extent, in which the former are included.
This progress of knowledge, from individual facts to
universal laws, — ^from particular propositions to
general ones, — ^and from these to others still more
general, with reference to which the former genera^,
lizations are particular, — is so far familiar to men's

12 HISTORY OF DTBUCnTE SCIENCES.

minds, that without here entering into further ex-»
{Sanation, its nature will be understood sufficiently
to pr^are the reader to recognise the exemplifica-
tions of such a process, which he will find at every
step of our advance.

Inductive Epochs ; Prdvdes ; Sequek.^^In our his-
tory, 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 etdtivators of philosophy, are not a necessary
part of our theme. Our narrative will therefore
consist mainly of successire steps of generalization,
flNidh as have just been mentioned. But among
these, we shall find some of eminent and decisive
importance, which have more peculiarly influenced
the fortunes of physical philosophy, and to which
we may consider the rest as subordinate and auxi-
liary. These primary movements, when the Induc-
tive process, by which science is formed, has been
exercised in a more energetic and powerful manner,
may be distinguished as the Indtidwe Epochs of
scientific history; and they deserve our more ex-
press and pointed notice. They are, for the most
port, marked by the great discoveries and the great
philosophical names which all civilized nations have
agreed in admiring. But, when we examine more
Nearly the history of such discoveries, we find that
these epochs have not occurred suddenly and with-
out preparation. They have been preceded by a

INTRODUCTION. 13

period, whioh we may call their Prelude^ during
which the ideas aad &ets on which they turned
were called into action ; — were gradually evolved
into clearness and connexion, permanency and cer-
tainty ; till at last the discovery which marks the
epoch, seized and fixed for ever the truth which had
till then been obscurely and doubtfully discerned.
And again, when this step has been made by the
principal discoverer, there may generally be ob-
served another period, which we may call the Sequd
of the epoch, during whieb the discovery has acquired
a more perfect certainty wti a more complete de^
velopement among the leaders • of the advance ; has
been diffiised 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 labour, often of difficulty and conflict. To
distribute the history of scieoice into such epochs,
with their preludes and sequels, if successfully
attempted, must needs make the series and con-
nexion of its occurrences more distinct and intel-
ligible. Such periods form resting-places, where we
pause till the dust of the confixsed march is laid, and
the prospect of the path is clear.

Inductive Charts. — Since the advance of science
consists in collecting by induction general laws from
particular facts, and in combining several laws into
one higher generalization, in which they still retain
their former truth, we might form a Chart, or Table,
of the progress of each science, by setting down the

14 HISTORY OF INDUCnTE SCIENCES.

particulars which thus flow together, so as to form
general truths, and marking the junction of these
general truths into others more comprehensive.
The table of the progress of any science would thus
resemble the map of a river, in which the waters
from separate sources unite and make rivulets, which
again meet with rivulets from other fountains, and
thus go on forming by their junction trunks of a
higher and higher order. The representation of the
state of a science in this form, would necessarily
exhibit all the principal doctrines of the science ;
for each general truth contains the particular truths
from which it was dmved, and may be followed
backwards till we have these before us in their sepa-
rate state. And the last and most advanced gene*
ralization would have, in such a scheme, its proper
place and the evidence of its validity. Hence such
an Indtictwe TaUe of each science would afford a
criterion of the correctness of our distribution of the
inductive epochs, by its coincidence vjith the views
of the best judges, as to the substantial contents of
the science in question. By forming, therefore, such
Inductive Tables of the principal sciences of which
I have here to speak, and by regulating by these
tables, my views of the history of the sciences, I
conceive that I have secured the distribution of my
history from material error ; for no merely arbitrary
division of the events could Satisfy such conditions.
But though I have constructed such charts to direct
the course of the present history, I shall not insert

INTRODUCTION. 16

them iu the work, reserving them for the illustration
of the philosophy of the sulyect ; for to this they
more properly belong* being a part of the Logic ijf

Staiionmy Periods. — ^By the lines of such maps
tiie real advance of science is depicted, and nothing
else. But there are several occurrences of other
kinds, too interesting and too instructive to be alto-
gether omitted. In order to understand the condi-
tions of the progress of knowledge, we must attend,
in some measure, to the Mlures as well as the sue*
cesses 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 staMonary periods ; what field could
be found which admitted of so wide a deviation, or
at least so protracted a wandering. It is highly
necessary to our purpose, to describe the baffled
enterprises as well as the achievements of human
i|)eeulation.

i70c?^^^on.•*^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 sdence,
the conjunction of dear ideas with distinct facts, was
interrupted ; and, in su<ih cases^r men dealt with ideas
alone. They employed themselves in reasoning from
principles^ and they arranged, and classified, and
analysed their ideas, so as to make their reasonings

16 HISTORY OF INDUCTIVE SCIENCES.

r

satisfy the requisitions of our rational &eulties.
This process of drawing conclusions from our prin-
ciples, 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 d^nonstration rests, have
not first been obtained by the induction of &cts, so
as to supply the sole materials of substantial truth.
Without such materials, a series of demonstrationd
resembles physical science only as a shadow resem-
bles a real object. To give a real significance to
our propositions, Induction must provide what De-
duction itself cannot supply. From a pictured hook
we can only hang a pictured chain.

Distinction of common Noiiom and Scientific Ideas. —
When the notions with which men are conversant
in the common course of practical life, which give
meaning to their fismiiliar language, and employment
to their hourly thoughts, are compared with the
ideas on which exact science is founded, we find that
the two classes of intellectual operations have much
that is common and much that is different. With-
out here attempting fully to explain this relation,
(which, indeed, is one of the hardest problems of our
philosophy,) we may observe that they have this in
common, that both are acquired by acts of the mind
exercised in connecting external impressions, and
may be employed in conducting a train of reasoning ;
or, speaking loosely, (for we cannot here pursue the

INTRODUCTION. 17

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, tliat the former are precise and stable,
the latter vague and ambiguoujs; the former are
possessed with dear insight, and employed in a sense
rigorously limited^ and always identically the same ;
the latter have grown up in the mind from a thou-
sand div^*se and obscure suggestions, and the ob-
scurity and inconsistency of liieir origin hangs about
all their applications. Scientific ideas can often be
adequately exhiUted for all the purposes of reason-
ing, by means of definitions and axioms; all
attempts to reason by means of definitions from
common notions, lead to empty forms or entire
confitsioxi.

Such common notions are sufiicient for the
conunon practical conduct of human life ; but man
is not a practical creature merely ; he has within
him a speculcUive tendency, a pleasure in the con-
templation 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 analyses such notions, reasons upon them,
combines, constructs, infers ; for it feels that intel-
lectual things ought to be able to bear such handling.
Even practical knowledge, we see clearly, is not
possible without the reason; and the speculative

VOL. I. c

18 HISTORY OP INDUCTIVE SCIENCES.

reason is only the reason satisfying itself of its own
consistency. This specnlative 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
bairen abstractions and ever-recurring cycles of
subtlety. Such notions are like waters naturally
stagnant, and howeyer much we urge and agitate
them, they only revolve in stationary whirlpools.
But the mind is capable of acquiring scientific ideas,
which are fitted to undergo this discussion and im*
pulsion. When our speculations are duly fed from
the spring-heads of observation, and often drawn ofi*
to the region of applied science, we may have a
living stream of consistent and progressive know-
ledge. 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 PAifo5()pA^.~- While, however, attempts are
made to form sciences, without such a verification
and realization of their Amdamental ideas, there is,
in the natural series of speculation, no self-correcting
principle. A philosophy constructed on notions
obscure, vague, and unsubstantial, and not arrested
in its career by the want. of correspondence between
its doctrines and the actual train of physical events,
may long subsist, and occupy men's minds. Such a
philosophy must depend for its permanence upon
the pleasure which men feel in tracing the operations

INTRODUCTION. 19

of their own and other men's minds, and in reducing
them to logical consistency and systematical ar-
rangement.

In these cases the subjects of attention are not
external objects, but speculations previously deliver-
ed ; the object is not to interpret nature, but man's
mind. The opinions of the masters are the facts
which the disciples endeavour 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 PhUosophy ;
whether their agreement in such a mode of seeking
knowledge arise from personal communication and
tradition, or be merely the result of a community of
intellectual character and propensity. The two
great periods of school philosophy (it will be recol-
lected that we are here directing our attention mainly
to physical science), were that of the Greeks and
that of the middle ages, — ^the period of the first
waking of science, and that of its mid-day slumber.

What has been said thus briefly and imperfectly,
would require great detail and much explanation, to
give it its fiill significance and authority. But it
was 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 metaphy-
sical, and, it may be, repulsive ; and must give them

c 2

20 HISTORY OF INDUCTIVE SCIENCES.

without adequate developement and proof. Such
an introduction may be compared to the geographical
sketch of a country, with which the historian of its
fortunes often begins his narration. So much of
metaphysics is as necessary to us as such a portion
of geography is to the historian of an empire ; and
what has hitherto been said, is intended as a slight
outline of the geography of that intellectual world,
of which we have here to study the history.
To that history we now proceed.

BOOK I.

HISTORY

OF THE

GREEK SCHOOL PHILOSOPHY,

WITH RBFBRBNCB TO

PHYSICAL SCIENCE.

Tk yctp apxO' Bi^aro vaim\la<;;
Tk Bk /clvSvvo<; Kparepol*; aSafiav-

T0<: Srjaev a\o49;
'BttcI S^ifi^oXov

Kpcfiacrav ayxvpa^ virepOev
Xpvaiav ')(elp€<Tat \afia)v <l>uiKav
^Ap'xp^ €V TTpvfiva irarip ^OvpaviZav
^Eyx^ecxipavvov Zrjvay kol m/cvTrSpov^
Kvfidrciyv phra^;^ avefitov r iKoKetj
NvKTa<i re, koL irovrov KeKevOov^j
^^Afiard T ev^povoy koX
fiXlav vioToio fiolpav.

PiKDAR. Ppi/L iv. 124, a49.

Whence came their voyage ? them what peril held
With adamantine rivets firmly bound ?

But soon as on the vessel's bow

The anchor was hung up.
Then took the Leaders on the prow

In hands a golden cup,
And on great &ther 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 fiur auspicious days.

And loved return at last

BOOK I.

mSTOBY OF THE GBEEK SCHOOL PHILOSOPHY, WITH
REFERENCE TO PHYSICAL SCIENCE.

CHAPTER I.

Prelude to the GitEEK School Philosophy.

SecL 1. — First Attempts of the Speculative Faculhf in

Physical Inquiries.

At an early period of history there appeared in men
a propensity to speculative inquiries concerning the
various parts and properties of the material world.
What they saw excited them to meditate, to con-
jecture, and to reason : they endeavoured to account
for natural events, to trace their causes, to reduce
them to their principles. This habit of mind, or,
at least that modification of it which we have here
to consider, seems to have been first unfolded
among the Greeks. And during that obscure intro-
ductory 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 loise men — iro<f>o\. But

24 THE GREEK SCHOOL PHILOSOPHY.

when it came to be clearly felt by such persons that
their endeavours were suggested by the love of
knowledge, a motive different from those 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
Herodotus, instead of having this title, is called a

powerfill sophist — ^EXKrjvcuv oi rm aadeveardrcp ao<f>LaTy

Ilvdayopr)*; 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 place Pythagoras at the
origin of the Italic school, one of the two main lines
of succession of the early Greek philosophers : but
the other, the Ionic school, which more peculiarly
demands our attention, in consequence of its cha-
racter and subsequent progress, is deduced from
Thales, who preceded the age of philosophy, and
was one of the sophi^ 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 universe ; and to these were soon added all
the great questions which our moral condition and

' Cic. Tusc. T. 3. » Herod, iy. 95.

PRELUDE. 25

&culties 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 vigour ; and yet it must be allowed,
(for, at least so far as physical science is concerned,
none will contest this,) to have been entirely unsuc-
cessful. We cannot consider otherwise than as an
utter failure, an endeavour 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 fBie 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 vigour and confidence of the question-
ing spirit, as yet untamed by labours and reverses.
It was for later ages to learn that the man must
acquire, slowly and patiently, letter by letter, the
alphabet in which nature writes her answers to such
inquiries ; the first students wished to divine, at a
single glance, the whole import of her book. They
endeavoured to discover the origin and principle of

26 THE GREEK SCHOOL PHILOSOPHY.

the universe; according to Thales, waJUr was the
origin of all things, according to Anajdmenes, airi
and Heraclitus considered ^re as the essential prin*
ciple of the universe. It has been conjectured,
with ^reat plausibility, that this tendency to rive to
their ^Iphy the form of . co^nogony. w«
owing to the influence of the poetical cosmogonies
and theogonies which had been produced and ad-
mired at a still earlier age. Indeed, such wide and
ambitious doctrines as those which have been men-
tioned, 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 (^p%^), signified at
first Me 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
theolc^cal views which at this period were only just
beginning to be separated fix>m 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

PRELUDE. 27

the universal element, resulted from the manifest
importance of moisture in the support of animal
and vegetable Iif6^ 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
curiosity concerning the causes of natural appear-
ances, and in the attempts made to satisfy these, we
appear to discern a more genuine prelude to the
true spirit of physical inquiry. One of the most
remarkable instances of this kind is to be foimd in
the speculations which Herodotus records, relative
to the cause of the floods of the Nile. " Concern-
ing the nature of this river," says the fieither of his-
tory*, " I was not able to learn anything, either from
the priests or from any one besides, though I ques-
tioned 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 anything satis-
factory 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."

We may see, I think, in the historian's account,
that the Grecian mind felt a craving to discover the
reasons of things which other nations did not feel.
The Egyptians, it appears, had no theory^ and felt

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

28 THE GREEK SCHOOL PHILOSOPHY.

the want of none. Not so the Greeks ; they had
their reasons to render, though they were not such
as satisfied Herodotus. " Some of the Greeks," he
says, " who wish to be considered great philosophers,

have propounded three ways of accounting for these
floods. Two of them," he adds, " I do not think
worthy of record, except just so far as to mention
them." But as these are some of the earliest Greek
essays in physical philosophy, it will be worth while,
even at this day, to preserve the brief notice he has
given of them, and his own reasonings upon the
same subject.

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

"The next opinion is still more unscientific,
{dv€7ncrTrffjLov€<TTiprj) 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

PRELUDE. 29

ocean-river, goes into the region of fable, where it
is not easy to demonstrate that he is wrong. I know
of no such river. But I suppose that Homer or
some of the earlier poets invented this fiction and
introduced it into their poetry."

He then proceeds to a third account, which to a
modem reasoner would appear not at all unphilo-
sophical in itself, but which he, nevertheless, rejects
in a manner no less decided than the others. ^* The
third opinion, though much the most plausible, is
still more wrong than the others ; for it asserts an
impossibility, namely, that the Nile proceeds from
the melting of the snow. Now the Nile flows out
of Libya, and through Ethiopia, which are very hot
countries, and thus comes into Egypt, which is a
colder region. How then can it proceed fit)m
snow ?'' He then offers several other reasons " to
show," as he says, *^ to any one capable of reasoning

on such subjects {avBpl ye Xoyl^eaOai roiovray iripi

ot<p T€ lorrt), that the assertion cannot be true. The
winds which blow from the southern regions are
hot; the inhabitants are black; the swallows and
kites (UtIvoi) stay in the country the whole year ;
the cranes fly the colds of Scythia, and seek their
warm winter-quarters there; which would not be
if it snowed ever so little." He adds another reason,
founded apparently upon some limited empirical
maxim of weather-wisdom taken from the climate
of Greece. " Libya," he says, " has neither rain nor
ice, and therefore no snow ; fovy in five days after* a

30 THE GREEK SCHOOL PHILOSOPHY.

£all of snow there must be a &11 of ram ; so that if
it snowed in those regions it must rain too." I need
not observe that Herodotus was not aware of the
difference between the climate of high mountains
and plains in a torrid region ; but it is impossible
not to be struck both with the activity and the co-
herency of thought displayed by the Greek mind in
this primitive physical inquiry.

But I must not omit the hypothesis which Hero-
dotus himself proposes, after rejecting those which
have been already given. It does not appear to me
easy to catch his exact meaning, but the statement
will still be curious. " If," he says, ** one who has
condemned opuuon, ,r^^j U^gaM ™,
put forwards 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 pro-
pounds at first with an oracular brevity, which it is
difficult to suppose that he did not intend to be
impressive. " In winter the sun is carried by the
seasons away from his former course, and goes to
the upper parts of Libya. And thercy in short, is
the whole account; for that region to which this
divinity (the sun) is nearest, must naturally be most
scant of water, and the river-sources of that country
must be dried up."

But the lively and garrulous Ionian immediately
relaxes from this apparent reserve. " To explain
the matter more at length," he proceeds, " it is thus.
The sun, when he traverses the upper parts of Libya,

PBELUDE. 31

does what he commonly does in summer ; — he draws
the water to him (^x^ret iif" k^vrov to 0&dp) 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 melt in moisture.
And thus the winds which blow from those coun-
tries, Libs and Notus, are the most moist of all
winds. Now when the winter relaxes and the sun
returns to the north, he still draws water from all
the rivers, but they are increased by showers and
rain-torrents, so that they are in flood till the
summer comes ; and then, the rain foiling and the
sun still drawing them, they become small. But
the Nile, not being fed by rains, but being dravm
by the sun, is, alone of all rivers, much more scanty
in the vrinter than in the summer. For in summer
it is drawn like all other rivers, but in winter it
alone has its supplies shut up. And in this way, I
have been led to think the sun is the cause of the
occurrence in question." We may remark that the
historian here appears to 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 pro-
duced whether the sun increase the sources in winter
by melting the snows, or diminish them in summer
by what he calls dramng them upwards.

This specimen of the early efforts of the Greeks
in physical speculations, appears to me to speak

32 THE GREEK SCHOOL PHILOSOPHY.

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

Sect. 2. — Primitive Mistake in Ghreek 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

* Thirl wall, Hist, Gr.^ ii. 130 ; and, as there quoted, Ritter,
Geschichte der Pkilosophie, i. 159 — 173.

PRELUDE. 33

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 al-
most up to the present time. It is not necessary
here to decide why those feculties which appear to
be bestowed upon us for the discovery of truth, were
permitted by Providence to fidl 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
immediately lead man to profound physical know-
ledge, answered some nobler and better purpose in
his 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 remark-
able phrase used by Herodotus, in his own explana-
tion of these inundations. He says that the sun
draws, or attracts, the water ; a metaphorical term,
obviously intended to denote some more general
and abstract conception than that of the visible
operation which the word primarily signifies. This
abstract notion of ' drawing' is, in the historian, as

VOL. I. , D

34 THE GREEK SCHOOL PHILOSOPHY.

we see, very vague and loose ; it might, witli equal
propriety, be explained to mean what we now un-
derstand by mechanical or by chemical attraction,
pressure, or evaporation. And in like manner, all
the first attempts to comprehend the operations of
nature, led to the introduction of abstract concep-
tions, often vague indeed, but not, therefore, un-
meaning; such as motion and velocity, force and
pressure, impetus and momentum (po'^'v)* And the
next step, in philosophizing, necessarily was to en-
deavour 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 fects
and things which bring these abstract terms into
use. The latter, the method of real inquiry, was
the way to success; but the Greeks followed the
former, the verbal or notional course, and failed.

If Herodotus, when the notion of the sun's at-
tracting 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 ascer-
tain whether this attraction which the sun exerted
upon the waters of rivers, depended on his influence

PRELUDE. 35

at their fountains only, or was exerted over their
whole course, and over waters which were not parts
of rivers, he would have been led to reject his
hypothesis, for he would have found, by observations
sufficiently obvious, that the sun's Attraction, as
shown in such cases, is a tendency to lessen all ex-
panded and open collections of moisture, whether
flowing firom a spring or not ; and it would then be
seen that this influence, operating on the whcrfe
surfiaice of the Nile, must diminish it lus well Hi
other rivers, in Summer, and therefore could not
be the cause of its overflow. He would thus have
corrected his first loose conjecture by a real study
of nature, and might, in the course of his medita-
tions, have been led to available notions of Evapora-
tion, or other natursd actions. And, in like manner,
in other cases, the i^ude attempts at explanation,
which the first exercise of the speculative faculty
produced, might have been gradually concentrated
and refined, so as to fall in, both with the requisi-
tions of the 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, with-
out any longer looking abroad into the world of
sense* They took for granted that philosophy must
result from the relations of those notions which are
involved in the common use of language, and they

D 2

36 THE GREEK SCHOOL PHILOSOPHY.

proceeded to seek it by studying such notions.
They ought to have reformed and fixed their usual
conceptions by observation ; they only analysed and
expanded them by reflection: they ought to have
sought by trial, among the notions which passed
through their minds, some one which admitted of
exact application to facts ; they selected arbitrarily,
and, consequently, erroneously, the notions according
to which facts should be assembled and arranged :
they ought to have collected clear fundamental ideas
from the world of things by inductive acts of thought ;
they only derived results by dedtwtion from one or
other of their familiar conceptions.

When this Mse 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.

37

CHAPTER II.

The Greek School Philosophy.

Sect. 1. — ITie general Foundation of iJie Greek School

Philosophy/.

The physical philosophy of the Greek Schools was
formed by looking at the material world through
the medium of that common language which men
employ to answer the common occasions of life;
and by adopting, arbitrarily, as the grounds of com-
parison of facts, and of inference from them, notions
more abstract and large than those with which men
are practically familiar, but not less vague and
obscure. Such a philosophy, however much it
might be systematized by classifying and analysing
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 com-
mon us^'ges of language may be discerned at a very
early period. Thus we have an example of it in a
saying which is reported of Thales, the founder of
Greek philosophy'. When he was asked " What is
the greatest thing?" he replied, " Place; for all other

* Plut. Conv» Sept, Sap, Diog. Laert. i. 35.

38 THE GREEK SCHOOL PHILOSOPHY.

m

things are in the world, but the world is in it." In
Aristotle we have the consummation of this mode
of speculation. The usual point from which he
starts in his inquiries is, that we say thus or thus in
common language. Thus, when he has to discuss
the question, whether there be, in any part of the
universe, a void, or space in which there is nothing,
he inquires first in how many senses we say that
one thing is in another. He enumerates many of
theses we say the part is in the whole, as the finger
is in the hand ; again we say, the species is in the
genus, as man is included in animal; again, the
government of Greece is in the king; and various
other senses are described or exemplified, but of all
these the Tnmt proper is when we say a thing is m a
vessel, and generally in place. He next examines
what place is, and comes to this conclusion, that
" if about a body there be another body including
it, it is in place, and if not, not." A body moves
when it changes its place; but 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 in-
cluded by each other ; so that while the whole does
not change its place, the parts may change tiieir
places in a circular order. Proceeding then to the
question of a fxridj he, as usual, examines the dif*
ferent senses in which the term is used, and adopts,
as the most proper, piace without matter; with no
useful result, as we shall soon see.

■ Physic. Ausc. iy. 3.

JTS FOUNDATION. 39

AgainS in a question concerning mechanical
action, he says, '^ When a man moves a stone by
pushing it with a stick, we say both that the man
moves the stone, and that the stick moves the stone,
but the latter more properly.'^

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

The Dialogue of Plato, which is entitled Par^
menidesy appears at first as if its object were to show
the futility of this method of philosophizing; for
the philosopher whose name it bears, ifif^represented
as arguing with Aristotle, and, by a process of
metaphysical analysis, reducing him at least to this
conclusion, ^^ that whether One exist, or do not
exist, it follows that both it and other things, with
reference to themselves and to each other, all and in
all respects, both are and are not, both appear and
appear not." Yet the method of Plato, so &r as
concerns truth of that kind with which we are here

* Physic. Ausc. viii. 5.

40 THE GREEK SCHOOL PHILOSOPHY.

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
Timaeus, in the application of notions as loose as
those of the Peripatetics ; for example, the concep-
tions 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 imiverse. The philosopher is thus led to maxims
which agree with those of the Aristotelians, that
there can be no void, that things seek their own
place, and the like*.

Another mode of reasoning, very widely applied
in these attempts, was the doctrine of contrarieties,
in which it was assumed, that adjectives or sub-
stantives which are in common language, or in some
abstract mode of conception, opposed to each other,
must point at some fundamental antithesis in nature,
which it is important to study. Thus Aristotle*
says, that the Pythagoreans, from the contrasts
which number suggests, coUected ten principles,-
I^imited and Unlimited, Odd and Even, One and
Many, Right and Left, Male and Female, Rest and
Motion, Straight and Curved, Light and Darkness,
Good and Evil, Square and Oblong. We shall see
hereafter, that Aristotle himself deduced the doc-
trine of four elements, and other dogmas, by oppo-
sitions of the same kind.

* Timaeus, p. 80. * Metaph. 1. 5.

ARISTOTELIAN PHYSICS. 41

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

Sect: 2. — The Aristotelian Physical Phihsophy.

The principal physical treatises of Aristotle are,
the eight Books of " Physical Lectures," the four
Books "Of the Heavens," the two Books "Of
Production and Destruction :" for the Book " Of the
World" is now universally acknowledged to be
spurious ; and the " Meteorologies," though fall of
physical explanations of natural phenomena, does
not exhibit the doctrines and reasonings of the
school in so general a form ; the same may be said
of the " Mechanical Problems." The treatises on
the various subjects of Natural History, " On Ani-
mals," " On the Parts of Animals," " On Plants,"
« On Physiognomonics," " On Colours," "On Sound,"

42 THE GREEK SCHOOL PHILOSOPHY.

contain an extraordinarj accumulation of facts, and
manifest a wonderful power of systematising ; but
are not works which expound principles, and there-
fore do not require to be here considered.

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

The auihor^s introductory statement of his view
of the nature of philosophy fidls in very closely with
what has been said, that he takes his hcts and
generalisations as they are implied in the structure
of language. ** We must in aU cases proceed," he

ARISTOTELIilN PHYSICB. 43

3ays, " from what is known to what is unknown."
This will not be denied ; bnt we can hardly follow
him in his inference. He adds, *^ we must proceed,
therefore, from universal to particular. And some-
thing of this," he pursues, ^^ may be seen in lan-
guage ; for names signify things in a general and
indefinite manner, as cirde^ and by defining we un-
fold 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 endeavours 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 farther: — ^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 empty, and therefore without a
void there could be no motion : — and, on the other
hand, there is no void, for the intervals between
bodies s^e filled with air, and air is something*
These opinions had even been supported by reference
to expCTiment. On the one hand, Anaxagoras and
his school had shown, that air when confined, re-
sisted compression, by squeezing a blown bladder.

44 THE GREEK SCHOOL PHILOSOPHy.

tad 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* : — ^In a void there could be no difference of up
and down ; for as in nothing there are no differences,
so there are none in a privation or negation ; but a
void is merely a privation or negation of matter ;
therefore, in a void, bodies could not move up and
down, which it is in their nature to do. It is easily
seen that such a mode of reasoning elevates the
familiar forms of language and the intellectual con-*'
nexions of terms, to a supremacy over facts ; making
truth depend upon whether terms are or are not
privative, and whether we say that bodies fall
naturally. In such a philosophy every new result
of observation would be compelled to conform to
the usual combinations of phrases, as they had been
associated by the modes of apprehension previously
familiar.

It is not intended here to intimate that the com-
mon modes of apprehension, which are the basis of
common lansfuasfe, are limited and casual. They

conditions of our perceptions and conceptions : thus
all things axe necessarily apprehended as existing

• Physic. Ausc. iv. 7* p« 215.

ARISTOTELIAN PHYSICS. 45

in time and space, and as connected by relations of
cause and effect ; and so far as the Aristotelian phi*-
losophj reasons from these assumptions, it has a
real foundation, though even in this case the con-
clusions are often insecure. We have an example
of this reasoning in the eighth book^ where he
proves that there never was a time in which change
and motion did not exist ; " For if all things were
?it rest, the first motion must have been produced
by some change in some of these things ; that is,
there must have been a change before the first
change;" and again, "How can before and after
apply when time is not ? or how can time be when
motion is not ? If," he adds, " time is a numeration
of motion, and if time be eternal, motion must be
etemaL" But we have sometimes principles intro-
duced of a more arbitrary character; and besides the
general relations of thought^ the inventions of pre-
vious speculators are taken for granted ; such, for
instance, as the then commonly received opinions con-
cerning 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 rea-
soning, to identify this eternal motion with the
diurnal motion of the heavens. " There must," he
says, "be something which is the first moved":"
this follows from the relation of causes and effectsc
Again, "motion must go on constantly, and, there-

^ Physic. Ausc. viii. 1. p. 251.
* Physic. Ausc. viii. 6. p. 258.

46 THE GREEK SCHOOL PHILOSOPHY.

fore, must be either continuous or successive. Now
what is continuous is more properly said to take place
constandyy than what is successive. Also the con-
tinuous 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 con-
tinuous, if such an eternal motion be possible." We
here see the vague judgment of better and worse
introduced, as that of natural and unnatural ^as
before, into physical reasonings.

I proceed with Aristotle's argument*. " We have
now, therefore, to show that there may be an infinite,
single, continuous motion, and that this is circular."
This is, in feet, proved, as may readily be conceived,
from the consideration that a body may go on per-
petually revolving uniformly in a circle. And thus
we have a demonstration, on the principles of this
philosophy, that thare is and must be a first mover,
revolving etemally 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 to exemplify it, that we may
afberwards advance, confid^it that we have done it
no ii^ustice.

I will now pass from the doctrines relating to the
motions of the heavens, to those whi<^ concern the
material elements of the universe. And here it
mxy be remarked that the tendency (of which we

• viii. a

ARISTOTELIAN PHYSICS. 47

are here tracing the devdopement) to extract specu-
lative 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 mectives hat and
eddy wet and d/rjf^ is much older than Aristotle, and
was probably one of the earliest of philosophical
dogmas. The great master of this philosophy, how-
ever, puts the opinion in a more systematic manner
than his predecessors.

" We seek," he says^*, " the principles of sensible
things, that is, of tangible bodies. We must take,
therefore, not all the contrarieties of quality, but
those only which have reference to the touch. Thus
black and white, sweet and bitter, do not differ as
tangible qualities, tod 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 quali-
ties ; the others, because they are combinations of
the four first, which therefore he infers to be the
four elementary qualities.

" **Now in four things there are six combinations
of two ; but the combinations of two opposites, as

10

De Gen. et Corrupt ii. 2. " iii. 3.

48 THE GREEK SCItOOL PHILOSOPHY.

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 common elementary quality must exist in
the cases in which we habitually apply a common
adjective, as it began before the reign of the Aris-
totelian philosophy, so also survived its influence.
Not to mention other cases, it would be difficult to
free Bacon's Inquisitio in naturam calidi^ " Exami-
nation of the nature of heat," from the charge of
confounding together very different classes of phe-
nomena under the cover of the word hot.

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

These are still founded upon the same mode of
reasoning from adjectives ; but in this case, the result
follows, not only from the opposition of the words,
but also from the distinction of their being absolutely
or relaiivehf true. " Former writers," says Aristotle,
" have considered heavy and light relatively only,
taking cases, where both things have weight, but one

ARISTOTELIAN PHYSICS. 49

is lighter than the other ; and they imagined that,
in this way, they defined what was absolutely (ttTrXw?)
heavy and light." We now know that things which
rise by their lightness do so only because they are
pressed upwards by heavier surrounding bodies;
and this assumption of absolute levity, which is evi-
dently 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 phi-
losopher 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 il
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 fal-
lacies which have a verbal origin ; — from considering
light as opposite to heavy; and from considering
levity as a quality of a body, instead of as the effect
of surrounding bodies.

It is worth while to notice that a difficulty which

VOL. I. E

60 THE GREEK SCHOOL PHILOSOPHY.

often embarrasses persons on their entrance upon
physical speculations, — ^the difficulty of conceiving
that up and down are different direections in different
places, — ^had been completely got over by Aristotle
and the Greek philosophers. They were steadily con-
vinced 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 as
the heavy tends to the centre, the light tends to the
exterior, " for exterior is opposite to centre as heavy
is to Ught^V

The tendencies of bodies downwards and up-
wards, their weight, their fall, their floating or sink-
ing, were thus accounted for in a manner which,
however unsoimd, satisfied the greater part of the
speculative world till the time of Galileo and Ste-
vinus, though Archimedes in the mean time pub-
lished 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 suc-
cess. The motion of a body which is thrown along
the 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 charac-

18

De Ccelo, ir. 4.

ARISTOTELIAN PHYSICS. 51

ters of such motions in verse. The rule of natural
motion was**

Principium tepeat, medium cum fine calebit.
Cool at the firfit, it warm and warmer glows.

And of violent motion, the law was —

Principium ferret, medium calet, 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 mo-
tion, 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'*, "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 ceagfed to be acted on." It will be readily
seen that the whole of this difficulty, concerning a
body which moves forwards and is retarded till it
stops, arises from ascribing the retardation, not to the
real cause, the surrounding resistances, but to the
body itself, — ^to which the common forms of language
attribute it, as the nominative of the verb " move."

One of the doctrines which was the subject of the
warmest discussion between the defenders and

^' Alsted. Encyc. torn i. p. 687- ^* Phys. Ausc. viii. 10.

E 2

52 THE GREEK SCHOOL PHILOSOPHY.

opposers of Aristotte, at the revival of physical
knowledge, was that in which he asserts^* " That
body is heavier than another which in an equal bulk
moves downward quicker." The opinion maintained
by the Aristotelians at the time of Galileo was, that
bodies fall quicker exactly in proportion to their
weight. The master himself asserts this in express
terms, and reasons upon iV\ Yet in another passage
he appears to distinguish between weight and actual
motion downwards '^ "In physics, we call bodies
heavy and light from their power of motion ; but
these names are not applied to their actual opera-
tions (ivepyeiai^) except any one thinks mommtum
(poTTT)) to be a word of both applications. But
heavy and light are, as it were, the embers or sparks
of motion, and therefore proper to be treated of
here."

The distinction just alluded to between power
or faculty of action, and actual operation or energy,
is one very frequently referred to by Aristotle ; and
though not by any means useless, may easily be so
used as to lead to mere verbal refinements instead of
substantial "knowledge.

The Aristotelian distinction of causes has not any
very immediate bearing upon the parts of physics
of which we have here mainly spoken ; but it was
so extensively accepted, and so long retained, that
it may be proper to notice it*^ " One kind of

'' De Coelo, iy. 1, p. 308. '' De Coelo, iii. 2.

»7 De Ccelo, iv. 1, p. 307- '" Phys. ii. 3.

ARISTOTELIAN PHYSICS. 53

cause is the matter of which atiy thing is made, as
bronze of a statue, and silver of a phial ;* 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 anything is done, as health
is the cause of walking." These four kinds of cause,
the material, the formal, the efficient, and the ^nal,
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 insuliating some of the passages
which are most remote from modem notions. I
will only mention, as specimens, two such passages,
both very remarkable.

In the beginning of the book " On the Heavens,"
he proves '• 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
dimensiouB ; 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."

'' De Coelo, i. 1.

54 THE GREEK SCHOOL PHILOSOPHY.

The reader will still perceive the verbal fotuida-
tions 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 their natural
motions downwards; but besides these motions,
there is motion in a circle, which is unnatural to
these elements, but which is a more perfect motion
than the other, because a circle is a perfect line, and
a straight line is not ; and there must be something
to which this motion is natural. From this it is
evident," he adds, with obvious animation, " that
there is some essence of body different from those
of the four elements, more divine than those, and
superior to them. If things which move in a circle
move contrary to nature, it is marvellous, or* rather
absurd, that this, the unnatural motion, should alone
be continuous and eternal; for unnatural motions
decay speedily. So that fipom 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
" quirda essentid' of after writers, of which we have
a trace in our modern literature, in the word quiTdi-
essence.

ITS TECHNICAL FORMS. 55

Sect 3. — Technical Forms of the Ghreek Schools.

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

1. TechnicdForimof the Aristotelian Philosophy. —
We have already had occasion to cite some of the
distinctions introduced by Aristotle, which may be
considered as technical ; for instance, the classificatioji
of causes as material^ formal^ ejicient^ bhA final; and
the opposition of qualities as absdvte and relative.
A few more of the most important examples may
suffice. An analysis of objects into matter hxA form^
when metaphorically extended from visible objects
to things conceived in the most general manner,
became an habitual hypothesis of the Aristotelian
school. Indeed this metaphor is even yet one
of the most significant of those which we can
employ, to suggest one of the most comprehensive
and fiindamental antitheses with which philosophy

56 THE GREEK SCHOOL PHILOSOPHY.

Ims to do ; — ^the opposition of the sense and reason, of
impressions and laws. In this application, the Ger-
man philosophers have, up to the present time, rested
upon this distinction a great part of the weight of
their systems ; as when Kant says, that space and
time are the forms of sensation. Even in our own
language, we retain a trace of the influence of this
Aristotelian notion, in the word information^ when
used for that knowledge, which may be conceived as
moulding the mind into a definite shape, instead of
leaving it a mere ma&» of unimpressed susceptibility.

Another favourite Aristotelian antithesis is that of
power and «c< {hvvaiii^^ ivepyeia,} This distinction is
made the basis of most of the physical philosophy of
the school; being, however, generally introduced
with a peculiar limitation. Thus, light is defined to
be " the act of what is lucid, as far as it is 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 fer as it is 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 a Iticid
body.

Aristotle appears to be well satisfied with this
explanation, for he goes on to say, " Thus light is not
fire, nor any body whatever, or the emanation of any
body, (for that would be a kind of body,) but it is the
presence of something like fire in the body; it is,
however, impossible that two bodies should exist in
the same place, so that it is not a body;" and this

ITS TECHNICAL FORMS. 57

reasoning appears to leave him more satisfied with
his doctrine, that light is an energy or dcL

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
evTe\e;^eta. Thus the noted definition of motion in
the third book of the Physics '^ is that it is " the
enidechy^ or act, of a moveable body in respect of
being moveable ;" and the definition of the soul is
that it is ^' the enidechy 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 untranslateable.
Act and action are held to be inadequate substitutes;
the very act^ ipse cursm actionis is employed by some;
primm acttis is employed by many, but another school
use primm actus of a non-operating form. Budoeus
uses efficacia, Cicero*^ translates it " quasi quandam
continuatam motionem, et perennem ;" but this para*
phrase, though it may fiiU in with the description of
the soul, which is the subject with which Cicero is
concerned, does not appear to agree with the general
applications of the term. Hermolaus Barbarus is said
to have been so much oppressed with this difliculty
of translation, that he consulted the evil spirit by
night, entreating to be supplied with a more common
and femiliar substitute for this word : the mocking

"Phys. iii. J. "' Tusc. i. 10.

58 THE GREEK SCHOOL PHILOSOPHY.

fiend, however, suggested only a word equally obscure,
and the translator, discontented with this, invented
for himself the word perfedihabia.

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

"Crambe regretted extremely that mbstantial
formsy a race of harmless beings, which had lasted for
many years, and afforded a comfortable subsistence
to many poor philosophers, should now be hunted
down like so many wolves, without a possibility of
retreat. He considered that it had gone much harder
with them than with essences^ which had retired from
the schools into the apothecaries' shops, where some
of them had been advanced to the degree of quint-
esences^*.

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

as

Martinus Scriblerus, cap. vii.

ITS TECHNICAL FORMS. 59

2. Technical Forms of the PkUonists. — ^The other
sects of the Greek philosophy, as well as the Aris-
totelians, 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 conteitporaiy school
has acquired perhaps greater celebrity than any of
the terms of Aristotle. I mean the Ideas of Plato.
The account which Aristotle gives of the origin of
these will serve to explain their nature". "Plato,"
says he, " who, in his youth, was in habits of com-
munication first with Cratylus and the Heraclitean
opinions, which represent all the objects of sense m in
a perpetual flux, so that concerning these no science
nor certain knowledge can exist, retained 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 turned
his thoughts to definitions, Plato adopted similar
doctrines, and construed them in this way, that these
truths and definitions must be applicable to some-
thing else, and not to sensible things: for it was
impossible, he conceived, that there should be a
common definition of any sensible object, since such
were always in a state of change. The things, then,
which were the subjects of universal truths he called

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

60 THE GREEK SCHOOL PHILOSOPHY.

ideas ; and held that objects of sense had their names
according to them 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**, "O Socrates, philosophy has
not yet claimed you for her own, as, in my judg-
ment, she will claim you, and y<m will not dishonour
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 (eiSr)) of which things partake and receive ap-
plications according to that of which they partake :
thus those things which partake of likeness are called
like; those things which partake of greatness are
called great; those things which partake of heandy
and justice are called heavUful and justr To this
Socrates assents. And in another part of the
dialogue he shows that these ideas are not included
in our common knowledge, from whence he infers
that they are objects of the Divine mind.

In the Phaedo the same opinion is maintained, and
is sununed up in this way, by a reporter of the last
conversation of Socrates" eZva* n cKaarov t&v dh&Vy

** Parmenid., p. 131, abed. ** Phacdo, p. 102, a b.

ITS TECHNICAL FORMS. 61

Kol rovroov rdWa fieraXafifidvovra air&v - tovtodv rrjv
errcovvfilav X<T'xeiv ; " 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 con-
sider : 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," fiill of the models or archetypes of created
things. But it is not to our purpose here to con-
sider the Platonic Ideas in their theological bearings.
In physics they were applied in the same form as in
morals. The primum calidum^ primum fngidum^
were those ideas or fundamental principles by par-
ticipation of which, all things were hot or cold.

This school did not much employ itself in the
developement of its principles as applied to physical
inquiries : but we are not without examples of such
(peculations. Plutarch's Treatise Il^pi rov Jlptorov
Wvxpov, " 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,

62 THE GREEK SCHOOL PHILOSOPHY.

O Favorinus," he begins, " a first power and essence
of the Cold, as fire is of the Hot ; by a certain pre-
sence 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. Technicd Forms of the Pythagoreans, — The
Numbers of the Pythagoi-eans, when propounded as
the explanation of physical phenomena, as they were,
are still more obscure than the ideas of the Plato-
nists. There were, indeed, considerable resemblances
in the way in which these two kinds of notions were
spoken of. Plato called his ideas unities^ monads;
and as, according to him, ideas, so, according to the
Pythagoreans, numbers, were the causes of things
being what they are*^ But there was this difference^
that things shared the nature of the Platonic ideas
" by participation," while they shared the nature of
Pythagorean numbers *'by imitation." Moreover,
the Pythagoreans followed their notion out into much
greater developement than any other school, in-
vesting particular numbers with extraordinary attri-
butes, and applying them by very strange and forced
analogies. Thus the number Four, to which they
gave the name of TetractjfSy was held' to be the most
perfect number, and was conceived to correspond to
the human soul, in some way which appears to be
very imperfectly understood by the commentators of
this philosophy.

26

Arist. Metaph. i. 6.

ITS TECHNICAL FORMS. 63

It has been stated by a distinguished modern
scholar"^ that the place which Pythagoras ascribed
to his numbers is intelligible only by supposing that
he confounded, first a numerical unit with a geo-
metrical 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
fiilly represented by the relations of number, the
philosophy which supplied such an explanation of the
universe, might well be excused from explaining also
that existence of objects which is distinct from the
existence of all their qualities and properties. The
Pythagorean love of numerical speculations might
have been combined with the doctrine of atoms, and
the combination might have led to results well worth
notice. But so far as we are aware, no such com-
bination was attempted in the ancient schools of
philosophy ; and perhaps we of the present day are
only just beginning to perceive, through the dis*
closures of chemistry and crystallography, the
importance of such a line of inquiry.

4. Technical Forms of the Atomists mid Others. —
The atomic doctrine, of which we have just spoken,
was one of the most definite of the physical doctrines
of the ancients, and was applied with most perse-
verance and knowledge, to the explanation of phe-
nomena. Though, therefore, it led to no success of

«^ Thirlwairs Hist. Gr. ii. 142.

64 THE GKBEK SCHOOL PHILOSOPHY.

any coasequ^ice in ancient times, it served to trans^
mit, through a long series of ages, a habit of really
physical inquiry; and on this aoeomxt, has been
thought worthy of an historieal disquisition by
Bacon *\

The technical tenn, Aiom^ mari^ sufficiently the
nature of the opinion. According to this theory, the
world consists of a collection tof simple ^particles, of
one kind of matter^ aztd of indivisible smaliness, (as
the name indicates,) and hy the various configurations
and motions of <thes6, sdl kinds of matter and all
mat^al phenomena ^re produced.

To this, the atoibie daotidne ^f Leucippus and
Democritiis, wai opposed the H&moiomeria of Anax-
agoras ; that is, the opinion that material things con*
sist of particles which are homogeneous in each kind
of body» but various in different kinds : and 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, and
bone. As the former tenet points to the corpuscular
theories of modern times, so the latter may be con-
sidered as a dim glimpse of the idea of chemical
analysis. The Stoics also, who were, especially at a
later period, inclined to materialist views, had their
technical modes of speaking on such subjects. They
asserted that matter contained in itself tendencies or
dispositions to certain forms, which dispositions

" Parmenidis et Telesii et praecipue Democriti Philosophia,
&c., works, vol. ix. 317-

^ ITS TECHNICAL FOAHB. 65

they called Xoy&i awepfAarticoi, seminal prapm'tioii^j or
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 &r as physics was concerned), quenched
and overlaid by the predominance of trifling and
barren speculations; and by the love of subtilizing
and commenting upon the works of earlier writers,
instead of attempting to interpret the book of nature.
Hence these technical terms served to give fixity and
permanence to the traditional dogmas of the sect,
but led to no progress of knowledge.

The advances which were made in physical science
proceeded^ not from these schools of philosophy, (if
we except, perhaps, the obligations of the science of
harmonies 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 extra-
ordinary acuteness, invention, and range of thought ;
and above all, they had the merit of first completely
unfolding the speculative faculty ;*— of starting in that
keen and vigorous chase of knowledge, by which all
the subsequent culture and improvement of man's
intellectual stores have been occasioned. The sages

VOL. I. • F

66 THE GREEK SCHOOL PHILOSOPHY.

of early Greece form the heroic age of science. Like
the first navigators in their own mythology, they
boldly ventured their untried bark in a distant and
arduous voyage, urged on by the hopes of a super-
natural success ; and though they niissed the ima-
ginary golden prize which they sought, they unlocked
the gates of distant regions, and opened the seas to
the keels of the thousands of adventurers, who, in
succeeding times, sailed to and fro, to the indefinite
increase of the mental treasures of mankind.

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

67

CHAPTER III.

Failure of the Physical Philosophy of the

Gbeek Schools.

Sect 1. — ResitU of the Greek School PhUosophj/.

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

This assertion hardly requires proof, since in the
existing body of science there are no doctrines for

F 2

68 THE GREEK SCrfOOL PHILOSOPHY.

which we are indebted to the Aristotelian school.
Real truths, when once established, remain to the
end of time a part of the mental treasure of man,
and may be discerned through all the additions of
later days. But we can point out no physical doc-
trine now received, of which we trace the anticipation
in Aristotle, in the way in which we see the Coper-
nican system anticipated by Aristarchus, the resolu-
tion of the heavenly appearances into circular motions
suggested by Plato, and the numerical relations of
musical intervals ascribed to Pythagoras. But it
may be worth while to look at this matter more
closely.

Among the works of Aristotle, are thirty-eight
chapters of ** Problems," which may serve to exem-
plify thie progress he had really made in the reduc-
tion of phenomena to laws and causes. Of these
Problems, a large proportion are physiological, and
these I 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 facts and difficulties as it is the peculiar busi-
ness of theory to explain. Now it may be truly said,
that in scarcely any one instance are the answers,
which Aristotle gives to his questions, of any value.
For the most part, indeed, he propounds his answer
with a degree of hesitation or vacillation, which of
itself shows the absence of all scientific distinctness
of thought ; and the opinions so offered never appear
to involve any settled or general principle.

ITS FAILURE. 6d

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*,
« do smaU force8 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'? Is it because the wedge is
composed of two opposite levers?" "Why", when
a man rises from a chair, does he bend his leg and
his body to acute angles with his thigh ? Is it be-
cause a right aagle is connected with equality and
rest?" " Why* can a man throw a stone further
with a sling than with his hand ? Is it that when he
throws with his hand he moves the stone from rest,
but when he uses the sling he throws it already in
motion?" . "Why*, if a circle be thrown on the
ground, does it first describe a straight liije and then
a spiral, as it Mis ? Is it that the air first presses
equally on the two sides and supports it, and after-
wards presses on one side more?" "Why* is it
difficult to distinguish a musical note from the octave
above ? Is it that proportion stands in the place of
equality ?" It must be allowed that these are very
vague and worthless surmises ; for even if we were,
as some commentators have done, to interpret some
of them so as to agree with sound philosophy, we
should still be unable to point out, in this author's

' Mech. Prob. 4. ? lb. 18. » lb. 31. * lb. 13.

70 THE GREEK SCHOOL PHttOSOPHY.

works, any 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 consequently, when
it tried to explain facts, it had no principles which
were of any avail.

The same may be said of the physical speculations
of the other schools of philosophy. They arrived at
no doctrines from which they could deduce, by sound
reasoning, such fiiets as they saw ; though they often
venture so far to trust their principles as to infer
from them propositions beyond the domain of sense.
Thus, the principle that each element seeks its awn
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 empyreanj used by our
poets, still conveys a reminiscence. The Pythagorean
tenet that ten is a perfect number^ led them to assert
that the heavenly bodies are in number ten ; and as
nine only were known to them, they asserted that
there was an antiehthon, 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 connexion between proportions of

^ Arist. Metaph.

ITS FAILURE. 71

distance and musical notes, they assumed, on this
suggestion, 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 admirar
tion for classical antiquity has possessed the minds
of men, that some writers estimate their claims
much more highly than they are stated here. Among
such writers we may notice Dutens, who, in 1766,
published his " Origin of the Discoveries attributed
to the Modems ; in which it is shown that our most
celebrated Philosophers have received the greatest
part of their knowledge from the Works of the
Ancients." The thesis of this work is attempted
to be proved, as we might expect, by very large
interpretations of the general phrases used by the
ancients. Thus, when Tim«us, in Plato's dialogue,
says of the Creator of the world S " that he infused
into it two powers, the origins of motions, both of
that of the same thing, and of that of diiferent things;"
Dutens* finds in this a clear indication of the pro-
jectile and attractive forces of modem science. And
in some of the common declamation of the Pytha-^
goreans and Platonists, concerning the general pre-
valence of numerical relations in the universe, he
discovers their acquaintance with the law of the
inverse square of the distance by which gravitation

• Tim. 96 a. ' 3d ed. p. 83.

72 THE GREEK SCHOOL PHILOSOPHY.

is regulated, though he allows^® 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 of the Greek attempts at a general
physical phUosophy; or rather we may say, that
such arguments, since they are as good as can be
brought in favour of such an opinion, show more
clearly how entire the failure was. I proceed now
to endeavour to point out its causes.

Sect. 2. — Cause of the Failure of the Greek Physical

PhUosophy.

The cause of the failure of so toavlj of the at-
tempts of the Greeks to construct physical science
is so important, that we must, endeavour to bring it
into view here ; though the ftdl developement of
such subjects belongs rather to the philosophy of in-
duction. The subject must, at present, be treated
briefly only.

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

The cause of failure was iwt the neglect of facts.
It is often said that the Greeks disregarded experi-

10

lb. p. 88.

CAU»B OF IT8 FAILURE. 73

ence, 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 philo-
sophical method ; since the coincidence of all theory
with experience is requisite to its truth. 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, recognise the necessity and paramount
value of observations; did, in its origin, proceed
upon observed facts ; and did employ itself to no
small extent in classifying and arranging phen(»nena.
We must endeavour to illustrate these assertions,
because it is important to show that these steps
alone do not necessarily lead to science.

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

74 THE GREEK SCHOOL PHILOSOPHY.

"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 any art or science
whatever ; we must collect the facts, and the things
to which the fects happen, in each subject, and pro-
vide as large a supply of these as possible." He
then proceeds to say that we are net to look at once
at all this collected mass, but to consider small and
definite portions. "And thus it is the office of
obserration to supply principles in ea«h subject ; for
instance, astronomical observation supplies the prin-
ciples of astronomical science. For the phenomena
being properly assumed, the astronomical demon-
strations were from these discovered. And the
same applies to every art and science. So that if
we take the fiawjts {ra inrapxovra) belonging to each
subject, it is our task to mark out clearly the course
of the demonstrations. For if in our natural history
{Kaff ioTopvav) we have omitted nothing of the &cts
and properties which belong to the subject, we
shall learn what we can demonstrate and what we
cannot."

These facts, ra inrapxovra, he, at other times, in-
cludes in the term sensation. Thus he says'S " 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. Demon-

'' Anal. Prior, i. 30 '« Anal. Post. i. 18.

CAUSE OF ITS FAILURE. 76

stration proceeds from universal propositions, induc-
tion from particulars. But we cannot have universal
theoretical propositions except from induction ; and
we cannot make inductions without having sensa-
tion ; for sensation has to do with particulars."

In another placets after stating that principles
must be prior to, and better known than conclu-
sions, he distinguishes such principles into absolute,
and relative to us ; '^ such principles, relative to us,
are those which are nearer to the sensation; but
absolute principles are those which are more remote
from the sensation. The most general principles
are the more remote, the more particular are nearer.
The general principles which are necessary to know-
ledge are aanoms,^^

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^^
^^ Thus, proceeding in violation of sensation, and
disregarding it, because, as they held, they must
follow reason, some came to the conclusion that the
universe was one, and infinite, and at rest. As it
appeared, however, that though this ought to be by
reason, it would go near to madness to hold such
opinions as to the fact, (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

*' Anal.' Post. i. 2. '' De Gen. et Cor. i. i8.

'■*' ^'^ iw>t irreeourileaWe
'i«>ray. the motion and nml-
*>t>vio«s that the school to
ed tthe Ecleetje, miBt hsre
rin- ^tnmeh- inniRseed nidi
- "^ 'iieette* tmo i

CAUSE OF ITS FAILURE. 77

some measure platisible, and apparently confirmed
by f5sw5ts.

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
(Butirely of collections of facts, as for instance, those
" On Colours," " 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 phi-
losophy, therefore, wherever it may lie, exists neither
in the speculative depreciation of the value of facts,
nor in the practical neglect of their use.

3. Nor again, should we hit upon the truth, if we
were to say that Aristotle and other ancient philoso-
phers, did indeed collect facts; but that they took no
steps in classifying and comparing them ; and that
thus they failed to obtain from them any general
knowledge. For, in reality, the treatises of Aristotle
which we have mentioned, are as remarkable for the
power of classifying and systematising which they
exhibit, as for the industry shown in the accumula-
tion. But it is not classification of facts merely
which can lead us to knowledge, except we adopt

78 THE GREEK SCHOOL PHILOSOPHY.

that special arrangement, which, in each case, brings
into view the principles of the subject. We may
easily show how unprofitable an arbitrary or random
classification is, however orderly and systematic it
may be.

For instance, for a long period all unusual fiery
appearances in the sky were classed together as
meteors. Comets, shooting-stars, and globes of fire,
and the aurora borealis in all its forms, were thus
grouped together, and classifications of considerable
extent and minuteness were proposed with reference
to these objects. But this classification was of a
mixed and arbitrary kind. Figure, colour, motion,
duration, were all combined as characters, and the
imagination lent its aid, transforming these striking
appearances into fiery swords and spears, bears and
dragons, armies and chariots. The facts so classified
were, notwithstanding, worthless; and would not
have been one jot the less so, had they and their
classes been ten times as numerous as they were.
No rule or law that would stand the test of obser-
vation was or could be thus discovered. Such clas-
sifications have, therefore, long been neglected and
forgotten. Even the ancient descriptions of these
objects of curiosity are unintelligible, or unworthy of
trust, because the spectators had no steady conception
of the usual order of such phenomena. For, how-
ever much we may fear to be misled by preconceived
opinions, the caprices of imagination distort our
impressions fer more than the anticipations of reason.

CAUSE OF ITS FAILURE. 79

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 &cts» nor even for want of classifica-
tion of &cts ; but because the classification was one
in which no real principle was contained.

4. Since, as we have said before, two things are
requisite to science, — ^facts and ideas ; and since, as
we have seen, facts were not wanting in the physical
speculations of the ancients, we are naturally led to
ask. Were they then deficient in ideas ? Was there a
want among them of mental activity, and logical
connexion of thought? But it is so obvious that
the answer to this inquiry must be in the negative,
that we need not dwell upon it. No one who
knows anything of the history of the ancient Greek
mind, can question, that in acuteness» in ingeniuty,
in the power of close and distinct reasoning, they
have never been surpassed. The common opinion,
which considers this defect of their philosophical
character to reside in the exclusive activity of such
qualities, is at least so &r just.

5* We come back again, therefore, to the ques-
tion. What was the radical and &tal defect in the
physical speculations of the Greek philosophical
schools ?

To this I answer: The defect was, that though they
had in their possession facts and ideas, the ideas were
not dutinct and appropriate to the facts.

The peculiar characters of scientific ideas, which 1
have endeavoured to express by speaking of them as

80 THE GREEK SCHOOL PHILOSOPHY.

distinct and appropriate to the facts, must be more
fiilly 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 fects can be included
in general scientific truths; and that these ideas,
which may thus be termed appropriate^ must be pos-
sessed with entire distinctness and clearness, in order
that they may be successfully applied. It was the
want of such ideas, having a reference to material
phenomena, which rendered the ancient philosophers,
with very few exceptions, helpless and unsuccessftil
speculators on physical subjects.

This must be illustrated by one or two examples.
One of the facts which Aristotle endeavours 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 dis-
tance from the hole, is round, instead of imitating
the figure of the hole, as shadows resemble their
objects. We shall easily perceive this appearance to
be a necessary consequence of the circular figure of
the sun, if we conceive light to be diffiised from the
luminary by means of straight rays proceeding from
every point. But instead of this appropriate idea of
ragfSy Aristotle attempts to explain the fact by saying
that the sun's light has a circular nature, which it
always tends to manifest. And this vague and loose
conception of a circular qfjudityy employed instead of

CAUSB OP ITS FAILURE. 81

the distinct conception of rays, which is really appli-
eable, jwevented Aristotle from giving a true ac-
count, even of this very simple optical phenomenon.

Again^ to pass to a more extensive failure : why
was it that Aristotle, knowing the property of the
lever, »nd many other mechanical truths, was unable
to form them into a science of mechanics, as Archi-
medes afterwards did? ' ' •

The reason was, that, instead of cohWdering rest
and motion directly, and difetinctly, with reference to
the idea of cause, that is force, he'Wa'ndei'edin search
of reasons among other ideas and notions, which
could not be brought into steady connexion with the
facts ; — ^the ideas of properties of cfrcles, of propor-
tions of velocities, — ^the notions of iatrangeattd' com-
mon, of natural and unnatural. -Thusi in the proem '
to his Mechanical Problems, after stating donie <>f the
difficulties which he has to attack, he sayb, " Of all
such cases, the circle cbntail!!^ the principle of the
cause. And this is wha/t might be looked for ; for
it is nothing absurd, if something wonderftd is derived
from something more wonderfttl' still. Now the
most wonderful thing is, that opposites should be
combined ; and the circle is constituted of such com-
binations of opposites. For it is constructed by a
stationary point and a moving line, which are con-
trary to eadi other in nature-; and hence we may
the less be surprised at the resulting contrarieties.
And in the fiw* place, the circumference of the circle,
though a line witJiout breadth, has opposite qualities;

VOL. I. G

82 THE GREEK SCHOOL PHILOSOPHY.

for it is both corner and concave. In the next place,
it has, at the same time, opposite motions, for it
moves forward and backward at the same time. For
U„ ciH^^ferenee. .«tag ou. fro. .o, point, come,
to t^e same point agafn, so that by a continuous
progression, the last point becomes the first. So
that, as was before stated, it is not surprising that
the circle should be the principle of all wonderful
properties."

Aristotle afterwards proceeds to explain more
specially how he applies the properties of the circle
in this case. " The reason," he says, in his fourth
problem, " why a force, acting at a ^eat^r distance
fipom the fiilcruin, 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, nccording to nature^ the latter, contrary to
natwe. 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 L same fo«e th«, the weight moved, which i,
at the extremity of the shorter arm."

These loose and inappropriate notions of natural
and unnatural motions, were unfit to lead to any
scientific truths; and, with the habits of thought
which dictated these speculations, a perc^tion of

CAUSE OF ITS FAILURE. 83

the true grounds of mechanical properties was im-
possible.

Thus, in this instance, the error of Aristotle was
the neglect of the idea appropriate to the fEU^ts,
namely, the Idea of Mechanical Cause, which is
Force; and the substitution of vague or inappli-
cable notions involving only relations of space, or
emotions of wonder. The errors of those who fitiled
similarly in other instances, were of the same kind.
To detail or classify these would lead us too fisu* into
the philosophy of science ; since we should have to
enumerate the ideas which are appropriate, and the
various class of facts on which the different sciences
are foimded, — 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 among them.

In such ideas the ancients were very poor, and the
stunted and deformed growth of their physical sci-
ence was the result of this penury. The ideas of
space and time, number and motion, they did indeed
possess distinctly ; and so fiir as these went, their sci-
ence was tolerably healthy. They also caught a
glimpse of the idea of a medium by which the quali-
ties of bodies, as colours and sounds, are perceived.
But the idea of substance remained barren in their
hands ; in speculating about elements and qualities,
they went the wrong way, assuming that the proper-

G 2

84 THE GREEK SCHOOL PHILOSOPHY.

ties of the compounds must resemble those of the
elements which detennine them; and their loose
notions of contrariety never approached the form of
those ideas of polarity, which, in modern times, regu-
late many parts of physics and chemistry.

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

We shall, in the next book, see the influence of
the appropriate generial 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 philo-
sophy, 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,

CAUSE OF ITS FAILURE. 85

inferior to their teachers. They were as arbitrary
and loose in their ideas as the Greeks, without pos-
sessing their invention, acuteness, and spirit of sys-
tem. In addition to the vagueness which was com-
bined with the more elevated trains of philosophical
speculation among the Greeks, the Romans intro-
duced into their treatises a kind of declamatory
rhetoric, which arose probably from their forensic
and political habits, and which still fiirther 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
vigour and ambition. There is ^something Roman
in the public spirit and anticipait^on of universal
empire which they display, as citizens of the intellec-
tual 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.

•m^-:

BOOK II.

HISTORY

OP THB

PHYSICAL SCIENCES

IN

ANCIENT GREECE.

Napdr}KQifKripfOTOV Sk 0rfp&p,ai irvpo^
Ilrfyfjv Kkoiralavi r) hiZd(TKaXo(; re^xyv^
HdaT}^ PpoTol^ Treijyfjve koX p,€ya<; iropo^.

Prom. Vinct. 109.

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

BOOK 11.

HISTORY OF PHYSICAL SCIENCES IN ANCIENT

GREECE.

INTRODUCTION.

In order to the acquisition of any such exact and
real knowledge of nature as that which we properly
call physical science, it is requisite, as has already
been said, that men should possess ideas both 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 induc-
tion, as will elsewhere be more fully explained. We
proceed now to trace the formation of sciences
among the Greeks by such processes. The pro-
vinces of knowledge which thus demand our atten-
tion 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

90 PHYSICAL SCIENCES IN ANCIENT GREECE.

the intellectual activity of the Greeks. But I will
give a brief account of some of the other sciences
before I proceed to astronomy, for two reasons ; first,
because the origin of astronomy is lost in the obscu-
rity 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 pro-
gressive science which the ancient world produced.

91

CHAPTER I.

Earliest Stages op Mechanics and Hydro-
statics.

Sect 1. — Mechanics.

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

The great step made by Archimedes in mechanics
was the establishing, upon true grounds, the general
proposition concerning a straight lever, loaded with

92 PHYSICAL SCIENCES IN ANCIENT GREECE.

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 fiilcrum 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 real principle, which is the foundation of the
validity of this reasoning, and which is the condition
of all experimental knowledge on the subject, is
this ; — ^that when two equal weights are supported
on a lever, they act on the fulcrum of the lever with
the same effect as if they were both together sup-
ported immediately at that point. Or more gene-
rally, we may state the principle to be this ; — ^that
the pressure by which a heavy body is supported con-
tinues the same, however we alter the form or posi-
tion of the body, so long as the magnitude and
material continue the same.

The experimental truth of this principle is a

MECHANICS AND HYDROSTATICS. 93

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 posi-
tion of one weight, or the altered arrangement of
several, produces no change in their effect, so long
as their point of support remains unchanged.

This general fact is obvious, when we possess in
our minds the ideas which are requisite to appre-
hend it clearly. When we are so prepared, the
truth appears to be manifest,, independent of expe-
rience, 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 me-
chanical subjects? By attention to the course of
such reasonings, we perceive that it is the idea of
pressure ; pressure being conceived as a measurable
effect of heavy bodies at rest, distinguishable from
all other effects, such as motion, change of figure,
and the like. It is not here necessary to attempt
to trace the history of this idea in our minds ; but
it is certain that such an idea may be distinctly
formed, and that upon it the whole science of sta-
tics may be built. Pressure, load, weight, are names
by which this idea is denoted when the effect is
directly downwards; but we may have pressure
without motion, or dead pull, - in other cases, as at

94 PHYSICAL SCIENCES IN ANCIENT GREECE.

the critical instant when two nicely-matched
wrestlers are balanced by the exertion of the utmost
strength of each.

Pressure in any direction may thus exist without
any motion whatever. But the causes which pro-
duce such pressure are capable of producing motion,
and are generally seen producing motion, as in the
above instance of the wrestlers, or in a pair of scales
employed in weighing, and thus men come to con-
sider pressure as the exception, and motion as the
rule; or perhaps they imagine to thefliselves the
motion which might or would take place; for in-
stance, the motion which the arms of a lever would
have if they did move. They turn away from the
case teally before them, which is that of bodies at
rest, and balancing each other, and pass to another
case, which is arbitrarily assumed to represent the
first. Now this arbitrary and capricious evasion
we contrast with 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
numberof those who thus evaded the difficulties of
the problem of the lever, and consequently lost the
reward of success. He failed, as has before been
stated, in consequence of his seeking his principles
in motions, either vague and loose, as the distinction
of natural and unnatural motions, or else inappro-
priate, as the circle which the weight ^w^^ describe,
the velocity which it would have if it moved ; cir-

MECHANICS AND HYDROSTATICS. 95

cumstances which are not part of the fact under
consideration. The influence of such modes of spe-
culation was the main hinderance to the prosecution
of the true Archimedean form of the science.

Sect 2. — Hydrostatics.

Archimedes not only laid the foundations of the
statics of solid bodies, but also solved the principal
problem of hyd/rostaiics^ 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 Ardiimedes established on this sub-
ject remain unptirdued till the revival of science in
modem tim^s, but, when they were again put for-
ward, the main proposition was so far from obvious
that it was termed, and is to this day called, the hy-
drostatic paradox. The true doctrine of hydrostatics,
however, assuming the idea of pressure, which it in-
volves in common with statics, requires also a dis-
tinct idea of a fluid, as a body whose parts are per-
fectly moveable among each other by the slightest
partial pressure, and m which all pressure exerted
on one part is transferred to all other parts. From
this idea of fluidity, necessarily follows that multi-
plication of pressure which constitutes the hydro-
static paradox ; and the notion being seen to be
verified in nature, the consequences were also
realised as facts. This notion of fluidity is expressed
in the postulate which stands at the head of Archi-

96 PHYSICAL SCIENCES IN ANCIENT GREECE.

medes's " Treatise on Floating Bodies." And from
this principle are deduced the solutions, not only of
the simple problems of the science, but of some of
considerable complexity.

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 sub-
ject, sometimes admit into their reasonings an over-
sight or fallacy with regard to this very point. The
importance of the idea when clearly apprehended
and securely held, may be judged of from this, that
the whole science of hydrostatics in its most modem
form is only the developement of the idea. And
what kind of attempts at science would be made by
persons destitute of this idea, we may see in the
speculations of Aristotle concerning light and heavy
bodies, which we have already quoted ; where, by
considering light and heavy as opposite qualities,
residing in things themselves, and by an inability to
apprehend the effect of surrounding fluids in sup-
porting bodies, the subject was made a mass of false
or frivolous assertions, which the utmost ingenuity
could not reconcile with facts, and still less deduce
from them any additional truths.

In the case of statics and hydrostatics, the most
important condition of their advance was undoubt-
edly the distinct apprehension of these two appropriate
ideasy statical pressure^ and ht/drostatical pressure. For

MECHANICS AND HYDROSTATICS. 97

the ideas being once clearly possessed, the experi-
mental 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 idea of fluidity) were so obvious,
that there was no doubt nor difficulty about them.
These two ideas lie at the root of all mechanical
science ; and the Arm possession of them is, to this
day, the first requisite for a student of the subject.
After being clearly awakened in the mind of Ar*
chimedes, 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 demonstra-
tions as geometry itself, and as copious and interest-
ing in their conclusions ; but which, besides this
recommendation, possess one of a different order ;— *
that they exhibit the exact impress of the laws of the
physical world ; and unfold a portion of the rules
according to which the phenomena of nature take
place, and must take place, till nature herself shall
alter.

VOL. I. H

98 PHYSICAL SCIENCES IN ANCIENT GREECE.

CHAPTER ir.

Earliest Stages of Optics.

The progress made by the aBcients in Optics was
nearly proportional to that which they made in
statics. As they discovered the true grounds of the
doctrine of equilibrium, without obtaining any sound
principles concerning motion, bo they discovered the
law of the reflection of light, but had none but the
most indistinct notiotis 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 sur&ces
(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 fell on a coneave specHlum.

It may be observed that the idea which is here
introduced, is that of visual rays, or lines along which
vision is produced and light carried. This idea once
clearly apprehended, it was not difficult to show that
these lines are straight Hues, both in the case of
light and of sight. In the beginning of Euclid's
" Treatise on .Optics," some of the arguments are
mentioned by which this was established. We are

OPTICS. 99

told in the Proem, " In explaining what concerns
the sight, he adduced certain arguments from which
he inferred that all light is carried in straight lines*
The greatest proof of this is shadows, and the bright
spots which are produced by light coming through
windows and cracks, and which could not be, except
the rays of the sun were carried in straight lines.
So in fires, the shadows are greater than the bodies
if the fire be small, but less than the bodies if the
fire be greater." A clear comprehension of the
principle would lead to the perception of innume-
rable proofe df 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 jt3 image in a
plane mirror, (as the sur&ce of still ' water, for in-
stance,) which is a consequence of this law, would
affi>rd convincing evidence of its truth in that case,
and would be confirmed by the examuii|.tion of other
cases.

With these true principles was mixed much error
and indistinctness, even in the best writers. Euclid,
$asA the Platonists, maintained that vision is exer-
cised by rays proceeding from the eye, not to it ; so
that when we see objects, we learn their form as a
bUnd 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
iiyurious ; for the mathematical conclusions on each
supposition are necessarily the same. Another curious

H 2

100 PHYSICAL SCIENCES IN ANCIENT GREECE.

m

assumption is, that these visual rays are not close
together, but separated by intervals, like the fingers
when the hand is spread. The motive for this
invention was the wish to account for the fact, that
in looking for a small object, as a needle, we often
cannot see it when it is under our nose ; which it
was conceived would be impossible if the visual rays
reached to all points of the surface before us.

These errors would not have prevented the pro-
gress 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 ob-^
ject 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 ; colour is not
the absolute visible, but something which is on the
absolute visible; colour has the power of setting
the transparent in action; it is not, however, all
colours that are seen by means of light, but only the
proper colour of each object ; for some things, as the
heads, and scales, and eyes of fish, are seen in the
dark ; but then they are not seen with their proper
colour '-

^ De Anim. ii..6.

OPTICS. 101

In all this there is no steady adherence either to
one notion, or to one class of fects. The distinction
of power and act is introduced to modify the idea
of transparency, according to the formula of the
school; then colour is made to be something un-
known in addition to visibility ; and the distinction
of proper and improper colours is assumed, as suf-
ficient to account for a phenomenon. Such classi-
fications 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 conditions of successful
physical speculation, which we have laid down.

102 PHYSICAL SCIENCES IN ANCIENT GREECE.

CHAPTER III.

Earliest Stages of Harmonics.

Among the ancients, the science of Music was an
application of arithmetic, as optics and mechsmics
were of geometry. The story which is told con-
cerning the origin of their arithmetical music, is the
following, as it stands in the Arithmetical Treatise of
Nicomachus.

Pythagoras, walking one day, meditating on the
means of measuring musical notes, happened to pass
near a blacksmith's shop, and had his attention
arrested by hearing the hammers, as they struck the
anvil, produce 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 wefghing 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, and
finally discovered, that if he stretched musical strings
of equal length, by weights which have the same
proportion as those above described, they also pro-
duced the intervals above mentioned. This observa-
tion gave an arithmetical measure of the principal

HARMONICS. 103

musical intervals, and made music an arithmetical
subject of speculation.

This story, if not entirely a philosophical fable,
is undoubtedly inaccurate ; for the musical intervals
thus spoken of, would not be produced by striking
with hammers of the weights there stated. But the
experiment of the strings is perfectly correct, and is
to this day the groundwork of the theory of muoical
concords and discords.

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 aiseidental dis*
coveries in science, it will be found, that it was
exactly the possession of such an idea which made
the .iideut poBsibla.

Pytibagoras, assuming the truth of the tamlition,
must have had an exact iumI ready apprehension
of those relaidons of musical sounds* which are
called lespectively an octave, a fifth, and a fourtii.
If he had not been able to conceive distinctly this
relation* the sounds of the anvil would have struck
his ears to no more purpose than they did those of
the smiths themselves. He must have had, too, a
ready familiarity with numerical ratios ; and, more-
over, (that in which, probably, his superiority most
consisted,) a disposition to connect one notion with
the other — the musical relation with the arithmetical,

1 04 PHYSICAL SCIENCES IN ANCIENT GREECE.

if it were found possible. When the connexion was
once suggested, it was easy to devise experiments by
which it might be confirmed.

"The philosophers of the Pythagojrean school*,
and in particular, Lasus of Hermione, and Hippasus
of Metapontum, made many such experiments upon
strings ; varying both their lengths and the weights
which stretched them ; and also upon vessels filled
with water, in a greater or less degree." And thus
was established that connexion 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 dis-
covery 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 ad-
vances beyond these. There took place among them
no additional inductive processes, by which new facts
were brought under the dominion of principles, or
by which principles were presented in a more com-
prehensive shape than before. Their advance termi-
nated in a single stride. Archimedes had stirred
the intellectual world, but had not put it in pro-
gressive motion : the science of mechanics stopped

* Moutucla, iii. 10.

HARMONICS. 105

where he left it. And though, in some subjects, as
in Harmonics, much was written, the works thus
produced consisted of deductions from the fundar
mental principles, by means of arithmetical calcular
tions ; occasionally modified, indeed, by reference to
the pleasures which music, as an art, affords, but
not enriched by any new scientific truths.

BOOK III.

HISTORY

OF

GREEK ASTRONOMY.

ToBe Be firjBei^ irork (^o^TfOy r&v 'JBXXiyvwv, C09 oi xpV
irepi ra Oeia irork nrparffiareveaOai Ovrjroif^ Xvra^' irav Be
TOVTOV Bcavoffdrjvai rovvavrlovy o>9 ovre a^pov €<m wore
TO Oelovy ovre a/yvoei irov rfjv avdptoTrlvrjv <l>v<riv' dXX' olBev
0TI9 BvBda-KovTO^ airroVf ^waKoXovOijaei xal fiadi^aerai ra
BiZdaicofieva,

Plato, Epinomis^ p. 988.

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

INTRODUCTION.

The earliest and fundamental conceptions of men
respecting the objects with which Astronomy is con-
cerned, are formed by &miliar processes of thought,
without appearing to have in them anything tech*
nical or scientific. Days, years, months, the sky,
the constellations, are notions which the most un-
cultured and incurious minds possess. Yet these
are elements of the science of astronomy. The
reasons why, in this case alone, of all the provinces
of human knowledge, men were able, at an early
and unenlightened period, to construct a science out
of the obvious facts of observation, with the help
of the common furniture of their minds, will be
more apparent in the course of the philosophy of
science; but I may here barely mention two of
these reasons ; they are, first, that the familiar act of
thought, exercised for the common purposes of life,
by which we give to an assemblage of our impres-
sions such a unity as is implied in the above no-
tiojis and terms, a month, a year, the sky, and the
like, is, in reality, an indtictive acU and shares the
nature of the processes by which all sciences are
formed ; and, in the next place, that the ideas ap-
propriate to the induction in this case, are those

110 THE GREEK ASTRONOMY.

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.

W© must now trace in detail the peculiar course
which, in consequence of these causes, the know-
ledge of man respecting the heavenly bodies took,
from the earliest period of his history.

Ill

CHAPTER I.

Earliest Stages of Astronomy.

Sect. 1 . — Formation of the Notion of a Year.

The notion of a Dat/ is early and obviously im-
pressed upon man in almost any condition in which
we can imagine him. The recurrence of light and
darkness, of comparative warmth and cold, of noise
and silence, of the activity and repose of animals ; —
the rising, mounting, descending, and setting of the
sun ; — ^the varying colours 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 himself, either exactly ad-
justed to the period of this change, or at least readily
capable of being accommodated to it; — ^these cir-
cumstances, recurring at intervals, equal, so far as
man's obvious judgment of the passage of time can
decide ; and these intervals so short that the repe-
tition is noticed with no eflfort of attention or
memory; — ^this assemblage of suggestions makes
the notion of a day necessarily occur to man, if we

112 THE GREEK ASTRONOMV.

suppose him to have the conception of time, and of
recurrence. He naturally marks by a term such a
portion of time, and such a cycle of recurrence ; he
calls each portion of time, in which * this series of
appearances and occurrences come round, a day:
and such a group of particulars are considered as
appearing or happening in the same day.

A year is a notion formed in the same manner ;
implying in the same way the notion of recurring facts;
and also the faculty of atranging facts in time, and of
appreciating thdr i*ecurrence. But the notion of a
year, though undoulstedly very obvious, is, on many
accounts, leas fio^than that of a day. The repetition
of simiJar circumstaaees, at equal intervals, is less
manifest in. this €ase, and the intervals being much
kmgfia*,. some exertion of .memory becomes requisite
in order that the recjurrence may be perceived. A
cbild mi^t 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 supp(Hi; 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.

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 appear-

EARLIEST STAGES OF ASTRONOMY. 113

ances would be extremely different in diflferent
countries; and the contrasts and resemblances of
the seasons would be widely varied. In some places
the winter utterly alters the face of the country,
converting grassy hills, deep leafy woods of various
hues of green, and running waters, into snowy and
icy wastes, and bare snow-laden branches ; while in
others, the field retains its herbage, and the tree its
leaves, all the year ; and the rains and the sunshine
alone, or various agricultural employments quite
different from ours, mark the passing seasons. Yet
in all parts of the world the yearly cycle of changes
has been singled out from all others, and designated
by a peculiar name. The inhabitant of the equa-
torial 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 ^ 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 employments. Thus the Latin
annus signified a ring, as we see in the derivative
anntdus : the Greek term iyuLVTb<; implies something
which returns into itself: and the word as it exists

' Ideler, Berl. Trans. 18ia p. 51.
VOL. I. I

114 THE GREEK ASTRONOMY.

in Teutonic languages, of which our word year is an
example, is said to have its origin in the word yr%
which means a ring in Swedish, and is perhaps con-
nected with the Latin gyms.

Sect. 2. — Fiwaikm 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 iacultles and artifices
beyond what we have already mentioned* For in*
stance^ men cannot reckon as far as any number at
all approaching the number of days in the year,
without possessing a system of numeral terms, and
methods of practical nuMeration on which such a
system of terms is always founded ^ The South
American Indians, the Koussa Caffires and Hotten<-
tots, and the natives of New Holland, all of whom
are said to be unable to reckon further thaa the
fingers of their hands and feetS cannot include, in
their notion of a year, the fact of its consisting of
365 days, as we do. This feet is not likely to be

* Arithm. in Encyc. Metrop. (by Mr. Peacock,) Art. 8.
' Ibid. Art. 32.

ITS EARLIEST STAGES. 115

known to any nation except those which have ad-
vanced f&T beyond that which may be considered as
the earliest scientific process which we can trace in
the theoretical history of the hnman race, the forma-
tion of a method of designating the successive num-
bers 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 indefiniteness of the appearances which mark the
same season of the year, and the changes to which
they are subject as the seasons are early or late^
would leave much uncertainty respecting the dura-
tion of the year^ They would not obtain any accu-
racy on this head, till they had attended for a
considerable time to the motions and places of the
sun ; circumstances which require more precision of
notice than the general facts of the degrees of heat
and light. The motions of the sun, the succession
of the places of his rising and setting at different
times of the year, the greatest heights which he
reaches, the proportion of the length of day and
night, would all exhibit several cycles. The re-
turning back of the sun, when he had reached his
greatest distance to the south or to the north, as
shown either by his rising or by his height at noon,

I 2

116 THE GREEK ASTRONOMY.

would perhaps be the most observable of such cir-
cumstances. Accordingly the rpoiraX ^eXioco^ the
turnings of the sun, are used repeatedly by Hesiod
as a mark from which he reckons the seasons of
various employments. " Fifty days," he says, " after
the turning of the sun, is a seasonable time for be-
ginning a voyage*-"

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

Besides those notices of the sun. which offered
exact indications of the seasons, other more indefinite
natural occurrences were used ; as the arrival of the
swallow (xeXiBtoy) and the kite (iktiv.) The birds,
in Aristophanes's play of that name, mention, as one
of their offices, to mark the seasons ; Hesiod simi-
larly notices the cry of the crane as an indication of
the departure of winter *•

Among the Greeks the seasons were at first only
summer and winter (Oepo^ and 'xeifjL(av)y the latter

Ef rcXof fXBovros 0€p€os.

Op. et Dies, 661.
^ Ideier, i. 240.

ITS EARLIEST STAGES. 117

including all the rainy and cold portion of the year.
The winter was then subdivided into the xet/ACDv and
ea/o, and the summer, less definitely, into 0€po<: and
oTTcopa. Tacitus says that the Germans knew neither
the blessings nor the name of autumn, " Autumni
perinde nomen ac bona ignorantur.*' Yet harvesU
herbsU is certainly an old German word".

In the same period in which the sun goes through
his cycle of positions, the stars also go through a
cycle of appearances belonging to them ; and these
perhaps were employed at as early a period as the
sun in determining the exact length of the year.
Many of the groups of fixed stars are readily recog-
nised, as exhibiting always the same configuration ;
and particular bright stars are singled out as objects
of attention. These are observed, at particular
seasons, to appear in the west after sunset ; but it is
noted that when they do this, they are found nearer
and nearer to the sun every successive evening, and
at last disappear in his light. It is observed also,
that at a certain interval after this, they rise visibly
before the dawn of day renders the stars invisible ;
and after they are seen to do this, they rise every
day at a longer interval before the sun. The risings
and settings of the stars under these circumstances,
or under others which are easily recognised, were, in
countries where the sky is usually clear, employed
at an early period, to mark the seasons of the year.

• Ideler, i. 243.

118 THE GREEK ASTRONOMY.

Eschylus ' makes Prometheus mention this among
the benefits of which he, the teacher of arts to the
earliest race of men, was the communicator.

Thus, for instance, the rising' of the Pleiades in
the evening was a mark of the approach of winter*
The rising of the waters of the Nile in Egypt coin-
cided with the heliacal rising of Sirius, which the
Egyptians called Sothis. Even without any arti-
ficial measure of time or position, it was not diffi-
cult to carry observations of this kind to such a
degree of accuracy as to learn from them the num-
ber of days which compose the year; and to
fix the precise season from the appearance of the
stars.

A knowledge concerning the stars appears toiiave

^ OvK rjp yap avrois ovre xfiftaros TtKfiap,
OvT avOtfuofktvs fpos, ovdc Kopwmov
Otptovs ptfftuov aXX' arep yvtop,rjs ro ira»
"EirpcLaraoVt €0T€ Ihj axfnv aparoKas cy<o
Aarponv tbtt^d, ras re tvfrKpvnvi dvcrcif.

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

The autumn of the Greeks, dn-oipo, was earlier than our
autumn, for Homer calls Sirius amfp ^<apu/og, which rose at the
end of July.

ITS EABUEST STAGES. 119

been first cultivated with the last-mentioned view,
and makes its first appearance in literature with this
for its object. Thus Hesiod directs the husbandman
when to reap by the rising, and when to plough by
the setting of the Pleiades'. In like manner
Sirius'^ Arcturus*\ the Hyades and Orion**, are
noticed.

By such means it was determined that the year
consisted, at least, nearly, of 365 days. The Egyp-
tians, as we learn from Herodotus*', claimed the
honour of this discovery. The {)rie8ts informed

* nXi/iadttv ArXaycvrwv €7riTtKKofi€vatov»
Apxto-ff ofiriTov* apoToio bty dvo-ofitvaav.
'Ai di; roc wieras re koi rffAora T€ir(r€paKOpra
Kc/Kpvf^oroi, avTis de ireptirXo/ieyov cviovrov

^(UVOPTCU,

Op. et Dies, 1. 381.
'' 1. 413.

^^ EOr' ay ^i^Kovra ftcra rponat tftKtoio

Xciftcpi, cicrcXccn; Zfvr ijfiara, di; pa tot atmfp
ApKTOvpos^ vpoXmmv Upov poov Ojccayoio
Tlpovrw irofjuilKuvoif fmreXXfrof aKpoKV€<lkuos,

Op. et Di. 562.

Evr* ov d'npicay km 2(ipios ts pxtrov f\$if
Ovpavov, ApKTOvpov d'co'td;; pododcucrvXor ^or.

607.

*' avTop €irr)v Hrf

XJiKffiadts 'Yader re to re a6€vos Qpuovos
Avvwriv,

612.

These methods were employed to a late period, hecause the
Greek months, being lunar, did not correspond to the seasons.
Tables of such motions were called n-apaTnfyfMira.-— Ideler, Hist.
Untersuchungen, p. 209.

18

ii. 4.

120 THE €»tEEK ASTRONOMY.

him, he says, " that the Egyptians were the fiw*^
men who discovered the year, dividing it into twelve:
equal parts ; and this they asserted that they dis--
covered 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 comes 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 (Gren. vii. 11) to the I7th
day of the seventh month (Gen. viii. 4,) that is, 6
months of 30 days.

A year thus settled as a period of a certain num-
ber of days is called a cit)U 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 dis-
covery 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 CivU Year. (Julian

Calendar.)

In reality, by such a mode of reckoning as we
have described, the circle of the seasons would not
come round exactly. The real length of the year is
very nearly 365 days and a quarter. If a year of
365 days were used, in four years the year would

ITS EAISLIEST STAGES. 121

begin a day too socm, when considered with refer-
ence to the sun and stars ; and in 60 years it would
begin 16 days too soon, a quantity perceptible to
the loosest degree of attention. The civil year
would be found not to c<Hncide with the year of the
seasons; the beginning of the former wonld take
place at different periods of the latter; it would
Wfrnder into various seasons, instead of remaining
fixed to the same season ; the term year, and any
number of years, would become ambiguous; some
correction, at least some comparison, would be
requisite.

We do not know by whom the insufficiency of
the year of 365 days was first discovered^* ; we find
this knowledge diffiised among all civilized nations,
and various artifices used in making the correction.
The method which we employ, and which consists
in reckoning an additional day at the end of Fe-
bruary every fourth or leap year, is an example of the
principle of intercfdoMany by which the correction
was most commonly made. Methods of intercalar
tion 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 octaeteris or
cycle of 8 years ;) but it had the additional object
of accommodating itself to the motions of the

** Syncellus (Chronographia, p. 123,) says, that according to
the legend, it was King Aseth who first added the 5 additional
dajs to 360, for the year, in the eighteenth century B. c.

122 THE GREEK A8TB0N0HY.

moon, and therefore niust be treated of hereafter.
The Egyptians, on the other hand, knowingly per-e
mitted their civil year to wander, at least so far as
their religious observances were concerned. " They
do not wish," says Greminus^', ** the same sacrifices
of the gods to be made perpetually at the same
time of the year, but that they should go throv^h
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 365i 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 y£i;^ year was determined ; and for the
same reason it is called the canictdar period ^^

Other nations did not r^rulate their civil year by
intercalation at short intervals, but rectified it by a
reform when this became necessary. The Persians
are said to have added a month of 30 days every
120 years. The Roman calendar, at first very rude
in its structure, was reformed by Nimaa, and was
directed to be kept in order by the perpetual inter-
position of the augurs. This, however, was, from
various causes, not properly done ; and the conse-
quence was, that the reckoning fell into utter dis-
order, in which state it was found by Julius Csesar,
when he became dictator. By the advice of So-

** Uranol. p. 33.

^* Censorinus de Die Natali, c. 18.

ITS EARLIESrr STAGES. 123

sigenes, he adopted the mode of intercalation of
one day in 4 years, which we still retain ; and in
order to correct the derangement which had already
been produced, he added 90 days to a year of the
usual length, which thus became what was called
the year of conftmon* The Julian Calendar, thus
reformed, came into use, January 1, b. c. 46.

Sect. 4. — Attempts ai the Fia^ation of the Month.

The circle of changes through which the moon passes
in about thirty days, is marked, in the earliest stages
of language, by a word which implies the space of
time which one such circle occupies; just as the
circle of changes of the seasons is designated by the
word year. The lunar changes are, indeed, more
obvious to the sense, and strike a more careless per-
son, than the annual ; the moon, when the sun is
absent, is almost the sole natural object which attracts
our notice ; and we look at her with a far more tran-
quil 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 unin-
terrupted, 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 desig-
nated in various languages, seem to refer us to the

124 THE GREEK ASTRONOMY.

early history of language. Our word month is con-
nected with the word moon, and a similar connexion
is noticeable in the other branches of the Teutonic.
The Greek word /^v in like manner is related to /xiyvi/,
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 ''•

The month is not any exact number of days, being
more than 29 and less than 80. The latter number
WBB first tried, for men more readily select nmnbers
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 agreiement between the days of the month and
the moon's appearance. A little further trial would
show that months of 29 and 30 days alternately,
would preserve, for a considerable period, this agree-
ment.

The Greeks adopted this calendar, and, in conse-

*^ Cicero derives this word from the verb to measure; "quia
mensa spatia conficiunt menses nominantur:" and other etymolo-
gists, with similar views, comiect the above-mentioned words
with the Hebrew manah^ to measure, (with which the Arabic
work alTnanach is connected.) Such a derivation would have
some analogy with that of annusy &c., noticed above : but if we
are to attempt to ascend to the earliest condition of language^
we must conceive it probable that men would have a name for
a most conspicuous visible object, the moon, before they would
have a verb denoting the very abstract and general notion, to
measure.

ITS £ARI.I£ST STAGES. 125

quenc^ considered the days of their month as repre-
senting the changes of the moon : the last day of
the month was called eyv ical via, " the old and new,"
as belonging to both the waning and the reappear-
ing mooni": and their 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 per-
suasion, a correct system 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 hali^ 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.

OvK aycLV Ta<; '^/Jbipa^
'OuS^v 6p6w, aX\* dvco T€ Koi Kdrto Kvhoiioirav
^flar aTreCkelv (prjalv dvT'p tou9 0€ov^ kKaarore
^Hviic ay '^^evaOSxrt heiirvov KamLtotriv oXkoZ^
Tri% ioprfj^ fbi) tvxovt€^ Kara Xoyov r&v rip,ep&v.

Nubes 615—19.

*^ Aratus says of the moon, in a passage quoted by Geminus,
p. 33.

Aif i d*aXXo^ci/ <iyXa irapaKkipov<ra fierama
Eipiff 6rro<rT€urj iirfvos TrrpircXXcroi ^wf.

126 THE OREEK ASnUONOMY.

The Moon by us to jou her greeting sends,

But bidd us say that she 's an ill-used moon.

And takes it much amiss that you will still

Shuffle her days, and turn them topsy turvy;

So that when gods (who know their feast-days well,)

By your false -count are sent home supperless.

They scold and storm at her for your neglect.

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

Sect. 5. — Invention of Lunisalar Years.

There are 12 complete lunations in a year ; which
according to the above rule, would make 354 days,
leaving 12j 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 inter-
polating a month of 30 days every alternate year ;
and Herodotus^* relates a conversation of Solon, im-
plying a still ruder mode of intercalation. This can
hardly be considered as an advance in the know-
ledge of the motions of the heavens.

The first cycle which produced any near corre-
spondence of the reckoning of the moon and the sun,
was the Octaeterisj or period of 8 years : 8 years of

»» B. i. c. 15.

ITS EARLIEST STAGES. 127

354 daySy together with 3 months of 30 days each,
make up 2922 days ; which is exactly the amount of
8 years of 365 i days each. Hence this period would
answer its purpose so &r 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
intercalary months were distributed. The customary
method was to add a thirteenth month at the end of
the third, fifth, and eighth year of the cycle. This
period is ascribed to various persons and times ; pro-
bably different persons proposed different forms of
it. Dodwell places its introduction in the 59th
olympiad, or in the 6th century, b. c. : but Ideler
thinks the astronomical knowledge of the Greeks
of 'that age was too limited to allow of such a dis-
covery.

This cycle, however, was imperfect. The duration
of 99 lunations is something more than 2922 days ;
it is more nearly 2923^; hence in 16 years there was
a deficiency of 3 days, with regard to the motions of
the moon. This cycle of 16 years {Hecccedecdeteris),
with 3 interpolated days at the end, was used, it is
said, to bring the calculation right with regard to
the moon ; but in this way tlie origin of the year
was displaced with regard to the sun. After 10
revolutions of this cycle, or 160 years, the inter-
polated 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

128 THE GUBEEK ASHtC^OMY.

would again be brought into agreciment: and we
have thus a cycle of 160 years'*.

This cycle of 160 years, howeyer, was caleulated
from the cycle of 16 yearsir; and was probably nenner
used in civil reckoning; which the otfaers^oratleast
that of 8 years, appear to have been.

The cycles of 16 and 160 years, were corrections
of the cycle of 8 years ; and were readily suggested,
when the leng^ of the solar, and lunar periods be^
came known with aoeufacy. But -a much more exact
cyde, independent of these, was^ djseovered and
introduced by M^ton", 432 yews b. c. This cycle
consisted of 19 years, and is so correct iind conver
nienty that it ia in use among ourselves to this day*
The time occupied by Id.years^ and by 235 kmatitmsi,
is very nearly the same; (the former time is less
than 6940 days by 9^ hourss the latter by 7^ hours.)
Hence, if the 19 years be divided into 236 months;
so as to agree with the changes of the moon ; at the
end of that period the same succession may b^n
again with great exactness.

In order that 235 months, of 30 and 29 days> may
make up 6940 days, we must have 125 of the foimer,
which were called full mcmths, and 110 of the latter,
which were termed hoBaw. An artifice was used in
order to distribute 110 hollow months among 6940
days. It will be found that there is a hollow month
for each 63 days nearly. Hence if we reckon 30

so

G^minus, Ideler. •' Ideler Hist. Unters. p. 208.

USSr&atLY ffTAGKB* 129

^tkys to evei^ iudnth^ but at evety 63d day leap over
a day in the reckoning; we shall) in the 19 yearg,
omit 110 days; and this accordingly was done.
Thus the 3d day of the 3d month, the 6th day of the
5th mondi) the dth day of the 7th, must be omitted,
so as to make these months * hollow/ Of the 19 .
years, sein^Q must consist of 18 months; and it does
not appear to be known according to what order
these seven years were selected. Some say they
were the 3d, 6th, 8th, 11th, 14th, 17th, and 19th;
others, the 3d, 5th, 8th, 11th, 13th, 16th, and f9th.
The near coinddence of tfee solar Bikd lunar periods
in this cycle of 19 years, was undoubtedly a consider-
able discovery at the time when it was first accom-
I^shed. It is not easy to trace the way in which such
a discovery was made at that time ; for we do not
eve«i know the manner in which men theil recorded
the agreement or difference between the calendar day
and the celestial phenomenon whidh ought to cor-
respond to it. It is most pTobable, that the length
of the month was obtained with considerable exact-
ness, 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 fall
moon".

** Thucyd. vii. 50. *H o-eXi/vi^ ricXcMrcf ^rxr/xovf yo^ ifavp-tXrivoi

ov<ra. iv. 32. 'Tov r/kiov (KKvtres ri rywrro ircpi yovfirjviav. ii. 28.

Novfjoipt^ Kara {rtXriVTjv {wnrfp kcu fiopov doxcT elvat yiyvftrBai

hwarov) 6 ^Xios c^Xittc /*fTa fjsftnjfifipuw koi irakuf€irkrjp<i^t^ yevopitifos

lirivo€iBrjs K(u aaT€pci>v riv<ov €K<l>av€VTV>v,

VOL. I. K

ITS EARLY STAGES. 131

ill Ptolemy's Almagest, in stating observations of
eclipses.

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

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

Considered as a part of the progress of our astro-*

nomical knowledge, improvements in the calendar

do not offer many points to our observation, but they

exhibit a few very important steps. Calendars which,

'^ng apparently to unscientific ages and nations,

K 2

132 THE GREEK ASTRONOMY.

possess a great degree of accordance with the true
motions of the sun and moon, like the solar calendar
of 'the Mexicans, and the lunar calendar of the
Greeks, contain the only record now extant of dis-
coveries which must have required a great deal of
observation, of thought, and probably of time, ^he
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 astrono-
mical determinations, and are posterior in time, and
inferior in accuracy, to the knowledge on which they
depend: still, cycles of correction, which are both short
and close to exactness, like that of Meton, may per-
haps be the original form of the knowledge which they
imply ; and certainly require both accurate facts and
sagacious arithmetical reasonings. The discovery of
such a cycle must always have the appearance of a
happy guess, like other discoveries of laws of nature.
Beyond this point, the interest of the study of calen-
dars, as bearing on our subject, ceases : they may be
considered as belonging rather to art than to science ;
rather as an application of a part of our knowledge
to the uses of life, than a means or an evidence of
its extension.

Sect. 6. — The Constellatiom.

Some tendency to consider the stars as formed into
groups, is inevitable when men begin to attend to

ITS EARLY STAGES. 138

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 diffi-
cult to determine. Single stars, and very close
groups, as the Pleiades, were named in the time of
Homer and Hesiod, and at a still earlier period, as
we find in the book of Job".

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 configura-
tions; and, second, that these figures, in different
countries, are so far similar, as to imply some com-
munication. The axbitrary nature of the^e figures
shows that they were rather the work of the imagi-
native and mythological tendencies of man, than of
mere convenience and love of arrangement* "The
constellations," says an astronomer of our own time**,
seem to have been almost purposely named and
delineated to cause as much confusion and iAcon-

** Job xxxviii. 31. " Canst thou bind the sweet influences of
Ohima (the Pleiades) or loose the bands of Kesil (Orion)? Canst
thou bring forth Mazzaroth (Sirius) in his season? or canst
thou guide Ash or Aisch (Arcturus) with his sons?"

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

Dupuis, vi. 545, thinks that Aisch was ui£, the goat and kids.
See Hyde, Ulughbeigh.

*• Heischel.

134 THE GREEK ASTRONOMY.

Tenience as possible. Innumerable snakes t%d»e
through long and contorted areas of the heavens,
where no memory can follow them : bears, lions, and
fishes, large and small, northern and southern, con-
fuse all nomenclature. A better system of constel-
lations might have been a material help as an artificial
memory.*' When men indicate the stars by figures,
borrowed from obvious resemblances, they are led
to combinations quite different from the received
constellations. Thus the common pec^e in our own
coimtry find a wain or waggon, or a plough, in a por-
tion of the great bear *^

The similarity of the constellations recognised in
different countries is very remarkable. The Chal-
dean, 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'*. But while the
figures are the same, the names and traditions con-
nected with them are different, according to the

*^ So also the Greeks. Homer, Od. I.

ApKTOV fiv KM afia^av eTrLKKrjaiP KuXcovo'tv,

The northern bear which oft the wain they call.

Afucros was the traditional name, a/xo^, that suggested bj the
form.

■• Dupuis, vi. 548. The Indian zodiac contains, in the place
of our Capricorn, a ram and a fish, which proves the resem-
blance without chance of mistake. Bailly, i. p. 157.

ITS BARLY STAGES. 135

histories and kx»lities of each country*'; the river
among the stars which the Greeks called the £ri-
danusi the Egyptians asserted to be the Nile. Some
conceive that the signs of the zodiac, or path along
which the sun and moon pass, had its divisions
marked by signs which had a reference to the course
of the seasons, to the motion of the sun, or the
employments of the husbandman. If we take the
position of the heavens, which, from the knowledge
we now possess, we are sure they must have had
15000 years ago, the i^gnificance of the signs of the
zodiac, in which the sxm was, as referred to the
Egyptian year, becomes very marked ^^ and has led
some to suppose that the zodiac was invented at
such a period. Others have rejected this as an im-
probably great antiquity, and have thought it more
iikely that the constellation assigned to each season
was that which at that season rose at the beginning
of the night : 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 fency,
and probably superstition, had a share in forming
the collection of constellations. It is certain
that, at an early period, superstitious notions were
associated with the stars". Astrology is of very

" Dupuis, vi. 549. ' " Laplace, Hist. Astron. p. 8.

'* Dupuis, vi. 546.

129 THE QKESBK ASTBONOlfY.

high antiquity in the Eairt* The ators were supposed
to influence the character and destiny of man, and
to be in some way connected with sop^or natuies
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 mean-
ing 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 connexion, was made in a wrong direc-
tion, 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 des-
tiny, were called into action. Man, young as a phi-
losopher at l^ast, had yet to learn what notions hid
successful guesses on these subjects must involve,
and what they must exclude. At that period,
nothing could be more natural or excusable than
this ignorance ; but it is curious to see how long
and 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
connexion between the one and the other may be
established.

We cannot, therefore, agree with those who con-
sider astrology in the early ages as " only a de-

ITS SABLY STAGES. 137

giraded astronomy, thie abuse of a more ancient
science'**," It was the first step to astronomy, by
leading to haUts and means of grouping phenomena ;
and, after a while, by showing that pictorial and
mythological relations among the stars had at least
no very obvious value. From that time, the induc-
tive process went on steadily in the true rOad, under
the guidance of . ideas of space, time, and number.

Sect 7. — The Plamts.

While men were becoming femiKar with the fixed
stars, the planets must have attracted their notice.
Venus, from her brightness, and from her accom-
panying the sun at no great distance, and thus
appearing as the morning and evening star, was very
conspicuous. Pythagoras is said to have maintained
that the evening and morning star are the same
body ; which certainly must have been one of the
earliest discoveries on this subject ; and indeed, we
can hardly conceive men noticing the stars for a
year or two without coming to this conclusion.
Jupiter and Mars, sometimes still brighter than
Venus, were also very noticeable. Saturn and Mer-
cury were less so, but in fine climates they and their
motion would soon be detected by persons observ-
ant of the heavens. To reduce to any rule the
movements of these luminaries must have taken

as

Dupuis yi. 546.

138 THE GREEK ASTRONOMY.

time «ad thought ; probably before this yms doi^e,
certainly very early, these heavenly bodies were
brought more peculiarly xmder 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 recognised order by the Egyp-
tians or some other ancient nation. Probably this
arrangement had been made according to the slow-
ness of their motionis 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 differ-
ence, led, in the ready fancy of early times, to the
attribution of a peculiar cdiaracter 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^^

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

*' Achilles Tatius (Uranol. p. 135, 136,) giyes the Grecian
and Egyptian names of the planets.

EgyptUn.

Greek;

Saturn .

Ne/iorctts

Kpovov aaufp

^Miv&y

Jupiter .

• Oo-cpidof

Atos

ffkuBuMf

Mars

. 'HpaieXeovff

irvpo€is

Venus .

A<l>podvnfs

i&a<l>opos

Mercury

• AiroXX«>vof

^Epfiou

mXfimf

ITS EARLY STAGES. 139

structtti^ of one of the most femiliar of our mear
dures 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, Egyptians*\ The
same week is found in India among the Bramins ; it
has, there also, its days marked by those of the
heavenly bodies ; and it has been ascertained that
the same day has, in that country, the name corre-
sponding 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 eJM5h correspond to one of the heavenly bodies,
which were, in the earliest systems of the world,
conceived to be the following, enumerating them in
the order of their remoteness from the earth";
Saturn, Jupiter, Mars, the Sun, Venus, Mercury,
the Moon. At a later period, the received systems
placed these seven luminaries in the seven spheres.
The knowledge which was implied in this view, and
the time when it was obtained, we must consider here-
after. 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

a«

Laplace, Hist. Astron. p. 16. '* Philol. Mus. No. I.

140 TH£ 6RBEK ASTROm)MV.

other ; all the methods proceeding upon certain artA-
traiy arithmetical processes, connected in some way
with astrological views. It is perhaps not worth our
while here to examine further the steps of this pro-
cess ; it would be difficult to determine with certainty
why the former order of the planets was adopted, and
how and why the latter was deduced from it. But
there is something very remarkable in the univer-
sality of the notions, apparently so fantastic, which
have produced this result; and we may probably
consider the week, with Laplace**, as ^' the most
ancient monument of astronomical knowledge."
This period has gone on without interruption or
irregularity from the earliest recorded times to our
own days, traversing the extent of ages and the
revolutions of empires; the names of the ancient
deities which were associated with the stars have
been replaced by those of the objects of the worship
of our Teutonic ancestors, according to their views
of the corr^pondeiM^e of the two mythologies ; and
the Quakers, in rejecting these names of days, hate
east aside the most ancient existing relic of astro-
logical as well as idolatrous superstition.

Sect 8. — The Cirdes of the Sphere.

The inventions hitherto noticed, though undoubtedly
they were steps in astronomical knowledge, can

^« Hist. Ast. p. It

ITS EARLY STAGES. 14l

hardly be considered as purely technical and scien-
tific speculations ; for the exact reckoning of time
is one of the wants, even of the least civilized
nations. But the distribution of the places and
nootions of the heavenly bodies by means of a celes-
tial sphere with imaginary lines drawn upon it, is a
step in speculative astronomy, and was occasioned
and rendered important by the scientific propensities
of man.

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

But this supposition does not at all explain the

142 THE GREEK ASTRONOMY.

way in which the appearances of different nights
succeed each other. This^ however, may be ex-
plained, it appears, by supposing the sun also to
move among the stars on the sur&ce of the concave
sphere. The sun by his brightness makes the stars
invisible which are on his side of the heavens ; this
we can easily believe ; for the moon, when bright,
also puts out all but the largest stars, and we see
the stars appearing in the evening, each in its place,
according to their degree of splendour, as fiEUSt as
the declining light of day allows them to become
visible. And as the sun brings day, and his absence
night, if he move through the circuit of the stars in
a year, we shall have, in the course of that time,
every part of the starry sphere in succession pre-
sented to us as our nocturnal sky.

This notion, that the susi moves round among the
stars in a yeaar^ is the basis of astronomy, and a con-
siderable part of the science is only the develope-
ment and particularisation of this general concep-
tion. It is not easy to ascertain either the exact
method by which the path of the sun among the
stars was deterpiined, or the author and date of the
discovery. That there is some difficulty in tracing
the course of the sun among the stars will be clearly
seen, when it is considered that no 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
sig^nsy it is estimated by Autolycus, the oldest
writer on these subjects whose works remain to

ITS EARLY STAGES. 143

us% that the stars in one of these parts are absorbed
by the solar rays, so that they cannot be seen. Hence
the stars which are seen nearest to the place of the
setting and the rising sun in the eyening and in the
morning, are distant from him by the half of a sign ;
the evening stars being to the west, and the morn-
ing stars to the east of him. If the observer had
previously obtained a knowledge of the places of
all the principal stars, he might in this way 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 de-
termined 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" states that Anaximander% a scholar of
Thales, was the first person who pointed out this

'^ Delamb. A. A. p. xiii. *® Lib. ii. c, (viii.)

'• Plutarch, De Plac. Phil. lib. ii. cap. xii, says Pythagoras
was the author of this discovery.

144 THE OREIEK ASTRONOMY.

obliquity, and thus, as lie 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 jt?ofe and another pole opposite
to this, and these poles were connected by an imagi-
nary ajds. The circle which divided the sphere
exactly midway between these poles was called the
equaioT {larffMepivo^.) The two circles parallel to this
which bounded the sun's path among the stars were
called tropics {rpoTriKai) 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 cirde {cup/cTiKo^y from apxro^^ 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

*^ The arctic and antarctic circles of modem astronomers are
difterent from these.

ITS EAJOJPST STAGES. 145

ifun's path or ciroje of the signs is called the zodiac^
QX circle of animals ; the points where this circle
ni^ets the equator are the equinoctial points^ the days
and nights being equal when the sun is in them ;
title ^titial points ^xe tjiose where the sun's path
touches the tropica ; his nouotion to the south or to
the north ceases when he is there» and he appears in
that respect to stand still. The cplures {KoXovpoi^
mutilated) are circlps 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 (opc^eDy) 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 Phcenomena (^atvofieva), We possess two
treatises written by Autolycus*^ (about 300 B.C.)
which trace deductiveh/ the results of the doctrine of
the sphere. Supposing its diurnal motion to be uni-
form, in a work entitled Ilepi KivovfMevr)^ S<l>aLpa^, " On
the Moving Sphere," he demonstrates various pro-
perties of the diurnal risings, settings, and motions
of the stars. In another work, Ilepc Eimoktov Kai
AvGexov, " On Risings and Settings", tadUy assuming

41

Delambre, Astron. Ancienne, p. 19. ** lb. p. 25.

VOL. I. L

146 THE GREEK ASTRONOMY.

the sun's motion in his circle to be uniform, he proves
certain propositions, with regard to the risings and
settings of the stars, at the same time when the sun
rises and sets*', or vice versd**; and also their apparent
risings and settings when they cease to be visible
after sun-«et, or begin to be visible after sun-rise**.
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. Delambre** finds in it evidence that Euclid
was merely a book-astronomer, who had never ob-
served 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 prom 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 favourite mode of exer-
cising 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 inge]Quity ; a few simple astronomical
truths being assumed as the basis of the reasoning.

*' Cosmtcal setting and rising. ** AcronicaL

** Heliacal *« A. A. p. 53.

ITS EARLIEST STAGES. 147

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 doum are
different directions in diflerent 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 re-
collect how recently the doctrine of the antipodes^ or
the existence of inhabitants of the earth, who stand on
the opposite side of it, with their feet turned towards
ours, was considered both monstrous and heretical.

Yet the different positions of the horizon at
different places, necessarily led the student of spheri-
cal astronomy toward this notion of the earth as
a round body. Anaximander*^ 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 ex-
tent of land and water. As, however, we do not
know the arguments upon which he maintained this
opinion, we cannot judge of its value ; it may have
been no better founded than a different opinion

*^ See Brucker, vol. i. p. 486.

L 2

148 THE GREEK ASTRONOMY.

ascribed to him by Laertius, that the earth had the
shape of a pillar. Probably, the authors of the doc-
trine 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, wbs proportional to the change
of place of the horizon in the celestial sphere ; and
as the horizon is» at every place, in the direction of
the earth's apparently level surface, this observation
would naturally suggest to them the opinion that the
earth is placed within the celestial sphere, as a small
globe in the middle of a much larger one.

We find this doctrine so distinctly insisted on by
Aristotle, that we may almost look on him as the
establisher of it*'. " As to the figure of the earth,
it must necessarily be spherical." This he proves,
first by the tendency of things, in all places, down-
wards. He then adds*', " And, moreover, from the
phenomena according to sense : for if it were not so,
the eclipses of the moon would not have such sec-
tions as they have. For in the configurations in the
course* of a month, the deficient part takes all differ-
ences ; for it is straight, and concave, and convex ; but
in eclipses it always has the line of division convex ;
whjerefore, since the moon is eclipsed in consequence
of the interposition of the earth, the periphery of
the earth, having a spherical form, must be the cause

48
49

Arist. de C(b1o« lib. ii. cap. xiv. Casaub. p. 290 F.
p. 291 O.

ITS EARLIEST STAGES. 149

of this. ' And again, by the appearances of the stars,
it is clear, not only that it is spherical, but that its
size is not very large : for when we make a small
removal to the south or the north, the circle of the
horizon becomes palpably different ; so that the stars
vertically over us undergo a great change, and are
not the same to those that travel to the north and
•to the south. For some stars are seen in Egypt or
at Cyprus, but are not seen in the countries to the
north of these ; and the stars that in the north are
visible while they make a complete circuit, there
undergo a setting. So that from this it is manifest,
not only that the form of the earth is round, but also
that it is a part of not a very large sphere : for other-
wise the difference would not be so obvious to per-
sons making so small a change of place. Wherefore
we may judge that those persons who connect the
region m the neighbourhood of the pillars of Hercules
with thai towards Indict and who assert that in this way
the sea is one, do not assert things very improbable.
They confirm this conjecture by the elephants, which
are said to be of the same species (761/09) towards
each extreme ; as if this circumstance was a conse-
quence of the conjunction of the extremes. The
mathematicians, who try to gather from reasoning
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 de-

/

150 THE GREEK ASTRONOMY.

fended and confirmed by such arguments as we find
in later writers: for instance *°, that the tendency of
all things was to fall to the place of heavy bodies,
and that this place being the centre of iixe earth, the
whole earth had no such tendency ; that the inequa-
lities 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 sur&ce; that the end of the ocean would
fall if it were not rounded off; that we see ships,
when they go out to sea, disappearing downwards,
which shows the surface to be convex. These are
the arguments still employed in impi^essiiig tlie doc-
trines 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 spherical, and to suppose
the sun to be beyond the orbit of the moon, and they
would find that they had obtained an explaoation of
the vaiying forms whidi the bi^ht part of the moon
s^ssumes in the course of a month. For the convex

do

Pliny, Nat. Hist...ii. lxv.

ITS EARLIEST STAGES. 151

side of the orescent-moon, and her ftill edge when
she is gibbous, are always turned towards the sun.
And this explanation, once suggested, would be con-
firmed, the more it was examined. For instance, if
there be near us a spherical stone, on which the sun
is shining, and if we place ourselves so that this stone
and the lAoon 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 muminated by the sun, is exactly sunUar 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 enligh-*
tened by the sun, the bright parts are the same in
figure ; the only difference is, that the dark part of
the moon is usually not visible at all.

This doctrine is ascribed to Ana^mander. An*,
totle was aware of it. (Prob. 15.) It could not well
escape the Chaldeans and Egyptians, if they specu-
lated- at all about the causes of the appearances in
the heavens.

Sect 11. — Eclipses.

These occurrences, from the earliest times, were
regarded with a peculiar interest. The notions of
superhuman influences and relations, which, as we
have seen, were associated, from the earliest times,
with the luminaries of the sky, made men look with
alarm at any sudden and striking change in those

152 THE OREEK ASTTRONOaiY.

objects ; and as the constant and steady comrse of
the celestial revolutions was contemplated with a
feeling of admiration and awe, any marked inter-
ruption iand deviation in this course, was regarded
with surprise and terror. This appears to be the
case with all nations at an early period 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 in-
formation which we possess. When men had dis-
covered some of the laws of succession of other
astronomical phenomena, for instance, of the usual
appearances of the moon and sun, it might then
occur to them that these unusual appearances also
might probably be governed by some rule.

The search after this rule was successful at an
early period. The Chaldeans were able to predict
eclipses of the moon. This they did, probably, by
means of their cycle of 223 months, or about 18
years ; for at the end of this time, the eclipses of the
moon begin to return, at the same intervals and in
the same order as at the beginning^'. Probably this
was the first instance of the prediction of peculiar
astronomical phenomena. The Chinese have, indeed,
a legend, in which it is related that a solar eclipse
happened in the reign of Tchong-kang, above 2000

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

ITS EARLIEST STAGES. 153

years before Christ, and that the emperor was so
much irritated against two great officers of state, who
had neglected to predict this eclipse, that he put
them to death. But this cannot be accepted as a
real event: for during the next ten centuries, we
find no single observation, or fact, connected with
astronomy, in the Chinese histories ; and their astro-
nomy has 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 suppositions with regard
to the degree of science by which they were led to
it. We may suppose, with Delambre**, that they
carefully recorded the eclipses which happened, and
then, by the inspection of their registers, discovered
that those of the moon recurred after a certain period.
Or we may suppose, with other authors, that they
sedulously determined the motions of the moon, and
having obtained these with considerable accuracy,
sought and found a period which should include
cycles of these motions. This latter mode of pro-
ceeding would imply a considerable degree of
knowledga

It appears probable rather that such a period was
discovered by noticing the recurrence of eclipses, than
by studying the moon's motions. After 6585 j days,
or 223 lunations, the same eclipses nearly will recur..

ss

A. A.; p. 212.

154 THE OBBEK A8I1KXNOMY.

It is not contested that the Chaldeans were ac*
qiudnted with this period, which thej called Saras ;
or that they calculated eclipses hj means of it.

Sect. 12. — Sequel to the Early Stages of Astrofiwmy.

Every stage of science has its train of practical ap«
pUcations and systematic inferences, arising both
from the demands of convenience and curiosity, and
from the pleasure, which, as we have abeady said,
ingenious 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 Edipses. — ^The cycles which served
to keep in order the calendar of the early nations of
antiquity, in some instances enabled them, also, as
has just been stated, to predict eclipses ; and this
application of knowledge necessarily excited great
notice.

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 its surface was divided by various imaginary
circles ; among the re&rt;, the eqmktor, 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.

ITS EARLIEST STAeEB. 165

that there must be some marked difference in the
stripes or zones into which the earth's surface was thus
divided. In going to the south, men 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, en-
tirely 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 (tiflerent places.

Cfnamonick.'-^ Another important result of the
doctrine of the sphere was Cfnomanick or DiaUing.
Anaximenes is said by Pliny to have first taught
this art in Greece ; and both he and Anaximander
are reported to have erected the first dial at Lace^
demon.

Mmswre of the Sun's Distanoe. — ^The explanation
of the phases of the moon led to no result so re^
markable 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 fiiU in
position (that is a quadrant from the sun) she would
be somewhat more than a half moon ; and the place
when she was dichotomised^ that is, was an exact semi-
circle, the bright part being bounded by a straight

156 THE GREEK ASTRONOMY.

line, would depend upon the sun's distance from the
earth. Aristarchus endeavoured to fix the exact
place of this dichotomy ; but the irregularity of the
edge which bounds the bright part of the sun, and
the diflSiculty of measuring with accuracy, by means
then in use, either the precise time, when the boun-
dary was most nearly a straight line or the exact dis-
tance of the moon from the sun at that time, rendered
his conclusion £alse and valueless. He collected that
the sun is at 18 times the distance of the moon
from us 4 we now know that be is at 400 times the
moon's distance.

It would be easy to dwell longer on subjects of
this kind ; but we have already perhaps entered too
much into detail. We have been t^npted to do
this by the interest which the mathematical spirit of
the Greeks gave to the earliest astron(Hnical dis-
coveries, when these were the subjects of their rear
sonings : but we must now proceed to contemplate
them engaged in a worthier employment, in adding
to these discoveries.

16

ly

CHAPTER II.

Prelude to the Inductive Epoch op

HiPPABCHUS.

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

In the steps previously made in astronomical
knowledge, no ingenuity had been required, to devise
the view which was adopted. The motions of the
stars and sun were most naturally and almost irre-
sistibly 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 present a globular
shape. In these cases the first conjectures, the sup-
position of the simplest form, of the most unifonn

♦"^w

168 THE GREEK ASTRONOMY.

motion, required no after-correetion. But this mani-
fest simplicity, this easy and obvious explanation, did
not apply to the movement of all the heavenly bodies.
The planets, the " wandering stars," could not be so
easily understood; the motion of each, as Cicero says,
" undergoing very remarkable changes in its course,
going before and behind, quicker and slower, appearing
in the evening, but gradually lost there, and emerging
again in the morning ^" A continued attention to
these stars would, however, detect a kind of intricate
regularity in their motions, which might naturally
be described as ^^a dance." The Chaldeans are
stated by Diodoru8^ to have observed assiduously
the risings and sitings of the plants, from the top
of the temple of Belus. By doing this, they would
find the times in which the forwards and backwards
movements of Saturn, Jupiter, and Mars recur ; and
also the time in which they come round to the same
part of the heavens ^ Venus and Mercury never
recede far from the sun, and the intervals which
elapse while either of them leaves its greatest dis-
tance from the sun and returns again to the

* Cic. de Nat. D. lib. 2. p. 460. *' Ea qu« Saturni stella
dicitur, ^Muywyque a Gneds nominatur, quiB a terra abest plaii-
mum, XXX fere aimis cursum suum conficit ; in q-uo cursu multa
mirabiliter efiiciens, turn antecedendo, turn retardando, turn yes-
pertinis temporibus delitescendo, turn matutinis se rursum
aperiendo, sibU imnmtat sempitemis sadculonun »tatibus, qtam
eadem iisdem temponbus efficiat." And so of the other planets.

• Del. A. A. ; p. 4; * Hin. H. N. ii. p, 204.

PRELUDE TO THE EPOCH OF HIPPARCHUS. 159

greatest distance on the sasne 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, Sa-
turn goes 29 times through his emomalyy 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.

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 them--
selves a sensible image of the mechani^ by which
these complex motions were produced : nor did they
find this difficult. Venus, for instance, who, upon the
whole, moves from west to east among the stars, is
seen, at certain intervals, to return or move retrograde
a short way back from east to west, then to become
for a short time stationary, then to turn again and
resiune her direct motion westward, and so on. Now
this can be explained by supposing that she is placed

ft

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 ea^t, 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.

160 THE GREEK ASTRONOMY.

would, in some situations, counterbalance the general
motion of the centre, and make the planet retrograde^
while, on the whole, the westerly motion would pre-
yail. Just as if we suppose that a person, holdin&f a
lamp in his haad in the dark, and at a distance, so
that the lamp alone is visible, should run on turning
himself round ; we should see the light sometimes
stationary, sometimes retrograde, but on the whole
progressive.

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

The application of such mechanism to the planets
appears to have arisen in Greece about the time of
Aristotle. In the works of Plato we find a strong
taste for this kind of mechanical speculation. In
the tenth book of the " Polity," we have the apologue
of Alcinus the Pamphylian, who, being supposed to
be killed in battle, revived when he was placed on
the funeral pyre, and related what he had seen
during his trance. Among other revelations, he
beheld the machinery by which all the celestial
bodies revolve. The axis of these revolutions is the
adamantine distafi^ which Destiny holds between her
knees; on this are fixed, by means of diflferent
sockets, flat rings, by which the planets are carried.
The order and magnitude of these spindles are mi-
nutely detailed. Also, in the "Epilogue to the
Laws" (Epinomis), he again describes the various
movements of the sky, so as to show a distinct

PRELUDE TO THE EPOCH OF HIPPARCHUS. 161

acquaintance with the general character of the
planetary motions : and, after speaking of the Egyp-
tians and Syrians as the original cultivators of such
knowledge, he adds some very remarkable exhorta-
tions to Ms countrymen to prosecute the subject.
" Whatever we Greeks,** he says, " receive from the
barbarians, we improve and perfect ; there is good
hope and promise, therefore, that Greeks will carry
this knowledge far beyond that which was introduced
from abroad." To this task, however, he looks with
a due appreciation of the qualities and preparation
which it requires. " An astronomer must be,'* he
says, " the wisest of men ; his mind must be duly dis-
ciplined in youth ; especially is mathematical study
necessary ; both an acquaintance with the doctrine
of number, and also with that other branch of matlie-
matics, which, closely connected as it is with the
science of the heavens^ we very absurdly call geometry^
tbe measurement of the earth*' T

These anticipations were very remarkably verified
in the subsequent career of the Greek astro-
nomy.

The theory, once suggested, probably made rapid
progress. Simplicius* relates, that Eudoxus of
Cnidus, introduced the hypothesis of revolving circles
or spheres.. Calippus of Cyzicus, having visite4
Polemarchus, an > intimate friend of Eudoxus, they
went together to Athens, and communicated to Aris-t

^ EpiAomis, pp. 988, 990.

* Lib. ii. de Coelo. BuUialdus, p. 18.

VOL. I. M

162 THE GREEK ASTRONOMY.

totle the invention of Eudoxus, and with his help
improved and corrected it.

Probably at first this hypothesis was applied only
to account for the general phenomena of the pro-
gressions, retrogradations, and stations of the planet ;
but it was soon found that the motions of the sun
and moon, and the circular motions of the planets,
which the hypothesis supposed, had anomalies or irre-
gularities, 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 endeavour
to obtain any accuracy in their observations. We
have already stated (Chap. I.) that the Chaldeans
were in possession of a period of about 18 years,
which they used in the calculation of eclipses, and
which might have been discovered by close observa-
tion 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 lati^
tvde^ or distance from the equator, has ^ cycle different
from its revolution among the stars ; and its nodes^
or the points where it cuts the equator, are per-
petually changing their position. In addition to this,
the moon's motion in her own path is not uniform ; in

PRELUDE TO THE EPOCH OP mPPARCHUS. 169

the course of eaeh 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 be the same as
at the first, and all the circumstances on which lunar
eclipses depend being the same, the eclipses will
occur in the same order. In 0586J days there are
289 revolutions of anomaly, 241 revolutions with
regard to one of the nodes, and, as we have said,
223 lunations or revolutions with regard to the sun.
Hence this period will bring about a succession of
the same lunar eclipses.

If the Chaldeans observed the moon's motion
among the stars with any considerable accuracy, so
as to detect this period by that means, they could
hardly avoid discovering the anomaly or unequal
motion of the moon ; for in every revolution, her
daily progression in the heavens varies from about
22 to 26 times her own diameter. But there is not.
In the existence of this period, any evidence that
they had measured the amount of this variation,
and Delambre* is probably right in attributing all
such observations to the Greeks.

• A. A. i. 212.

M 2

164 THE GREEK ASTRONOMY.

The sun's motion would also be seen to be irre-
gular as soon as men had any exact mode of deter-
mining 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 num-
ber of days if the motions were uniform, are, in fiu3t,
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 irre-
gularities of this kind. A wheel travelling round
the earth, while it revolved upon its centre, might
produce the effect of making the sun or moon fixed
in its rim go sometimes faster and sometimes slower
in appearance, just in the same way as the same
suppositions would account for a planet going some-
times forwards and sometimes backwards : the epi-
cycles of the sun and moon would, for this purpose,
be less than those of the planets. Accordingly, it
is probable that, at the time of Plato and Aristotle,
philosophers were already endeavouring 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 pro-
posed to them in a distinct form, was, " To reconcile
the celestial phenomena by the combination of
equable circular motions." That the circular mo-
tions should likewise be equable, was a condition,
which, if it had been merely tried at first, as the

PRELUDE TO THE EPOCH OF HIPPARCHUS. 165

most simple and definite conjecture, would have
deserved praise. But this condition, which is, in
reality, inconsistent with nature, was, in the sequel,
adhered to with a pertinacity which introduced end-
less complexity into the system. The history of
this assumption is one of the most marked in-
stances of that love of simplicity and symmetry,
which is the source of all general truths, though it
so often produces and perpetuates error. At pre-
sent we can easily see how fancifully the notion of
simplicity and perfection was interpreted, in the
arguments by which the opinion was defended, that
the real motions of the heavenly bodies must be cir-
cular and uniform. The Pythagoreans, as well as
the Platonists, maintained this dogma. According
to Geminus, " They supposed the motions of the sun,
and the moon, and the five planets, to be circular and
equable : for they would not allow of such disorder
among divine and eternal things, as that they should
sometimes move quicker, and sometimes slower, and
sometimes stand still; for no one would tolerate
such anomaly in the movements, even of a man, who
was decent and orderly. The occasions of life, how-
ever, 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 pro-
pounded this question, how the phenomena might be
represented by equable and circular motions."

These conjectures and assumptions led naturally

166 THE GREEK ASTRONOMY.

to the establishment of the various parts of the
theory of epicycles. It is probable that this theory
was adopted tnth respect to the planets at or before
the time of Plato. And Aristotle gives us an ac-
count of the system thus devised ^ "Eudoxus,"
he says, "attributed four spheres to each planet:
the first revolved with the fixed stars (and this pro-
duced the diurnal motion); the second gave it a
motion along the eclij)tic (the mean motion in
longitude); the third had its axis perpendicular' to
the ecliptic (and this gave the inequality of each
planetary motion); the fourth produced the oblique
motion transverse to this (the motion in latitude.)"
He is also said to have attributed a motion in lati-
tude and a corresponding sphere to the sun as well
as to the moon, of which it is difficult to understand
the meaning, if Aristotle has reported rightly of the
theory ; for it would be absurd to ascribe to Eudoxus
a knowledge of the motions by which the sun de-
viates 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

^ Metaph. xi. 8.

® Aristotle says " has its poles in the ecliptic," hut this must
he a mistake of his. He professes merely to receive these
opinions flfom the professed astronomers "ck rrjs oiKttorarris

PRELUDE TO THE EPOCH OF HIPPARCHUS. 167

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 of the
oblique motion of the moon into two separate mo-
tions, by Eudoxus, was not the simplest way of
conceiving it ; and Calippus imagined the connexion
of these spheres in some way which made it neces-
sary nearly to double their number ; in this manner
his system had no less than 55 spheres.

Such was the progress which the idea of the hypo-
thesis of epicycles had made in men's minds, pre-
viously to the establishment of the theory by Hip-
parchus. There had also been a preparation for
this step, on the other side, by the collection of
facts. We know that observations of the eclipses
of the moon were made by the Chaldeans 367
B.C. at Babylon, and were known to the Greeks;
for Hipparchus and Ptolemy found their theory of
the moon on these observations. Perhaps we can-
not consider, as equally certain, the story that, at the
time of Alexander's conquest, they had a series of
observations, which went back 1903 years, and
which Aristotle caused Callisthenes to bring to him
in Greece. All the Greek observations, which are of
any value, begin with the school of Alexandria.
Aristyllus and Timocharis appear, by the citations
of Hipparchus, to have observed the places of stars,
and planets, and the times of the solstices, at various

168 THE GREEK ASTRONOMY.

periods from b. c. 295 to b. c. 269. Without their
observations, indeed, it would not have been easy for
him to establish either the theory of the sun or the
precession of the equinoxes. In order that observa-
tions at distant intervals may be compared with each
other, they must be referred to some common era.
The Chaldeans dated by the era of Nabonassar,
which commenced 749 B. c. The Greek observations
were referred to the Calippic periods of 76 years,
of which the first began 331 B. c. These are the
dates used by Hipparchus and Ptolemy.

169

CHAPTER III.

Inductive Epoch of Hipparchus.

Sect, 1. — Establishment of the Theory of Epicycles

and Eccentrics,

Although, as we have already seen, the idea of
epicycles had been suggested, the problem of its
general application proposed, at the time of Plato,
and the solutions 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 mighty but showed that it musty
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

170 THE GREEK ASTRONOMY.

heavenly bodies were moved, in such a manner as to
account for their apparently irregular motions. We
may best understand what was the problem to be
solved by calling to mind what we now know to be
the real motions of the heavens. The true motion
of the earth round the sun, and therefore the appa-
rent annual motion of the sun, is performed, not in
a circle of which the earth is the centre, but' in an
ellipse or oval, the earth being nearer to one end
than to the other; and the motion is most rapid
when the sun is at the nearer end of this oval. But
instead of an oval, we may suppose the sun to move
uniformly in a circle, the earth being now not in
the centre, but nearer to one side ; for on this sup-
position, the sun will appear to move most quickly
when he is nearest to the earth, or in his perigee, as
that point is called. Such an orbit is called an
eccentric, and the distance of the earth from the
centre of the circle is called the eccentricity. It may
easily be shown by geometrical reasoning, that the
inequality of apparent motion so produced, is exactly
the same in detail, as the inequality which follows
from the hypothesis of a small epicycle, turning uni-
formly on its axis, and carrying the sun in its circum-
ference, 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 hjrpothesis of the
eccentric and the epicycle is proved by Ptolemy in
the third book of the " Almagest."
The Sun's Eccentric. — When Hipparchus had clearly

INDUCTIVE EPOCH OF HIPPARCHUS. 171

conceived these hypotheses, as possible ways of ac-
counting 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 num-
bers 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 exact-
ness ; he was able, in short, to construct Solar TaJbks^
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',) give
the anomaly^ or inequality of the sun's motion ; and
this they exhibit by means of the prosthapheresis, the
quantity 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 calcu-
lations 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

^ Syntax. 1. iii.

172 THE GREEK ASTRONOMY.

case ; and the genius of the discoverer appeared, as
it usually does appear, in his perceiving how small a
number of fieu^ts, rightly considered, were sufficient
to test 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 sum-
mer tropic is 94i days, and the time from the sum-
mer tropic to the autumnal equinox 92 i days, from
these phenomena alone he demonstrates that the
straight line joining the centre of the sun's eccentric
path with the centre of the zodiac (the spectator's
eye) is nearly the 24th part of the radius of the ec-
centric path ; and that its apogee precedes the sum-
mer solstice by 24i degrees nearly, the zodiac
containing 360."

The exactness of the Solar Tables, or Cavwn, 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

INDUCTIVE EPOCH OF HIPPARCHUS. 173

soundness of the theory on which the tables were
calculated.

The MoovCs Eccentric* — The moon's motions have
many irregularities ; but when the hypothesis of an
eccentric or an epicycle had sufficed in the case of
the sun, it was natural to try to explain, in the same
way, the motions of the moon ; and it was shown
by Hipparchus that such hypotheses would account
for the more obvious anomalies. It is not very easy
to describe the several ways in which these hypo-
theses were applied, for it is, in truth, very difficult to
explain in words even the mere facts of the moon's
motion. If she were to leave a visible bright line
behind her in the heavens, wherever she moved,
the path thus exhibited would be of an extremely
complex nature ; the circle of each revolution slip-
ping away from the preceding, and the traces of
successive revolutions forming a sort of band of net-
work running round the middle of the sky*. In
each revolution, the motion in longitude is affected
by an anomaly of the same nature as the sun's
anomaly already spoken of; but besides this, the
path of the moon deviates from the ecliptic to the
north and to the south of the ecliptic, and thus she
has a motion in latitude. This motion in latitude is
sufficiently known if we knew the period of its
restoration^ that is, the time which the moon occu-

■ The reader will find an attempt to make the nature of this
path generally intelligible in the Companion to the British
Almanadk for 1834.

174 THE GREEK ASTRONOBTSr.

pies in moving from any latitude till she is restored

•

to the same latitude; as, for instance, from the
ecliptic on one side of the heavens to the ecliptic on
the same side of the heavens again. But it is found
that the period of the restoration of the latitude is
not the same as the period of the restoration of the
longitude, that is, as the period of the moon's revo-
lution among the 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 supposed 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 Hip-
parchus 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 6585^ days, there are 241 revolutions of the
moon with regard to the stars, but only 239 revolu-

INDUCTIVE EPOCH OF HIPPARCHUS. 175

tions with regard to the anomaly. This difference
could be suitably represented by supposing the
eccentric, in which the moon moves, to have itselt
an angular motion, perpetually carrying its apogee
in the same direction in which the moon travels ;
but this supposition being made, it was necessary to
determine, not only the eccentricity of the orbit, and
place of the apogee at a certain time, but also the
rate of motion of the apogee itself, in order to form
tables of the moon.

This task, as we have said, Hipparchus executed ;
and in this instance, as in the problem of the reduc-
tion 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'. Three of these, the records of which were
brought from Babylon, where a register of such oc-
currences was kept, happened in the 366th and
367th years from the era of Nabonassar, and enabled
Hipparchus to determine the eccentricity and apogee
of the moon's orbit at that time. The three others
were observed at Alexandria, in the 547th year of
Nabonassar, which gave him another position of the
orbit at an interval of 180 years ; and he thus be-
came acquainted with the motion of the orbit itself
as well as its form*.

The moon's motions are really affected by several

• Ptol. Syn. iv. 10.

* Ptolemy uses the hypothesis of an epicycle for the moon's
first inequality: hut Hipparchus employs the eccentric.

176 THE GREEK ASTRONOMY.

other inequalities, of very considerable amount,
besides those which were thus considered by Hip-
parchus; but the lunar p^aths, constructed on the
above data, possessed a considerable degree of cor-
rectness, 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.

The numerical explanation of the motions of the
sun and moon, by means of the hypothesis of eccen-
trics, and the consequent construction of tables, was
one of the great achievements of Hipparchus. The
generkl explanation of the motions of the planets,
by means of the hypothesis of epicycles, was in
circulation previously, as we have seen. The mo-
tions of the planets, in their epicycles, are, in reality,
ajSected 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 irregu-
larities by means of eccentrics. The whole mass of
good observations of the planets which he received
from preceding ages, did not contain so many, says
Ptolemy, as those which he has transmitted to us of
his own. " Hence* it was," he adds, " that while he
laboured, in the most assiduous manner, to represent

* Synt. ix. 2.

INDUCTIVE EPOCH OF HIPPARCHUS. 177

the motions of the sun and moon by means of
equable circular motions; with respect to the
planets, so far as his works show, he did not even
make the attempt, but merely put the extant obser-
vations in order, added to them himself more than
the whole of what he received from preceding ages,
and showed the insufficiency of the hjrpothesis
current among astronomers to explain the pheno-
mena." 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 Hippar-
chus 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, consti-
tute him a great astronomical discoverer, and justify
the reputation he has always possessed. There is,
indeed, no philosopher who is so uniformly spoken
of in terms of admiration. Ptolemy, to whom we owe
our principal knowledge of him, perpetually couples
with his name epithets of praise : he is not only an
excellent and carefiil observer, but " a" most truth-
loving and labour-loving person," one who had shown
extraordinary sagacity and remarkable desire of truth

• Synt. ix. 2.
VOL. I. N

178 THE GREEK ASTRONOMY.

in every part of science." Pliny, after mentioning
him and Thales, breaks out into one of his passages
of declamatory vehemence ; " Great men ! elevated
above the common standard of human nature, by
discovering the laws which celestial occurrences
obey, and by freeing the wretched mind of man
from the fears which eclipses inspired. — Hail to you
and to your genius, interpreters of heaven, worthy
recipients of the laws of the universe, authors of
principles which connect gods and men !" Modem
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^
that it is unfortunate for the memory of Aristarchus
that his work has come to us entire, and who cannot
refer" to the statement of an eclipse rightly predicted
by Halicon of Cyzicus without adding, that if the story
be true, Halicon was more lucky than prudent ;—
loses all his bitterness when he comes to Hipparchus*.
" In Hipparchus," says he, " we find one of the most
extraordinary men of antiquity ; the 'oery greaJbesU in
the sciences which require a combination of observa-
tion with geometry." Delambre adds, apparently
in the wish to reconcile this eulogium with the de-
preciating manner in which he habitually speaks of
all astronomers whose observations are inexact, ^^ a
long period and the continued efforts of many indus-

^ i. 75. « i. 17- ' i. 186.

INDUCTIVE EPOCH OF HIPPARCHUS. 179

trious men are requisite to produce good instru-
ments, but energy and assiduity depend on the man
himself."

Hipparchus was the author of other great dis-
coveries and improvements in astronomy, besides
the establishment of the doctrine of eccentrics and
epicycles; but this, being the greatest advance in
the theory of the celestial motions which was made
by the ancients, must be the leading subject of our
attention in the present work ; our object being to
discover in what the progress of real theoretical
knowledge consists, and under what circumstances
it has gone on.

Sect 2. — Estimate of the Value of the Theory of

Eccentrics and Epicycles.

It may be useful here to explain the value of the
theoretical step which Hipparchus thus made ; and
the more so, as there are, perhaps, opinions in
popular circulation, which might lead men to think
lightly of the merit of introducing or establishing
the doctrine of epicycles. For, in the first place,
this doctrine is now acknowledged to be false ; and
some of the greatest men in the more modern his-
tory of astronomy owe the brightest part of their
fame to their having been instrumental in over-
turning this hypothesis. And, moreover, in the
next place, the theory is not only false, but ex-
tremely perplexed and entangled, so that it is usually

N 2

180 THE GREEK ASTRONOMY.

conceived as a mass of arbitrary and absurd compli-
cation. Most persons are familiar with passages in
which it is thus spoken of '°.

He his fabric of the heavens

Hath left to their disputes, perhaps to more
His laughter at their quaint opinions wide ;
Hereafter when thej 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 com-
plex system was explained to him; that "if God
had consulted him at the creation, the universe
should have been on a better and simpler plan."
In addition to this, the system is represented as
involving an extravagant conception of the nature
of the orbs which it introduces ; — ^that they are crys-
talline spheres, and that the vast spaces which inter-
vene between the celestial luminaries are a solid mass,
formed by the fitting together of many masses per-
petually in motion; an imagination which is pre-
sumed to be incredible and monstrous.

We must endeavour to correct or remove these
prejudices, not only in order that we may do justice
to the Hipparchian, or, as it is usually called, Ptole-
maic system of astronomy, and to its founder ; but

^•P. L. viii. ^^ A.D. 1252.

INDUCTIVE EPOCH OF HIPPAKCHUS. 181

for another reason, much more important to the pur-
pose of this work ; namely, that we may see how
theories may be highly estimable, though they
contain false representations of the real state of
things, and may be extremely useful, though they
involve unnecessary complexity. In the advance of
knowledge, the value of the true part of a theory
may much outweigh the accompanying error, and
the use of a rule may be little impaired by its want of
simplicity. The first steps of our progress do not
lose their importance because they are not the last ;
and the outset of the journey may require no less
vigour and activity than its close.

That which is true in the Hipparchian theory, and
which no succeeding discoveries have deprived of its
value, is the resolution of the apparent motions of
the heavenly bodies into an assemblage of circular
motions. The test of the truth and reality of this
resolution is, that it leads to the construction of
theoretical tables of the motions of the luminaries,
by which their places are given at any time, agreeing
nearly with their places as actually observed. The
assumption that these circular motions, thus intro-
duced, are all exactly uniform, is the fundamental
principle of the whole process. This assumption is,
it may be said, false ; and we have seen how fantastic
some of the arguments were, which were originally
urged in its favour. But some assumption is neces-
sary, in order that the motions, at different points
of a revolution may be somewhat connected, that is,

182 THE GREEK ASTRONOMY.

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 fm observations, it deduces from these,
results agreeing with a// observations, however nume-
rous and distant. To express an inequality by means
of an epicycle, implies not only that there is an in-
equality, but further ; — that the inequality is at its
greatest value at a certain known place ; — diminishes
in proceeding from that place by a known law ; —
continues its diminution for a known portion of
the revolution of the luminary; — then increases
again ; and so on : that is, the introduction of the
epicycle represents the inequality of motion, as com-
pletely 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 hear
venly bodies into equable circular motions, is, in fact,
equivalent to the most recent and improved processes
by which modem astronomers deal with such motions.
Their universal method is to resolve all unequal
motions into a series of terms^ or expressions of par-
tial motions; and these terms involve sines and
cosines^ that is, certain technical modes of measuring
circular motion, the circular motion having some
constant relation to the time. And thus the pro-
blem of the resolution of the celestial motions into

INDUCTIVE EPOCH OF HIPPARCHUS. 183

equable circular ones, which was propounded above
two thousand years ago in the school of Plato, is
still the great object of the study of modem astro-
nomers, whether observers or calculators.

That Hipparchus should have succeeded in the
first great steps of this resolution for the sun and
moon, and should have seen its applicability in other
cases, is a circumstance which gives him one of the
most distinguished places in the roll of great astro-
nomers. 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 astrono-
mer, 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'*, "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

IS

Synt. xiii. 2.

184 THE GREEK ASTRONOMY.

which entitles us to suppose that any inconsistency
will result ?"

But it may be said, we now know that the mo-
tions are more simple than they were thus repre-
sented, 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
Aristotle, appear to have taught that the celestial
spheres were real solid bodies, they are spoken of by
Ptolemy as imaginary'^; 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 in-
tended to pass for no more than geometrical concep-
tions, in which view they are true representations
of the apparent motions.

It is true, that the real motions of the heavenly
bodies are simpler than the apparent motions ; and
that we, who are in the habit of representing to our
minds their real arrangement, become impatient of
the seeming confusion and disorder of the ancient
hypotheses. But this real arrangement never could
have been detected by philosophers, if the apparent
motions had not been strictly examined and success-
fiiUy analyzed. How far the connexion between the
facts and the true theory is from being obvious or

18

Synt. iii. 3.

INDUCTIVE EPOCH t)F HIPPARCHUS. 185

easily traced, any one may satisfy himself by en-
deavouring, from a general conception of the moon's
real motions, to discover the rules which regulate
the occurrences of eclipses ; or even to explain to a
learner, of what nature the apparent motions of the
moon among the stars will be.

The unquestionable evidence of the merit and
value of the theory of epicycles is to be found in
this circumstance ; — ^that it served to embody all the
most exact knowledge then extant, to direct astro-
nomers to the proper methods of making it more
exact and complete, to point out new objects of
attention and research ; and that, after doing this at
first, it was also able to take in, and preserve, all the
new results of the active and persevering labours of
a long series of Greek, Latin, Arabian, and modem
European astronomers, till a new theory arose which
could discharge this ofBce. It may, perhaps, surprise
some readers to be told, that the author of this next
great step in astronomical theory, Copernicus, adopted
the theory of epicycles ; that is, he employed that
which we have spoken of as its really valuable charac-
teristic. " We ^* 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 they were circular ; for a circle
alone can make that which has been, recur again."

^* Copernicus. De Rev. 1. i, c. 4.

186 THE GREEK ASTRONOMY.

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

A moment's reflection will show that, in the
events just spoken of, the introduction and esta-
^ blishment of the theory of epicycles, those characte-
ristics were strictly exemplified, which we have
asserted to be the conditions of every real advance
in progressive science; namely, the application of
distinct and appropriate ideas to a real series of
facts. The distinctness of the geometrical concep-
tions which enabled Hipparchus to assign the orbits
of the sun and moon, requires no illustration ; and
we have just explained how these ideas combined
into a connected whole the various motions and
places of those luminaries. To make this step in
astronomy, required diligence and care exerted in
collecting observations, mathematical clearness and
steadiness of view exercised in seeing and showing
that the theory was a successful analysis of the
observations.

Sect. 3. — Discacery of the Precession of the

Equinoxes.

The same qualities which we trace in the researches
of Hipparchus already examined, — diligence in col-

INDUCTIVE EPOCH OF HIPPARCHUS. 187

lecting observations, and clearness of idea in repre-
senting them, — appear also in other discoveries of his,
which we must not pass unnoticed. The precession
of the equinoxes, in particular, is one of the most
important of these discoveries.

The circumstance here brought into notice was a
change of longitude of the fixed stars. The longi-
tudes 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 hap-
pens, however, is not very easy to decide ; for the sun's
path among the stars is made out, not by merely look-
ing at the heavens, but by a series of inferences from
ether observable facts. Hipparchus used for this pur-
pose eclipses of the moon ; for these, being exactly
opposite to the sun, afford data in marking out his
path. By comparing the eclipses of his own time with
those observed at an earlier period by Timocharis.
he found that the bright star, Spica Virginis, was six
degrees from the equinoctial point in his own time,
and had been eight degrees distant from the same
point at an earlier epoch. The suspicion was thus
suggested, that the longitudes of all the stars increase
perpetually ; but Hipparchus had too truly philoso-
phical a spirit to take this for granted. He examined
the places of Regulus, and those of other stars,
as he had done those of Spica; and he found, in
all these instances, a change of place which could
be explained by a certain alteration of position in
the circles to which the stars are referred, which

188 THE GREEK ASTRONOMY.

alteration is described as the Precession of the
Equinoxes.

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

The two discoveries which have been described,
the mode of constructing solar and lunar tables, and

INDUCTIVE EPOCH OF HIPPARCHUS. 189

the precession, were advances of the greatest im-
portance in astronomy, not only in themselves, but
in the new objects and undertakings which they
suggested to astronomers. The one detected a con-
stant law and order in the midst of perpetual change
and apparent disorder ; the other disclosed mutation
and movement perpetually operating where every-
thing had been supposed fixed and stationary. Such
discoveries were well adapted to call up many
questionings in the minds of speculative men ; for,
after this, nothing could be supposed constant till it
had been ascertained to be so by close examina-
tion ; and no apparent complexity or confusion could
justify the philosopher in turning away in despair
from the task of simplification. To answer the
inquiries thus suggested, new methods of observing
the facts were requisite, more exact and uniform
than those hitherto employed. Moreover the dis-
coveries which were made, and others which could
not fail to follow in their train, led to many conse-
quences, required to be reasoned upon, systematized,
completed, enlarged. In short, the epoch of indtection
led, as we have stated that such epochs must always
lead, to a period of developement, of verification, appli--
catioUf and ewtefision.

190

CHAPTER lY.

Sequel to the Inductive Epoch of Hipparchus.

Sect. 1. — Researches which verified the Theorjf.

The discovery of the leading laws of the solar and
lunar motions, and the detection of the precession,
may be considered as the great positive steps in the
Hipparchian astronomy; — ^the parent discoveries, from
which many minor improvements proceeded. The
task of preserving the collateral and consequent re-
searches which now offered themselves, — of bringing
the other parts of astronomy up to the level of its
most improved portions, — ^was prosecuted by a suc-
cession of zealous observers and calculators, first, in
the school of Alexandria, and afterwards in other
parts of the world. We must notice the various
labours of this series of astronomers ; but we shall
do so very briefly ; for the ulterior developement 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

SEQUEL TO THE EPOCH OF HIPPARCHUS. 191

nowhere be studied with so much advantage as in
the history of astronomy.

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

The verification of the laws of the changes which
he assigned to the skies, impUed that the condition
of the heavens was constant, except so far as it was
affected by those changes. Thus, the doctrine that
the changes of position of the stars were rightly
represented by t)ie precession of the equinoxes,
supposed that the stars were fixed with regard to
each other; and the doctrine that the unequal
number of days, in certain subdivisions of months
and years, was acfequately explained by the theory
of epicycles, asstfmed that years and days were
always of constatit iiengths. But Hipparchus was
not content with assi^ing these bases of his theory,
he endeavoured to prove them.

1. Fixity of tke Stars. The question necessarily
arose after the discovery of the precession, even if
such a question had never suggested itself before,
whether the stars which were called fixed, and to
which the motions of the other luminaries are re-
ferred, do really retain constantly the same relative
position. In ord^r to determine this fundamental

192 THE GREEK ASTRONOMY.

question, Hipparchus undertook to constract 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 conspi-
cuous stars. These positions are described by means
of alineaiions ; that is, three or more such stars are
selected as can be touched by an apparent straight
line drawn in the heavens. Thus Hipparchus ob-
served 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 Hip-
parchus 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 \ who speaks of it with
admiration as a wonderful and superhuman task
(" ausus rem etiam Deo improbam, annumerare pos-
teris Stellas") asserts the undertaking to have been
suggested by a remarkable astronomical event, the
appearance of a new star ; " novam stellam et aliam
in aevo suo genitam deprehendit ; ejusque motu, qua
die fulsit, ad dubitationem est adductus anne hoc

* lib. ii. (xxyi.)

SEQUEL TO THE EPOCH OF HIPPARCHUS. 193

ssepius fieret, moverenturque et ese quas putamus
affixas." There is nothing inherently improbable in
this tradition, but we may observe, with Delambre%
that we are not informed whether this new star
remained in the sky or soon disappeared again.
Ptolemy makes no mention of the star or the story ;
and his catalogue contains no bright star which is
not found in the <* Catasterisms" of Eratosthenes.
These Catasterisms were an enumeration of 475 of
the principal stars» according to the constellations in
which they are; and were published about sixty
years before Hipparehus.

2. Constant Length of Ymrs. — Hipparehus also
attempted to ascertain whether successive years are
all of the same length ; and though, with his scru-
pulous love of accuracy", he does not appear to have
thought himself justified in asserting that the years
Were always exactly equal, he showed, both by ob-
servations of the time when the sun passed the
equinoxes, and by eclipses, that the difference of
successive y^rs, 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 durar
tion of the year.

3. CcThstant Length of Days. JEquation ofTime*'-^
The eqiiality of days was more difficult to ascertain
than that of years ; for the year is measured, as on

■ A. A. i. 290. . • Ptolem. Synt. iii. 2.

VOL. I. O

194 THS GREEK ASTRONOMY.

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 medbanical skill
of the ancients did not enable them to attain any
conriderable accuracy in the measure of such por-
tions of time ; though clepsydras and similar instru<«
ments were used by astronomers. The equality of
days could only be proved, therefore, by the cons&«
quences of such a supposition ; and in this manner
it appears to have been assumed, as the ftict really
is, that the apparent revolution of the stars is acoUf^
rately uniform, never becoming either quicker or
slower. It followed as a consequence of this, that
the solar days (or rather the nycthemerSf compounded
of a night and a day,) would be unequal, in conse*
quence of tiie sun's unequal motion, thus giving rise
to what we now call the equaiUon of time ;«^the in*
terval by which the time, as marked on a dial, is
before or after the time, as indicated by the accurate
time-pieces which modem skill can produce. This
inequality was fully taken account of by the anci^at
astronomers, which was in fact assuming the equa^-
lity of the sidereal days.

Sect 2. — Researches which did not verify the Theory.

Some of the researches of Hipparchus and his fol-
lowers fell upon the weak parts of his theory ; and
if the observations had been sufficiently exact, must
have led to its being corrected or rented.

Among these we may notice the researches which

SEQUEL TO THE EPOCH OF HIPPABCHUS. 106

vrere made oonceming the ParaUaa? of the heayenly
bodies, that is^ their apparent displacement by the
alteration of position of the observer from one part of
the earth's sur&ce to the other. This subject is
treated of at length by Ptolemy ; and there can be
no doubt that it was well examined by Hipparchus,
who inyented a paraUacHc dnstrumerU for that pur^
pose. The idea of parallax, as a geometrical pos«
sibility, was indeed too obvious to be overlooked at
any time ; and in the period of establishment of the
doctrine of the sphere, it must have appeared
strange, that every place on the earth's surface might
aUke be considered as the centre of the celestial
motions* But if this vras true with respect to tihe
motions of the fixed stars, was it also true with
regard to those of the sun and moon ? The displace*
ment of the sun by parallax is so small that the best
observers among the ancients could never be sure
of its existence : but with respect to the moon, the
case is different. She may be displaced by this
cause to the amount of twice her own breadth, a
quantity easily noticed by the rudest process of in*
Btrumental observation. The law of the displace*
ment 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. Pto-
lemy has given a table of the effects of parallax,
calculated according to the apparent altitude of the

o 2

196 THE GREEK ASTRONOMY.

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 &ct this hypothesis, though a very close repre^
sentation of the truth, so &r as the positions of the
luminaries sure concerned, £sdls altogether when we
apply it to their distances. The radius of the epi-
cycle, or the eccentricity of the eccentric, are deter-i
mined so as to satisfy the observations of the
apparent motions of the bodies : but, inasmuch as
the hypothetical motions are different altogether
from the ireal motions, the hypothesis does not, at
the same time, satisfy the observations of the di&r
tances 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 in some degree falsified in conse-
quence of the reigning opinion. In fact, however,
the imperfection of the methods of measuring pa-
rallax and magnitude, which. were in use at this
period, was such, that the results could not lead to
any degree of conviction deserving to be set in op-

SEQUEL TO THE EPOCH OF HIPPARCHUS, 19/

position to a theory which was so satisfactory with
regard to the more certain observations.

The eccentricity, or the radius of the epicycle,
which would satisfy 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 consequence of the sup-
position of uniform circular motions, on which the
epicyclic hypothesis proceeds.

We see, therefore, that this part of the Hippar*
chian theoiy carries in itself the germ of its own
destruction. As soon as the art of celestial measure-
ment was so far perfected, that astronomers could
be sure of the apparent diameter of the moon within
Jjj or ij 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 Cheek

Astronomers.

We must now say a word concerning the methods
above spoken of. Since one of the most important
tasks of a period of verification, is to ascertain with
accuracy the magnitude of the quantities which enter,
as elements, into .the theory which signalizes the

198 THE GREEK ASTRONOMY.

period ; the improTement of instruments, and me-
thods of observing and experimenting, are principal
features in such periods. We shall, therefore, men-
tion some of the facts which bear upon this point.

The estimation of distances among the stars by
the eye, is an extremely inexact process. In some
of the ancient observations, however, this appears to
be the method employed : and stars are described as
being a cubit or tivo cubits from other stars. We
may form some notion of the scale of this kind of
measurement, from what Cleomedes remarks*, that
the sun appears to be about a foot broad ; an opinion
which he conftites at length.

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

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 shadoujs or of sights.

Probably the oldest and most obvious measure-

* Del. ^. A. i. 222.

SEQUEL TO THE EPOCH OP HIPPARCHUS. 199

ments of the poBitions of the heavenly bodies were
those in which the elevation of the sun was detennined
by comparing the length of the shadow of an up-
right staff or gnomon^ with the length of the staff
itself. ^^It appears \ from a memoir of Gautil, first
printed in the Connaissance des Temps for 1809, that,
at the lower town of Loyang, now called Hon«an-
fou, Tchon-kong found the length of the shadow of
the gnomon, at the summer solstice, equal to one
foot and a half, the gnomon itself being eight feet
in length." This was about 1100 B. o. The Greeks,
at an early period, used the same method. Strabo
says' 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 fol-
lows Pytheas."

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

Instruments were soon invented for measuring
angles, by means of circles, which had a border, or limb^

* lib. U. K. Hist. A«t. p. 5. • Del. A. A. i. 257.

200 THE GBEBK ASTRONOMY.

divided into equal parts. The whole circumference
was divided into 360 degrees : perhaps because the
circles, first so divided, were those which represented
the sun's annual path ; one auch degree would be
the sun's daily advance, more nearly than any other
convenient aliquot part which could be taken. The
position of the sun was determined by means of the
shadow of one part of the instrument upon the other.
The most ancient instrument of this kind appears to
be the Hemisphere of Berosus. A hollow hemisphere
was placed with its rim horizontal, and a style was
erected in such a manner that the extremity of the
style was exactly at the centre of the sphere. The
shadow of this extremity, on the concave sur&ce,
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. But this instru-
ment was in fact used rather for dividing the day
into portions of time than for determining position.

Eratosthenes' observed the amount of the oblir
quity of the sun's path to the equator ; we are not
informed what instruments he used for this purpose :
but he is said to have obtained, from the munificence
of Ptolemy Euergetes, two Armils, or instruments
composed of circles, which were placed in the portico
at Alexandria, and long used for observations. If a
circular rim were placed so as to coincide with the
direction of the equator, the inner concave edge
would be enlightened by the sun's rays which came

^ Delambre, A. A« i. 86.

SEQUEL TO THE EPOCH OF HIPPARCHUS. 201

under the front edge, wken the sun was south of the
equator, and by the rays which came over the front
edge, when the sun was north of the equator : the
moment of the transition would be the time of the
equinox. Such an instrument appears to be referred
to by Hipparchus, as quoted by Ptolemy*. " 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 sur-
iace begins to be enlightened from the other side."
Such an instrument was called an equinoctial armil.

A solstitial armil is described by Ptolemy, con-
sisting of two circular rims, one sliding round within
the other, and the inner one frimished with two pegs
standing out from its surface, and diametrically op-
posite to each other. These circles being fixed in
the plane of the meridian, and the inner one
turned, till, at noon, the shadow of the peg in front
falls upon the peg behind, the position of the sun at
noon would be determined by the degrees on the
outer circle.

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

The angles, observed by means of these divisions,

» Ptol. Synt. iii. 2.

202 THE GREEK AETTRONOMY.

were expressed as a fraction of the cireumference.
Thus Eratosthenes stated the interval between the
tropics to be fe of the circumference'.

It was soon remarked that the whole circum-
ference of the circle was not wanted for such obser-
vations. Ptolemy^* says, that he found it more
convenient to observe altitudes by means of a square
flat piece of stone or wood, vnth. a quadrant of a
circle described on one of its flat faces, about a
centre near one of the angles. A peg was placed at
the centre, and one of the extreme radii of the
quadrant being perpendicular to the horison, the ele-
vation 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. They 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 flumb line^\

• Delambre, A. A. i. 87. It is probable that his obserration

gave him 47| degrees.^^ The fraction gj = M = 1^? = ^^^

which is very nearly --

^« Syiit. i. 1.

" The curvature of the plane of the circle, by warping, was
noticed. Ptol. iii. 2. p. 155, observes that his equatorial circle

SEQUEL TO THE EPOCH OP HIPPARCHUS. 203

In this maimer, 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", the
observer looked along the face of the circle of the
armil, so as to see its two edges apparently brought
together, and the star apparently touching them*'.

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 Astro-'
labe^ was invented, of which we have a description
in Ptolemy**. This also consisted of circular rims,
moveable 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 ; which,
in a larger form, is the mural quadrant^ and has been
used up to the most recent times.

It may be considered surprising**, that Hipparchus,
after having observed, for some time, right ascensions

was illuminated on the hollow side twice in the same day. (He
did not know that this might arise from refraction.)

** Delamb. A. A. i. 185.

*^ Ptol. Sjnt. i. 1. Qawep KeKoXXjjfitvos afA<j>iTtp<us avraif reus
eirifficivfuus 6 acTrfp €v ry Bi axrrav eniTTtbtj^ fitoTrrruiyTat.

** Synt. Y. 1. '' Del. A. A. 181.

204 THE GREEK ASTRONOMY.

and declinations, quitted equatorial armils for the
astrolabe, which immediately refers the stars to the
ecliptic. He probably did this because, after the
discovery of precession, he found the latitudes con-
stant, and wanted to know the motion in longitude.

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

The following example of an observation, taken
from Ptolemy, may seem to show the form in which
the results of the instruments, just described, were
usually stated**.

" In the 2nd year of Antoninus, the 9th day of
Pharmouthi, the sun being near setting, the last
division of Taurus being on the meridian (that is,
5i 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, 57i degrees more forwards than the
moon in longitude." From these data the longitude
of Regulus is calculated.

" Del. A. A. ii. 248.

SEQUEL TO THE EPOCH OP HIPPARCHUS. 205

From what has been said respecting the observa-
tions of the Alexandrian astrcmomers, 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 Hipparchiaii
theory, operated very unfavourably 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 imper-
fect 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 con-
viction and intuitive clearness which would have
given a progressive impulse to their knowledge.

Sect. 4. — Period from Ilipparchus to Ptolemy.

We have now to speak of the cultivators of astro-
nomy from the time of Hipparchus to that of
Ptolemy, the next great name which occurs in the
history of this science ; though even he holds place
only among those who verified, developed, and, in
some points, materially extended the theory of Hip-
parchus. The astronomers who lived in the inter-

206 THE GSEEK A8IB0N0MT.

timei indeed, did little, eyen in this way ;
though it might haye been supposed that their
studies were carried on imder consideiable adyan-
tages, inasmnch as they all enjoyed the liberal
patronage of the kings of Egypt '^ The ^diyine
school of Alexandria," as it is called by Synesius, in
the fourth century, appears to haye produced few
persons capable of canying forwards, or eyen of yen-
fying, the labours of its great astronomical teacher.
The mathematicians of the school wrote much, and
apparently they obseryed sometimes ; but their obs^r^
yations are of little yalue : and their books are expo*
sitions of the theory and its geometrical consequences^
without any attempt to compare it with obseryation.
For instance, it does not appear that any one yerified
the remarkable discoyery of the precession, till the
time of Ptolemy, 250 years after ; nor does the state-
ment of this motion of the heayens appear in the
treatises of the intermediate writers; nor does Ptolemy
quote a single obseryation 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 pre-
ceded Hipparchus^ are not unfrequent« «

This Alexandrian period, so inactiye 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 Hippar-

'^ Delamb. A. A. ii. 240.

SEQUEL TO THE EPOCH OF HIPPARCHUS. 207

chus are lost. We have the " Uranologion" of
Geminus^% a systematio treatise on astronomy, ex-
pounding correctly the Hipparchian theories and
their consequences, and containing a good account
of the use of the various cycles^ which ended in the
adoption of the Calippic period. We have likewise
"The Circular Theory of the Celestial Bodies" of
Cleomedes ^% of which the principal part is a developed
ment of the doctrine of the sphere, including the
consequences of the globular form of the earth. We
have also another work on " Spherics" by Theodosius
of Bithynia'^ which contains some of the most import
taut propositions of the subject, and has been used
as a book of instruction even in modem 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 con-
struction of solar and lunar tables, as we have already
seen ; and this process required the formation of a
trigonametfy^ 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

^''B.c.70. ^•b.c. 60. "b.c. 50.

208 THE GREEK ASTRONOMY.

ancient astronomy'^ 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 trigoruh
metrj/y in order to enable mathematicians to calculate
its results ; and this branch of science also appears to
have been formed by Hipparchus*', who gives results
that imply the possession of such a method. Hyp-
sicles, who was a contemporary of Ptolemy, also
made some attempts at the solution of such pro-
blems : but it is extraordinary that the writers whom
we have mentioned as coming after Hipparchus,
Theodosius, Cleomedes, and Menelaus, do not even -
mention the calculation of triangles", either plane or
spherical ; though the latter writer'* is said to have
written on " the Table of Chords," a work which is
now lost.

We shall see, hereafter, how prevalent a disposi-
tion 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", who lived 270 b. c. at the court of Anti-
gonus, king of Macedonia, described the celestial
constellations in two poems, entitled " Phsenomena,"
and " Prognostics." These poems were little more
than a versification of the treatise of Eudoxus on the
acronycal and heliacal risings and settings of the

«^ Delamb. A. A. ii. 37- " A. A. i. 117.

" A. A. i. 249. " A. A. ii. 37. " A. A. i. 74.

SEQUEL TO THE EPOCH OF HIPPARCHUS. 209

stars. The work was the subject of a comment by
Hipparchus, who perhaps found this the easiest way of
giving connexion 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 extant** ; 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■^ The
." Astronomica" of Manilius, the " Poeticon Astrono-
micon'* of Hyginus, both belonging to the time of
Augustus, are, like the work of Aratus, poems which
combine mythological ornament with elementary
astronomical exposition ; but have no value in the
history of science. We may pass nearly the same
judgment upon the explanations and declamations
of Cicero, Seneca, and Pliny, for they do not aipprize
us of any additions to astronomical knowledge ; and
they do not always indicate a very clear apprehen-
sion 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 per-
suasion of a boundless progress in science to which

■' Two copies of this translation, illustrated by drawings of
different ages, one set Roman, and the other Saxon, according
to Mr. Ottlej, are described in the Archceologia^ vol. 18.

" Mont. i. 221.

VOL. I. P

210 THE GREEK ASTRONOMY.

man was destined* Though this belief was no more
than a vague and arbitrary conjecture, it suggested
other coiyectures in detail, some of which, having
been verified, have attracted much notice. For
instance, in speaking of comets '% Seneca says^
**The time wiU come when those things which are
now hidden shall be brought to light by time and
persevering diligence. Our posterity will wonder
that we should be ignorant of what is so obvious."
The motions of the planets, he adds, complex and
seemingly confused, have been reduced to rule ; and
some one will come hereafter, who will reveal to us
the paths of comets. Such convictions and conjec-
tures are not to be admired for their wisdom ; for
Seneca was led rather by enthusiasm, than by any
solid reasons, to entertain this opinion ; nor, again,
are they to be considered as merely lucky guesses,
implying no merit : they are remarkable as showing
how the persuasion of the universality of law, and the
belief of the probability of its discovery by man,
grow up in men's minds, when speculative know-
ledge becomes a prominent object of attention.

An important practical application of astronomical
knowledge was made by Julius Csesar, in his correco
tion of the calendar, which we have already noticed :
and this^ was strictly due to the Alexandrian school,
for Sosigenes, an astronomer, came from Egypt to
Rome for the purpose.

88

Seneca. Qu. N. vii. 25.

211

Sect. 5. — Measures of the Earth.

There were, as we have said, few attempts made, at
the period of which we are speaking, to improve the
accuracy of any of the determinations of the early
Alexandrian astronomers. One question naturally
excited much attention at all times, the magnitude
of the earth, its figure being universally acknow*
ledged to be a globe. The Chaldeans, at an earlier
period, had asserted that a man, walking without
stopping, might go round the circuit of the earth in
a year ; but this might be a mere fitncy, 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 waa enlightened to the bottom by the sun's
rays. At Alexandria, on the same day, the sun
was, at noon, distant from the zenith by a fiftieth
part of the circumference. These two cities were
north and south from each other; and the distance
had been determined, by the royal overseers of the
roads, to be 5000 stadia. This gave a circumference
of 250,000 stadia to the earth, and a radius of about
40,000. Aristotle" says that the mathematicians
make the circumference 400,000 stadia. Hippar^
ehus conceived that the measure of Eratosthenes

■• De Ccelo. ii. ad fin.

P 2

':-'<■: [. Ci: -. j:. me meri;

■. -^nrrr -

SEQUEL TO THE EPOCH OF HIPPARCHUS. 213

to remove all doubt concerning the scale of this
measure, we are informed that the cubit is that
called the black cubit, which consists of 27 inches,
each inch being the thickness of six grains of barley.

Sect 6. — Ptolemy's Discovery of Evection.

By referring, in this place, to the last-mentioned
measure of the earth, we include the labours of the
Arabian as well as the Alexandrian astronomers, in
the period of mere detail, which forms the sequel to
the great astronomical revolution of the Hipparchian
epoch. And this period of verification is rightly
extended to those later times ; not merely because
astronomers were then still employed in determining
the magnitude of the earth, and the amount of other
elements of the theory ; for those are their employ-
ments 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 intellec-
tual features of this period, than to offer a useless
catalogue of obscure and worthless writers, and of
opinions either borrowed or unsound. But before
we do this, there is one writer whom we cannot
leave undistinguished in the crowd ; since his name
is more celebrated even than that of Hipparchus ;

214 THE GREEK ASTRONOMY.

his works contain ninety-nine hundredths of what
we know of the Greek astronomy ; and though he
was not the author of a new theory, he made some
very remarkable steps in the verification, correction,
and extension of the theory which he received. I
speak of Ptolemy, whose work, " The Mathematical
Construction" (of the heavens) contains a complete
exposition of the state of astronomy in his time, the
reigns of Adrian and Antonine. This book is &mi-
liarly known to us by a term which contains the
record of our having received our first knowledge of
it from the Arabic writers. The " Megiste Syntaxis,"
or great construction, gave rise, among them, to the
title Al Magisth or Almagest, by which the work is
commonly described. As a mathematical exposi-
tion of the theory of epicycles and eccentrics, of the
observations and calculations which were employed
in Order to apply this theory to the sun, moon, and
planets, and of the other calculations which are
requisite, in order to deduce the consequences of
this theory, the work is a splendid and lasting monu-
ment of diligence, skill and judgment. Indeed, all
the other astronomical works of the ancients hardly
add anything whatever to the information we obtain
jfrom the Almagest ; and the knowledge which the
student possesses of the ancient astronomy must
depend mainly upon his acquaintance with Ptolemy.
Among other merits, Ptolemy has that of giving us
a very copious account of the manner in which
Hipparchus established the main points of his

SEQUEL TO THE EPOCH OF HIPPARCHUS. 215

theories; an account the more agreeable, in con-
sequence of the admiration and enthusiasm with
which this author everywhere speaks of the great
master of the astronomical school.

In our present survey of the writings of Ptolemy,
we are concerned less with his exposition of what
had been done before him, than with his own ori-
ginal labours. In most of the branches of the
subject, he gave additional exactness to what Hip^
parchus had done ; but our main business, at pre-
sent, is with those parts of the Almagest which
contain new steps in the application of the Hippar-
chian hypothesis; there are two such cases, both
very remarkable, — ^that of the moon's evection^ and
that of the planetary motions.

The law of the moon's anomaly, that is, of the
leading and obvious inequality of her motion, could
be represented, as we have seen, either by an eccen-
tric or an epicycle ; and the amount of this inequality
had been collected by observations of eclipses. But
though the hypothesis of an epicycle, for instance,
would bring the moon to her proper place, so far as
eclipses could show it, that is, at new and full moon,
this hypothesis did not rightly represent her motions
at other points of her course. This appeared, when
Ptolemy set about measuring her distances from the
sun at diiferent times. "These," he'* says, "some-
times agreed and sometimes disagreed." But by
further attention to the facts, a rule was detected

'^ Synt. T. 2.

216 THE GREEK ASTRONOMY.

in these differences. "As my knowledge became
more complete and more connected, so as to show
the order of this new inequality, I perceived that
this difference was small, or nothing, at new and full
moon ; and that at both the dichotomies (when the
moon is half illuminated,) it was small, or nothing,
if the moon was at the apogee or perigee of the
epicycle, and was greatest when she was in the
middle of the interval, and therefore when the first
inequality was greatest also." He then adds some
further remarks on the circumstances according to
which the moon's place, as affected by this new
inequality, is before or behind the place, as given by
the epicyclical hypothesis.

Such is the announcement of the celebrated
discovery of the moon's second inequality, after-
wards called (by BuUialdus) the evection. Ptolemy
soon proceeded to represent this inequality by a
combination of circular motions, uniting, for this
purpose, the hypothesis of an epicycle, already
employed to explain the first inequality, with the
hypothesis of an eccentric, in the circumference of
which the centre of the epicycle was supposed to
move. The mode of combining these was some-
what complex; more complex we may, perhaps,
say, -than was absolutely requisite '° ; the apogee of

" If Ptolemy had used the hypothesis of an eccentric instead
of an epicycle for the first inequality of the moon, an epicycle
would hare represented the second inequality more simply than
his method did.

SEQUEL TO THE EPOCH OF HIPPARCHUS. 217

the eccentric moved backwards, or contrary to the
order of the signs, and the centre of the epicyle
moved forwards nearly twice as fast upon the cir-
cumference 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.

The discovery of the evection, and the reduction
of it to the epicyclical theory, was, for several rea-
sons, an important step in astronomy ; some of these
reasons may be stated.

1. It obviously suggested, or confirmed, the suspi-
cion that the motions of the heavenly bodies might
be subject to many inequalities ; — ^that when one set
of anomalies had been discovered and reduced to
rule, another set might come into view ; — ^that the
discovery of a rule was a step to the discovery of
deviations from the rule, which would require to be
expressed in other rules; — ^that in the application
of theory to observation, we find, not only the sMed
phenomena^ for which the theory does account, but
also residual phenomena^ which remain unaccounted
for, and stand out beyond the calculation ;— that
thus nature is not simple and regular, according to
the simplicity and regularity of our hypothesis, but

218 THE GREEK ASTRONOMY.

leads us forwards to apparent complexity, and to an
accumulation of rules and relations. A fact like the
evection, explained by an hypothesis like Ptolemy's,
tended altogether to discourage any disposition to
guess at the laws of nature from mere ideal views,
or from a few phenomena.

2. The discovery of evection had an importance
which did not come into view till long afterwards,
in being the first of a numerous series of inequalities
of the moon, which result from the disturbing force
of the sun. These inequalities were successively
discovered ; and led finally to the establishment of
the law of imiversal gravitation. The moon's first
inequality arises from a different cause ; — ^from the
same cause as the inequality of the sun's motion ;— •
from the motion in an ellipse, so £eir as the central
attraction is undisturbed by any other. This first
inequality is called the elliptic inequality, or, more
usually, the eqtiation of the centre. All the planets
have such inequalities, but the evection is peculiar
to the moon. The discovery of other inequalities of
the moon's motion, the variation and annual equa-
tion, made an immediate sequel in the order of
the subject to the discoveries of Ptolemy, although
separated by a long interval of time ; for these dis-
coveries were only made by Tycho Brahe in the
sixteenth century. The imperfection of astrono-
mical instruments was the great cause of this long
delay.

3. The epicyclical hypothesis was found capable

SEQUEL TO THE EPOCH OF HIPPARCHUS. 219

of accommodating itself to such new discoveries.
These new inequalities could be represented by new
combinations of eccentrics and epicycles: all the
real and imaginary discoveries of astronomers, up to
Copernicus, were actually embodied in these hypo-
theses ; Copernicus, as we have seen, did not reject
such hypotheses ; the lunar inequalities which Tycho
detected might have been similarly exhibited ; and
even Newton'* represents the motion of the moon's
apogee by means of an epicyle. As a mode of
expressing the law of the irregularity, and of calcu-
lating its results in particular cases, the epicyclical
theory was capable of continuing to render great
service to astronomy, however extensive the pro-
gress of the science might be. It was, in fact, as we
have already said, the modem 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 pro-
gress of this hypothesis, it became more and more com-
plex, instead of becoming more simple ; which, as we
shall see, the true theory did. The notions concerning
the position and connexion of the heavenly bodies.

84

Principia, lib. iii. prop. xxxr.

220 THE GREEK ASTRONOMY.

which were suggested by one set of phenomena, were
not confirmed by the indications of another set of
phenomena ; for instance, those relations of the epi-
cycles which were adopted to account for the mo-
tions of the heavenly bodies, were not found to fall
in with the consequences of their apparent dia-
meters and parallaxes. In reality, as we have said,
if the relative distances of the sun and moon at dif-
ferent 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.

Sect 7. — Conclusion of the History of Greek

Astronomy.

I might now proceed to give an account of Pto-
lemy's other great step, the determination of the
planetaiy 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 appa-
rently moves about the earth. They will therefore
each have an elliptic inequality or equation of the
centre, for the same reason that the sun and moon
have such inequalities. And this inequality may be
represented, in the cases of the planets, just as in the
other two, by means of an eccentric ; the epicycle,
it will be recollected, had alreadv been used in order

SEQUEL TO THE EPOCH OF HIPPARCHUS- 221

to represent the more obvious changes of the plane-
tary motions. To determine the amount of the ec-
centricities and the places of the apogees of the
planetary orbits, was the task which Ptolemy under-
took; Hipparchus, as we have seen, having been
destitute of the observations which such a process
required. The determination of the eccentricities
in these cases involved some peculiarities which
might not at first sight occur to the reader. The
elliptical 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 eccentrici-
ties which he had to account for, were the compoimd
result of the eccentricity of the earth's orbit, and of
the proper eccentricity of the orbit of the planet.
He explained this result by the received mechanism
of an eccentric deferent, carrying an epicycle ; but
the motion in the deferent is uniform, not about the
centre of the circle, but about another point, the
equanl. Without going further into detail, it may
be sufficient to state that, by a combination of ec-
centrics and epicycles, he did account for the lead-
ing features of these motions; and by using his
own observations, compared with more aiicient ones,
(for instance, those of Timocharis for Venus,) he was
able to determine the dimensions and positions of
the orbits.

I shall here close my account of the astronomical
progress of the Greek school. My purpose is only

222 THE GREEK ASTRONOMY.

•

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
portions 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 the Greek astrono-
mical knowledge, as, for instance, their acquaintance
with refraction, did not assume any clear or definite
form, and can only be considered as the prelude to
modem discoveries on the same subject. And before
we can with propriety pass on to these, there is a
long and remarkable, though unproductive interval,
of which some account must be given.

Sect. 8. — Arabian Astronomy.

The interval to which I have just alluded may be
considered as extending from Ptolemy to Coper-
nicus; we have no advance in Greek astronomy
after the former ; no signs of a revival of the power
of discovery till the latter. During this interval of
1350 years*', the principal cultivators of astronomy
were the Arabians, who adopted this science from
the Grcebi whom they conquered, and from whom
the conquerors of western Europe again received
back their treasure, when the love of science and

^ Ptolemy died about a.i>. 150. C^opemicus was liTing a.d.
1500.

SEQUEL TO THE EPOCH OF HIPPARCHUS. 223

the capacity for it had been awakened in their
minds. In the intervening time, the precious de-
posit had undergone little change. The Arab astro**
nomer had been the scrupulous but unprofitable
servant, who kept his talent without apparent danger
of loss, but also without prospect of increase. There
is little in Arabic literature which bears upon the
progress of astronomy ; but as the little that there is
must be considered as a sequel to the Greek science,
I shall notice one or two points before I treat of the
stationary period in general.

When the sceptre of western Asia had passed
into the hands of the Abasside caliphs'^, Bagdad,
" the city of peace," rose to splendour and refine-
ment, and became the metropolis of science under
the successor^ of Almansor the Victorious, as Alexan-
dria had been under the successors of Alexander the
Great. Astronomy attracted peculiarly the favour of
the powerful as well as the learned ; and almost aU
the culture which was bestowed upon the science,
appears to have had its source in the patronage,
often in the personal studies, of Saracen princes.
Under such encouragement, much was done, in those
scientific labours which money and rank can com-
mand. Translations of Greek works were made, large
instruments were erected, observers were main-
tained ; and accordingly as observation showed the
defects and imperfection of the extant tables of the

^ Gibbon X. 31.

224 THE GREEK ASTRONOMY.

celestial motions, new ones were constructed. Thus
under Almansor, the Grecian works of science were
collected from all quarters, and many of them trans-
lated into Arabic''. The translation of the ** Megiste
Syntaxis" of Ptolemy, which thus became the Al-
magest, 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, Muhammed
ben Geber Albatani, the last appellation indicating
that he was bom at Batan, a city of Mesopotamia'^".
He wa. a Syrian prince, whose residence was at
Aracte or Racha in Mesopotamia ; a part of his ob-
servations were made at Antioch. His work still
remains to us in Latin. " After having read," he
says, « the Syntaxis of Ptolemy, and learnt the
methods of calculation employed by the Greeks, his
observations led him to conceive that some improve-
ments might be made in their results. He found it
necessary to add to Ptolemy's observations, as Pto-
lemy 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 Hakem (about a.d.
1000,) Ebn lounis published tables of the sun,
moon, and planets, which were hence called the

'^ Gibbon,, x. 36. •* Del., Astronomie du Moyen Age, 4.

SEQUEL TO THE EPOCH OP HIPPARCHUS. 225

Hakemite tables. Not long after, Arzachel of
Toledo published the Tohtan tables. In the 13th
century, Nasir Eddin published tables of the stars,
dedicated to Ilchan, a Tartar prince, and hence
termed the Ihhanic tables. Two centuries later,
Ulugh Beigh, the grandson of Tamerlane, and prince
of the countries beyond the Oxus, was a zealous
practical astronomer; and his tables, which were
published by Hyde in 1665, are referred to as im-
portant authority by modern astronomers. The
series of astronomical tables which we have thus
noticed, in which, however, many are omitted, leads
us to the Alphondne tables, which were put forth in
1488, and in succeeding years, under the auspices
of Alphonso, king of Castile ; and thus brings us to
the verge of modern astronomy.

For all these tables, the Ptolemaic hypotheses
were employed; and, for the most part, without
alteration. The Arabs sometimes felt the extreme
complexity and difficulty of the doctrine which they
studied ; but their minds did iiot 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 asto-
nished and stupified with this complexity, but that
afterwards " God was pleased to open to him the
occult secret in the theory of his orbs, and to make
known to him the truth of their essence, and the rec-

VOL. I. Q

226 THE GREEK ASTJEtONOMY.

titude of the quality of their motion." His system
consists, according to Delambre", in attributing to
the planets a spiral motion from east to west, an
idea already refuted by Ptolemy. Geber of Seville
criticizes Ptolemy very severely *^ but without intro-
ducing any essential alteration into his system. The
Arabian observations are in many cases valuable;
both because they were made with more skill and
with better instruments than those of the Greeks ;
and also because they illustrate the permanence or
variability of important elements, such as the obli-
quity 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 degreQS ; Ptolemy had placed it in longi-
tude 66 degrees. The difference of 17 degrees was
beyond all limit of probable error of calculation,
though the process is not capable of great precision ;
and the inference of the motion of the apogee was
so obvious, that we cannot agree with Delambre, in
doubting or extenuating the claim of Albategnius
to this discovery, on the ground of his not having
expressly stated it.

In detecting this motion, the Arabian astronomers
reasoned rightly from facts well observed ; they were

" Delambre, M. A. p. 7- *• M. A. p. 180, &c.

SEQUEL TO THE EPOCH OP HIPPARCHUS. 227

not always so fortunate. Arzachel, in the 11th cen-
tury, found the apogee of the sun to be less advanced
than Albategnius had found it, by some degrees ; he
inferred that it had receded in the intermediate
time ; but we now know, from an acquaintance with
its real rate of moving, that the true inference
would have been, that Albategnius, whose method
was less trustworthy than that of Arzachel, had
made an error to the amount of the difference thus
arising. A curious, but utterly false hypothesis was
founded on observations thus erroneously appre*
ciated ; namely, the trepidation of the jiwed $twrs.
Arzachel conceived that a uniform precession of
the equinoctial points would not account for the
apparent changes of position of the stars, and
that for this purpose, it was necessary to conceive
two circles of about 8 degrees radius described
round the equinoctial points of the immoveable
sphere, and to suppose the first points of Aries and
Libra to describe the circumferences 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
latitudes 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 re-
jected.

An important exception to the general unprogres-
sive character of Arabian science has been pointed

Q2

228 THE GBEEK ASTRONOMY.

out recently by M. Sedillot**. It appears that
Mohammed-Aboul We&ral-Bouzdjani, an Arabian
astronomer of the tenth century, who resided at Cairo,
and observed at Bagdad in 975, discoyered a third
inequality of the moon, in addition to the two ex-
pounded by Ptolemy, the equation of the centre,
and the evection. This third inequality, the vanar-
Hon, is usually supposed to have been discovered by
Tycho Brahe, six centuries later. It is an inequality
of the moon's motion, in virtue of which she moves
quickest when she is at new or full, and slowest at
the first and third quarter ; in consequence of this,
from the first quarter to the full, she is behind her
mean place ; at the fall, she does not differ from her
mean place ; from the full to the third quarter, she
is before her true place ; and so on ; and the greatest
effect of the inequaUty is in the octants, or points
half-way between the four quarters. In an Almagest
of Aboul Wefa, a part of which exists in the Royal
Library at Paris, after describing the two inequalities
of the moon, he has a Section ix., " Of the Third
Anomaly of the Moon called Muhazal or Prosnetms.'^
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,
^ observation of the moon, when she was nearly in
trine and in sea^tik with the sun, that she was a degree

** Sedillot. Nouvelles Rech. sur I'Hist. de TAstion. chez
les Arabes. Nouveau Journal Asiatique. 18S6.

SEQUEL TO THE EPOCH OP HIPPARCHUS, 229

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 favour-
able point of view than any circumstance with which
we were previously acquainted.

But this discovery of Aboul Wefa appears to have
excited bo notice among his contemporaries and
followers ; at least it had been long quite forgotten
when Tycho Brache rediscovered the same lunar
inequality. We can hardly help looking upon this
circumstance as an evidence of the servility of
intellect of the Arabian period. The learned Ara-
bians were so little in the habit of considering science
as progressive, and looking with pride and confidence
at examples of its progress, that they had not the
courage to believe in a discovery which they them-
selves had made, and were dragged back by the

230 TH£ GREEK ASTRONOMY.

chain of authority, even when they had advanced
beyond their Greek masters.

As the Arabians took the vj^hole 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 conse-
quences of the theory were obtained. Arithmetic
and trigonometry, two main branches of these pro-
cesses, received considerable improvements at their
hands. In the former, especially, they rendered a
service to the world which it is difficult to estimate
too highly, in abolishing the cumbrous sexagesimal
arithmetic of the Greeks, and introducing the nota*
tion by means of the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, 0,
which we now employ**. These numerals appear to
be of Indian origin, as is acknowledged by the Arabs
themselves ; and thus form no exception to the steri--
lity 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
corjectures concerning the origin of the word dm;
the most probable appears to be that sinus is the
Latin translation of the Arabic word giJ)^ which
signifies a fold, the two halves of the chord being
conceived to be folded together.

" Mont. i. 376.

SEQUEL TO THE EPOCH OP HIPPARCHUS. 231

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

Before quitting the subject, we may observe that
Astronomy brought back, from her sojourn among
the Arabs, a few terms which may still be perceived
in her phraseology. Such are the zenith^ and the
opposite imaginary point, the nadir ; — ^the circles of
the sphere termed (dmacantars and azimvtii circles.
The alidad of an instrument is its index, which pos-
sesses an angular motion. Some of the stars still
retain their Arabic names ; Aldebaran^ Rigel, Fomain
haul ; many others were known by such appellations
a little while ago. Perhaps the word almanac is the
most familiar vestige of the Arabic period of
astronomy**.

*' It is not to my purpose to note any eflforts of the intellec-
tual faculties among other nations, which may hare taken place
independently of the great system of progressive European
culture, &om which all our existing science is derived. Other-
wise I might speak of the astronomy of some of the Orientals,
for example, the Chinese, who are said, by Montucla (i. 465)
to have discovered the first equation of the moon, and the
proper motion of the fixed stars (the precession), in the third
century of our era. The Greeks had made these discoveries
500 years earlier.

BOOK IV.

HISTORY

OP

PHYSICAL SCIENCE IN THE MIDDLE AGES ;

OR,

VIEW OF THE STATIONARY PERIOD OF
INDUCTIVE SCIENCE. '

In vain, in vain ! the all-coniposing liour
Besistless 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 aU 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.

Dundady b. iv.

INTRODUCTION.

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

We have already stated, that real scientific pro-
gress requires distinct general ideas, applied to many
special and certain facts. In the period of which
we now have to speak, men's ideas were obscured,
their disposition to bring their general views into
accordance with facts was enfeebled. They were
thus led to employ themselves unprofitably, among

236 PHYSICAL SCIENCE IN THE MIDDLE AGES.

indistinct and unreal notions. And the evil of
these tendencies was further inflamed, by moral
peculiarities in the character of those times ; — by an
abjectness of thought on the one hand, which could
not help looking towards some intellectual superior ;
and by an impatience of dissent on the other. To
this must be added an enthusiastic temper, which,
when introduced into speculation, tends to subject
the mind's operations to ideas altogether distorted
and delusive.

These characteristics of the stationary period, its
obscurity of thought, its servility, its intolerant dis-
position, and its enthusiastic temper, will be treated
of in the four following chapters, on the Indistinct-
ness of Ideas, the Commentatorial Spirit, the Dog-
matism, and the Mysticism of the Middle Ages.

237

CHAPTER I.

On the Indistinctness of Ideas of the

Middle Ages.

That firm and entire possession of certain clear
and distinct general ideas which is necessary to
sound science, was the character of the minds of
those of the ancients who created the several sciences
which arose among them. It was indispensable, that
such inventors should have a luminous and stead-
fast apprehension of certain general relations, such as
those of space or number, of order and cause ; and
should be able to apply these notions with perfect
readiness and precision to special facts and cases.
It is necessary that such scientific notions should be
more definite and precise than those which common
language conveys ; but even in this state of unusual
clearness, they must be so familiar to the philoso-
pher, that they are the language in which he thinks.
And the discoverer is thus led to doctrines which
other men adopt and follow out, in proportion as
they seize the fundamental ideas, and become ac-
quainted with the leading facts. Thus Hipparchus,
conceiving clearly the motions and combinations of
motion which enter into his theory, saw that the
relative lengths of the seasons were sufficient data

238 PHYSICAL SCIENCE IN THE MIDDLE AGES.

for detennining the form of the sun's orbit ; thus Ar-
chimedes, 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 dis-
tribution of pressure in fluids, on which the science
of hydrostatics depends.

With such distinct ideas, the inductive sciences rise
and flourish ; with the decay and loss of such distinct
ideas, these sciences become stationary, languid, and
retrograde. When men merely repeat the terms of
science, without attaching to them any clear con**
ceptions ; — ^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 thft universe is really
governed; — ^it must inevitably happen, that men
will lose their hold on the truths 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 feeble and irresolute
a hand; probably they cannot even prevent their
sliding back towards the obscurity from which they
had been drawn, or from being lost altogether.
Such indistinctness and vacillation of thought ap-
pear to have prevailed in the stationary period, and
to be, in fiact, intimately connected vrith its sta-
tionary character. I shall point out some indica-

INDISTINCTNESS OF IDEAS. 289

tions 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 Dio-
genes LaCrtius gives in his " Lives of the Philoso-
phers." At an earlier period still, books of this
kind appear; as for instance, a large portion of
Pliny's Natural History, a work which has very
appropriately been called the Encyclopsedia of Anti-
qlyf e™a Ari,t«tle Mmself i. um,i in the luAit
of enumerating the opinions of those who had
preceded him. To present such statements as an
important part of physical philosophy, shows an
erroneous and loose apprehension of the nature
of such philosophy; for the only proof of which
its doctrines admit, is the possibility of appljring
the general theory to each particular case. The
authority of great men, which in moml and prac-
tical matters may or must have its weight, is here
of no force; and the technical precision of ideas
which the terms of a sound physical theory usually
demand, renders a mere statement of the doctrines
very imperfectly intelligible to readers femiliar with
common notions only. To dwell upon such col-
lections of opinions, therefore, implies, and pro-

240 PHYSICAL SCIENCE IN THE MIDDLE AGES.

duces, in writers and readers, an obscure and inade-
quate apprehension of the fall meaning of the
doctrines thus collected; if there be among them
any which really possess that clearness, solidity, and
reality, which make them important in the history
of science. Such diversities of opinion convey no
truth ; such a multiplicity of statements of what has
been said, in no degree teaches us what is ; such
accumulations of indistinct notions, however vast
and varied, do not make up one distinct idea. On
the contrary, the habit of dwelling upon the verbal
expressions of the views of other persons, and of
being content with such an apprehension of doo^
trines 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.

We may, therefore, consider the prevalence of
Collections of the kind just referred to, as indicating
a deficiency of philosophical talent in the ages now
under review. As evidence of the same character,
we may add the long train of publishers of Abstracts,
Epitomes, Bibliographical Notices, and similar wri-.
ters. All such writers are worthless for all purposes
of science, and their labouiis 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 know-
ledge ; and resemble the swarms of insects that are
bom from the perishing carcass of some nobler animal.

INDISTINCTNESS OF IDEAS. 241

2. Indistinctness of Ideas in Mechanics. — ^But the
indistinctness of thought which is so fatal a feature
in the intellect of the stationary period, may be traced
more directly in the works, even of the best authors,
of those times. We find that they did not retain
steadily the ideas on which the scientific success of the
previous period had depended. For instance, it is a
remarkable circumstance in the history of the science
of mechanics, that it did not make any advance from
the time of Archimedes to that of Stevinus and
Galileo. Archimedes had established the doctrine
of the lever ; several persons tried, in the interme-
diate time, to prove the property of the inclined
plane, and none of them succeeded. But let us
look to the attempts ; for example, that of Pappus,
in the eighth book of his Mathematical Collections,
and we may see the reason of the failure. His
problem shows, in the very terms in which it is
propounded, the want of a clear apprehiensioh of the
subject. " Having given the power which will draw
a given weight along a 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 rate
at which the body were drawn, and the nature of
the surface of the plane, were of no consequence.
The proper elementary problem is, to find the force
which will support a body on an inclined plane ; and
no doubt the solution of Pappus has more reference

VOL. I. R

242 PHYSICAL SCIENCE IN THE MIDDLE AGES.

to this problem than to his own. His reasoning is,
however, totally at yariance with mechanical ideas
on any view of the problem. He supposes the
weight to be formed into a sphere ; and this sphere
beiilg 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 levw, the
fulcrum being the point of contact of the sphere
with the plane, and the power acting at the circum-
ference of the sphere. Such an assumption implies
an entire absence of those distinct ideas of mechar-
nical pressure, on which our perception of the
identity or diflference of different modes of action
must depend ; — of those ideas by the help of which
Archimedes had been able to demonst^rate the preop-
tics 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 his
perceiving that the additional power, which he thus
obtained, vanished when the plane became horizontal,
and increased as the inclination became greater. Thus
his conceptions were vague ; he had no grounds of
rational conviction, and he tried a conjecture. This
is not the way to real knowledge.

Pappus (who lived about A. D. 400) was one of the
best mathematicians of the Alexandrian school;
and, on subjects where his ideas were so indistinct,
it is not likely that any much clearer were to be
found in the minds of his contemporaries. Accord-
ingly, on all subjects of speculative mechanics, there

INDISTINCTNESS OF IDEAS. 243

appears to have been an entire confusion and obscu*
rity of thought till modem times. Men's minds
were busy in endeavouring to systematize the dis-
tinctions and subtleties of the Aristotelian school,
concerning motion and power; and, being thus
employed among doctrines in which there was
involved no definite signification, capable of real
exemplification, they, of course, could not acquire
sound physical knowledge. We have already
seen that the physical opinions of Aristotle, even
as they came from him, had no proper scientific
precision. His followers, in their endeavours to
perfect and develop his statements, never attempted
to introduce clearer ideas than those of their master ;
and as they never referred, in any steady manner, to
fiicts, the vagueness of their notions was not cor-
rected by any collision with observation. The
physical doctrines which they extracted from Aris-
totle 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 de-
prived the terms of all steady meaning, the dogmas
continued to be repeated, till the world was per-
suaded 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 me-

244 PHYSICAL SCIENCE IN THE MIDDLE AGES.

chanics of fluids, as '* Hydrostatical Paradowes^
proved and illustrated by experiments." And
the opinions which he there opposes, are those
which the Aristotelian philosophers habitually pro-
pounded as certain and indisputable; such, for
instance, as thiat " 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 posi-
tive quality of bodies as well as gravity." So long
as these assertions were left uncontested and un-
tried, men heard and repeated them, without per-
ceiving the incongruities which they involved : and
thus they long evaded refutation amid the vague
notions and undoubting habits of the stationary
period. But when the controversies of Galileo's
time had made men think with more acuteness and
steadiness, it was discovered that many of these
doctrines were inconsistent with themselves, as well
as with experiment. We have an example of the
confusion of thought to which the Aristotelians were
liable, in their doctrine concerning felling bodies.
" Heavy bodies," said they, " must fall quicker than
light ones ; for weight is the cause of their fall, and
the weight of the greater bodies is greater." They
did not perceive that, if they considered the ,weight
of the body as a power acting to produce motion,
they must consider the body itself as offering a
resistance to motion; and that the effect must
depend on the proportion of the power to the resist-
ance ; in short, they had no clear idea of accelerating

INDISTINCTNESS OF IDEAS. 245

force. This defect runs through all their mecha-
nical speculations, and renders them, entirely value-
less.

We may exemplify the same confusion of thought
on mechanical subjects in writers of a less technical
character. Thus, if men had had any distinct idea
of mechanical action, they could not . have ac-
cepted for a moment the fable of the Echineis or
Remora, a little fish which was said to be able to
stop a large ship merely by sticking to it. Lucan*
refers to this legend in a poetical manner, and
notices this creature only in bringing together a
collection of monstrosities; but Pliny relates the
tale gravely, and moralizes upon it. after his manner.
" What," he cries s " 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 th^se when they all strain the same way.
. The winds may blow, the waves may rage ; but this
small creature controls their fiiry, and stops a vessel,

•

' Lucan is describing one of the poetical compounds intro-
duced in incantations.

Hue quicquid foetu genuit Natura sinistro
Miscetur: non spuma canum quibus unda timori est,
Viscera non Ijncis, non duree nodus hyanee
Defuit, et cervi pasti serpente medullaB;
Non puppes retinens. Euro tendente audentes
In medilB Echineis aqois, oculique draconum.

Etc. Pharsaliaj iy. 670.

" Plin. Hist. N. xxxii. 1.

246 PHYSICAL SaENCE IN THS MIDDLE AGES.

when chainai and anchors would not hold it: and
this it does, not by hard labour, but merely by ad-
hering to it. Alas, for human vanity ! when the
turretted ships which man has built, that he may
fight from castle^walls, at sea as well as at land^ are
held captive and motionless by a fish a foot and a
half long. Such a fish is said to have stopt the
admiral's ship at the battle of Actium, and eom-
pelled Antony to go into another. And in our own
memory, one of these animals held fast the ship
Caius, the emperor, when he was sailing from
Astura to Antium. The stopping of this ship, when
all the rest of the fleet went on, caused surprise ;
but this did not last long, for some of the men
jumped into the water to look for the fish, and found
it sticking to the rudder ; they showedlt to Caius,
who was indignant that this animal should inter-
pose its prohibition to his progress, when im«
pelled 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 is 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. —

INDISTINCTNESS OP IDEAS. 247

Perhaps it may serve to illustrate still further the ex-
tent to which, under the Roman empire, men's notions
of mechanical relations became faint, wavered, and
disappeared, if we observe the change which took
place in architecture. All architecture, to possess
genuine beauty, must be mechanically consistent.
The decorative members must represent a structure
which has in it a principle of support and stability.
Thus the Grecian colonnade was a straight hori-
zontal beam, resting on vertical props; and their
pediment imitate^ a frame like a roof, where oppo--
sitely-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,
thou^ they imitated the forms of the Grecian,
were destitute of their mechanical truth, belonged
to the decline of art; and showed that men had
lost the idea of force, and retained only that of
shape. Yet this was what the architects of the
empire did. Under their hands, the pediment was
severed at its vertex, or divided into sepawtte halves,
so that it was no longer a mechanical possibility.
The entablature no longer lay straight from pillar to
pillar, but, projecting over each column, turned back
to the wall, and adhered to it in the intervening-
space. The splendid remains of Palmyra, Balbec,
Petra, exhibit endless examples of this kind of
perverse inventiveness ; and show us, very instruc-
tively, how the decay of art and of science alike go

248 FHTSICAI. 8CIENC& IN THE UDDLE AGES.

along with this indistinctness of ideas which we are
endeayoming to explain.

4. Indistinctness of Ideas in Astronomy. — ^Retnm-
ing 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 mea-
sure, to apply, the doctrines previously estaUifibed.
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 unpossible for
these chains of elementary perception ever to be
much entangled. The later Greeks, the Arabians,
and the earliest modem astronomers, must have
conceived the hypotheses of the Ptolemaic system
in a tolerably complete degree. 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 Copemican
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 mathema-
ticians present the solutions of their problems, does
not indicate that clear apprehension of the relations
of space, and that delight in the contemplation of

INDISTINCTNESS OF IDEAS. 249

them, which the Greek geometrical speculations
imply. The Arabs are in the habit of giving con-
clusions 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* has been
obliged to exercise great ingenuity, in order to dis-
cover the method in which Ibn lounis proved his
solution of certain difficult problems.

5. Indistinctmss of Ideas shown by Sc€ptics.^^The
same unsteadiness of ideas which prevents men from
obtaining clear views, and steady and just convic-
tions, on special subjects, may lead them to despair
of or deny the possibility of acquiring certainty at
all, and may thus make them sceptics with regard
to all knowledge. Such sceptics are themselves
men of indistinct views, for they could not other-
wise avoid assenting to the demonstrated truths of
science ; and, so far as they may be taken as speci-
mens of their contemporaries, they prove that indis-
tinct ideas prevail in the age in which they appear.
In the stationary period, moreover, the indefinite
speculations and unprofitable subtleties of the schools
might further impel a man of bold and acute mind
to this universal scepticism, because they oiSered
nothing which could fix or satisfy him. And thus
the sceptical spirit may deserve our notice as indica-

«

* Delamb. M. A. p. 125-8.

250 PHYSICAL SCIENCE IN THE MIDDLE AGES.

tions of the defects of that system of doctrine which
was too feeble in demonstration to control such
resistance.

The most remarkable of these philosophical scep-
tics is Sextus Empiricus ; so called, from his belongs
ing to that medical sect which was termed the emfi"
ricalf in contradistinction to the rational and metiuh
diced sects. His works contain a series of treatises,
directed against all the divisions of the science of
his time. He has chapters against the Geometers,
against the Arithmeticians, against the Astrologers,
against the Musicians, as well as against Gramma*
rians. Rhetoricians and Logicians ; and, in short, as a
modem writer haa said, his scepticism is employed
as a sort of frame-work which embraces an encyclo-*
pedical view of human knowledge. It must be
stated, however, that his objections are rather to the
metaphysics, than to the details of the sciences ; he
rather denies the possibility of speculative truth in
general, than the experimental truths which had
been then obtained. Thus his objections to geo-
metry and arithmetic are founded on abstract cavils
concerning the nature of points, letters, unities, &c.
And when he comes to speak against astrology, he
says, ^^ I am not going to consider that perfect
science which rests upon geometry and arithmetic ;
for I have already shown the weakness of those
sciences; nor that fitculty of prediction (of
the motions of the heavens) which belongs to
the pupils of Eudoxus, and Hipparchus, and the

INDISTINCTNESS OF IDEAS. 251

rest, which some call astronomy; for that is an
observation of phenomena, like a^culture or navi-
gation ; but against the art of prediction from the
time of birth, which the Chaldeans exercise." Sex-
tus, therefore, though a sceptic by profession, was
not insensible to the difference between experimen-
tal knowledge and mystical dogmas, though the
f&rmer had nothing which excited his admiration.

The early writers of the Christian church deemed
lightly of the philosophy of their pagan antagonists ;
but this was on different grounds, as we shall here-
after see. The spirit of bold examination and denial
of authority appears to be still more uncongenial to the
Mohammedan temper of thought ; yet one remark-
able sceptic with regard to philosophy can be pointed
out among the Saracen writers. This is Algazel, or
Algezeli, who was a celebrated teacher at Bagdad in
the eleventh century, and who declared himself the
enemy, not only of the mixed peripatetic and Pla-
tonic philosophy of his time, but of Aristotle him-
self. His work, entitled " The Destructions of the
Philosophers," is known to us by the refutation of
it which Avicenna published, under the title of
<< Destruction of AlgaeeFs Destructions of the Phi«
lo60phers\" It appears that he contested the fimda^
mental principles of the Platonic and Aristotelian
sohools, and denied the possibility of a known con«
nexion between cause and efifect; thus making a
prelude to the celebrated argumentation of Hume«

* Degerando, Hist. Comp. des Syst. iy. 124.

252 PHYSICAL SCIENCE IN THE MIDDLE AGES,

In his work " On the Opinions of the Philosophers,"
he examined those opinions in particular which refer
to the principles of the physical sciences. We can-
not doubt that his objections, so far as they attacked
the really-estabUshed truths of astronomy and othw
sciences, must have implied confusion of apprehen-
sion both in him and in those whom he persuaded.

6. Neglect of Physical Redsoning in Christendom.^^
If the Arabians, who, during the ages of which we
are speaking, were the most eminent cultivators of
science, entertained only such comparatively feeble
and servile notions of its doctrines, it will easily be
supposed, that in the Christendom of that period,
where physical knowledge was comparatively negr
lected, there was still less distinctness. and vividness
in the prevalent idea^i on such subjects. Indeed,
during a considerable period of the history of the
Christian church, and by many of its principal autho-
rities, the study of natural philosophy was not only
disregarded but discommended. The great practical
doctrines which were presented to men's minds, ,and
the serious tasks, of the regulation of the will and
afiections, which religion impressed upon them,
made inquiries of mere curiosity seem to be a repre-
hensible misapplication of human powers ; . and many
of the fathers of the church revived, in a still , more
peremptory form, the opiniou of Socrates, that the
only valuable philosophy is that which teaches us
our moral duties and religious hopes*. Thus Euse-

' Brucker iii. 317-

INDISTINCTNESS OF IDEAS. 253

bius says', " It is not through ignorance of the things
admired by them, but through contempt of their
useless labour, that we think little of these matters,
turning our souls to the exercise of better things."
When the thoughts were thus intentionally averted
from those ideas which natural philosophy involves,
the ideas inevitably became very indistinct in their
minds; and they could not conceive that any other
persons could find, on such subjects, grounds of clear
conviction and certainty. They held the whole of
their philosophy to be, as Lactantius^ asserts it to be,
" empty and false." " To search," says he, " for the
causes of natural things ; to inquire whether the
sun be as large as he seems, whether the moon is
convex or concave, whether the stars are fixed in the
sky or float freely in the air ; of what size and of what
material are the heavens ; whether they be at rest or
in motion ; what is the magnitude of the earth ; on
what foundations it is suspended and balanced ; — ^to
dispute and conjecture on such matters, is just as if
we chose to discuss what we think of a city in a
remote country, of which we never heard but the
name." It is impossible to express more forcibly
that absence of any definite notions on physical sub-
jects which led to this tone of thought.

7. Question of Aniipodes.--^With such habits of
thought, we are not to be surprised if the relations
resulting from the best established theories were

• Praep. Ev. xy. 61. ^ I. iii. init.

254 PHYSICAL SCIENCE IN THE MIDDLE AGES.

apprehended in an imperfect and incongruous man-
ner. We have some remarkable examples of this ;
and a very noted one, in the celebrated question of
the existence of Antipodes^ or persons inhabiting the
opposite side of the globe of the earth, and conse-
quently having the soles of their feet directly op-
posed to ours. The doctrine of the globular form
of the earth results, as we have seen, by a geome-
trical necessity, from a clear conception of the vari-
ous points of knowledge which we obtain, bearing
upon that subject ; this doctrine was held distinctly
by the Greeks ; it was adopted by all astronomers,
Arabian and European, who followed them; and
was, in feet, an inevitable part of every system of
astronomy which gave a possible and intelligible
representation of phenomena. But those who did
not call before their minds any distinct representa-
tion at all, and who referred the whole question to
other relations than those of space, might still deny
this doctrine ; and they did so. The existence of
inhabitants on the opposite side of the terraqueous
globe, was a fact of which experience alone could
teach the truth or falsehood ; but the religious rela-
tions, which extend alike to all mankind, were sup-
posed to give the Christian philosopher grounds for
deciding against the possibility of such a race of
men. Lactantius" in the fourth century, argues this
matter, in a way very illustrative of that impatience

« 1. iii. 23.

INDISTINCTNESS OF IDEAS. 265

of such speculations, and consequent confusion of
thought which we have mentioned. " Is it possible,"
he says, ^^ that men can be so absurd as to believe
that the crops and trees on the other side of the
earth hang downwards, and that men there have
their feet higher than their heads ? If you ask of
them how they defend these monstrosities? — ^how
things do not fall away from the earth on that side ?
they reply, that the nature of things is such that
heavy bodies tend towards the centre, like the spokes
of a wheel, while light bodies, as clouds, smoke, fire,
tend from the centre towards the heavens on all
sides. Now I am really at a loss what to say of
those who, when they have once gone wrong, steadily
persevere in their folly, and defend one absurd opi-
nion by another." It is obvious that so long as the
writer reftised to admit into his thoughts the funda*
mental 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 Indico-
pleustes*) who does not rest in this obscurity of
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 ex-
plain the phenomena. He describes the earth as an

• Montfaucon, Collectio Nova Patrum, t. ii. p. 113. Cosmas
Indicopleustes. Christianorum Opiniones de Mundo, sire To-
pographia Christiana.

266 PHYSICAL SCIENCE IN THE MIDDLE AGES.

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** (who flourished a.d. 400) the
opinion is treated on other grounds ; and without de-
nying 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 amons: the de-
scendants of Adam. Considexutions of the same
kind operated in the well-known instance of Virgil,
bishop of Salzburg, in the eighth century. When
he was reported to Bonifece, archbishop of Mentz,
as holding the existence of Antipodes, the prelate
was shocked at the assumption, as it seemed to him,
of a world of human beings, out of the reach of the
conditions of salvation; and application was made
to Pope Zachary for a censure of the holder of this
dangerous doctrine. It does not however appear
that this led to any severity ; and the story of the
deposition of Virgil from his bishopric, which is
circulated by Kepler and by more modem writers,
is undoubtedly altogether felse. The same scruples
continued to prevail among Christian writers to a
later period ; and Tostatus * * notes the opinion of the
rotundity of the earth as an unsafe doctrine, only a
few years before Columbus visited the other hemi-
sphere.

'^ Civ. D. xvi. 9. '' Montfauc. Patr. t. ii.

INDISTINCTNESS OP IDEAS. 257

8. Intellectual Condition of the Meliffiotcs Orders. —
It must be recollected, however, that though these
were the views and tenets of many religious writers,
and though they may be taken as indications of the
prevalent and characteristic temper of the times of
which we speafc, they never were universal. Such
a confusion of thought affects the minds of many
persons, even in the most enlightened times ; and in
what we call the dark ages, though clear views on such
subjects might be more rare, those who gave their
minds to science, entertained the true opinion of the
figure of the earth. Thus Boethius*' (in the sixth
century) urges the smallness of the globe of the
earth, compared with the heavens, as a reason to
repress our love of glory. This work, it will be
recollected, was translated into the Anglo-Saxon by
our own Alfred. It was also commented on by
Bede, \dio, in what he says on this passage, assents
to the doctrine, and shows an acquaintance with
Ptolemy and his commentators, both Arabian and
Greek. Gerbert, in the tenth century, went from
France to Spain to study astronomy with the Ara-
bians, and soon surpassed his masters. He is re-
ported to have &bricated clocks, and an astrolabe of
peculiar construction. Gerbert afterwards, (in the
last year of the first thousand from the birth of
Christ,) became pope, by the name of Sylvester II.
Among other cultivators of the sciences, some of

la

Boetliius, Cons. ii. pr. 7»
VOL. I. S

258 PHYSICAL SCIENCE IN THE MIDDLE AGES.

whom, from their proficiency, must have possessed
with considerable clearness and steadiness the ele-
mentary ideas on which it depends, we may here
mention, after Montncla'*, Adelbold, whose work
On the Sphere was addressed to Pope Sylvester,
and whose geometrical reasonings are, according to
Montucla^\ vague and chimerical; Hermann Con-»
tractus, a monk of St. Gall, who, in 1050, published
astronomical works; William of Hirsaugen, who
followed this example in 1080 ; Robert of Lorraine,
who was made Bishop of Hereford by William the
Conqueror, in consequence of his astronomical know-f
ledge. In the next century, Adelhard Goth, an
Englishman, travelled among the Arabs for pur-
poses of study, as Gerbert had done in the preceding
age; and on his return, translated the Elements
of Euclid, which he had brought from Spain or
Egypt. Robert Grostete, Bishop of Lincoln, was
the author of an epitome on the Sphere ; Roger
Bacon, in his youth the contemporary of Robert
and his brother Adam Marsh, praises very highly
their knowledge in mathematics.

" And here," says the French historian of mathe-
matics, whom I have followed in the preceding rela-
tion, ^^ it is impos^ibl^ pot to reflect that all those men

who, if they did not augment the treasure of the
scieuces, at least served to transmit it, were monks, or
had been such originally. Convents were, during

" Mont. i. 602. " Mont. i. 503.

INDISTINCTNESS OF IDEAS. 259

these stormy ages, the asylum of sciences and letters.
Without these religious men, who, in the silence of
their monasteries, occupied themselves in trans-
cribing, 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 ancient litera*
ture would no more exist for us, than the works, if
there were any, published before the catastrophe
which annihilated that highly scientific nation,
which, according to Bailly, existed in remote ages
in the centre of Tartary, or at the roots of Cau-i
casus. In the sciences we should have had all to
create ; and at the moment when the human mind
i^ould have emerged from its stupor and shaken oiF
its slumbers, we should have been no more advanced
than the Greeks were after the taking of Troy."
He adds, that this consideration inspires feelings
towards the religious orders very different ftom those
which, when he wrote, were prevalent among his
countrymen.

Except so far as their religious opinions inter-
fered, it was natural that men who lived a life of
quiet and study, and were necessarily in a great
measure removed from the absorbing and blinding
interests with which practical life occupies the
thoughts, should cultivate science more successfully

s 2

260 PHYSICAL SCIENCE OF THE MIDDLE AGES.

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 neces-
sarily tended to fiivour this effect. The Trivium'\
indeed, which consisted of Grammar, Logic, and
Rhetoric, had no direct bearing upon those ideas
with which physical science is concerned ; but the
Quadriviunij Music, Arithmetic, Geometry, Astro-
nomy, could not be pursued with any attention,
without a corresponding improvement of the mind
for purposes of sound knowledge ^*.

9. Popular Opinions. — ^That, even in the best in-
tellects, something was wanting to fit them for
scientific progress and discovery, is obvious from
the fact that science was so long absolutely sta-
tionary. And I have endeavoured to show that one
part of this deficiency was the requisite clearness
and vigour 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

»» Brack, iii. 597.

*' Roger Bacon, in his Specula Mathematica, cap. i., says,
^^Harum scientiarum porta et clavis est mathematica, quam
sancti a principio mundi inyenerunt, etc. Cajus negligentia
jam per triginta vel quadraginia annos destruxit totum
studium Latinorum." I do not know on what occasion this
neglect took place.

INDISTINCTNESS OP IDEAS. 261

the belief, however crude and inconsistent, that the
fonn of the earth and heavens really is what at any
place it appears to be ; that the earth is flat, and the
waters of the sky sustained above a material floor,
through which in showers they descend. Yet the
true doctrines of astronomy appear to have had
some popular circulation. For instance, a French
poem of the time of Edward the Second, " called
" Ymage du Monde," contains a metrical account of
the earth and heavens, according to the Ptolemaic
views ; and in a manuscript of this poem, preserved
in the library of the University of Cambridge, there
are representations, in accordance with the text, of
a spherical earth, with men standing upright upon
it on every side: and by way of illustrating the
tendency of all things to the centre, perforations of
the earth, entirely through its mass, are described
and depicted; and figures are exhibited dropping
balls down each of these holes, so as to meet in the
interior. And, as bearing upon the perplexity
which attends the motions bf wp and dmim^ when
applied to the globular earth, and the change of the
direction of gravity which would occur in passing
the centre, the readers of Dante will recollect the
extraordinary manner in which the poet and his
guide emerge from the bottom of the abyss ; and the
explanation which Virgil imparts to him of what he
there sees. After they have crept through the aper-
ture in which Lucifer is placed, the poet says.

262 PHYSICAL 8CIEKCE OF THE MIDDLE AGES.

lo lerai gli occhi e credetti yedere
Ludfero com' io 1* area lasciato,
E yidili le gambe in su tenere.

" Quest! come e fitto

Ei sottasopra?* ....

" Quando mi yolsi, ta passast' il punto
Al qual 8i traggon d' ogni parte i pesi."

Inferno^ xxxiy.

I raised mine eyes,

Belieying that I Lucifer should see
Where he was lately left, but law him now
With legs held upward

"'How standeth he in posture thus reversed T

^ 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 heayy substance."

Cart.

This is more philosophical than Milton's repre-
sentation, in ft more scientific age, of Uriel sliding
to the earth on a sun-beam, and sliding back again
when the sun had sunk below the horizon.

Uriel to his charge

Betumed on that bright beam whose point now raised,
Bore him slope downward to the sun, now fallen
Beneath the Azores.

P. L. b. ir.

The philosophical notions of up and down are too
much at variance with the obvious suggestions of
our senses, to be held steadily and Justly by minds
undisciplined in science. Perhaps it was some mis-

INDISTINCTNESS OF IDEAS. 263

understood statement of the curved surface of the
ocean, which gave rise to the tradition of there
being a part of the sea directly oveY the earth, from
which at times an object has been known to fall, or
an anchor to be let down. Even such whimsical
famjies are not without instruction, and may serve to
show the reader what that vagueness and obscurity
of ideas is, of which I have been endeavouring 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.

264

CHAPTER II.

The Commentatorial Spirit of the

Middle Ages.

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

In some subjects, indeed, as, for instance, in the
domains of morals, poetry, and the arts which aim

THE COMMENTATORIAL SPIRIT. 265

at beauty, this opposition between the study of
former opinion and present reality, may not be so
distinct ; inasmuch as it may be said by some, that,
in these subjects^ opinions are realities; that the
thoughts and feelings which prevail in mgn's minds
are the material of our workmanship, the particulars
from which we are to generalize, the instruments,
which we are to use ; and that, therefore, to reject
the study of antiquity, or even its authority, would
be to show ourselves ignorant of the extent and
mutual bearing of the elements with which we have
to deal ;— would be to cut asunder that which we
ought to unite into a vital whole. Yet even in the
provinces of history and poetry, the poverty and
servility of men's minds during the middle ages, are
shown by indications so strong as to be truly re-
markable ; for instance, in the efforts of the anti-
quarians of almost every European country to assi-
milate 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 first business at present is, to trace the varying
spirit of the physical philosophy of different ages ;
trusting that, hereafter, this prefatory study will
enable us to throw some light upon the other parts
of philosophy. And in physics the case undoubt-
edly was, that the labour of observation, which is
one of the two great elements of the progress of
knowledge, was in a great measure superseded by

266 PHYSICAL SCIENCE IN THE MIDDLE AGES.

the collection, the analysis, the explanation, of pre-
vious authors and opinions; experimenters were
replaced by commentators ; criticism took the place
of induction; and instead of great discoverers we
had learned men.

1. Natural Bms to Anihority. — It is very easy to
see that, in such a bias of men's studies, there is
something very natural ; however strained and tech-
nical this erudition may have been, at least the
propensities on which it depends are very general,
and are easily seen. Deference to the authority of
thoughtful and sagacious men, a disposition which
we neither reject nor think we ought to reject, in
practical matters, naturally clings to us, even in
speculation. It is a satisfaction to us to suppose
that there are, or have been, minds of transcendent
powers, of wide and wise views, superior to the
common errors and blindnesses of our nature. The
pleasure of admiration, and the repose of confidence,
are inducements to such a belief There are also other
reasons why we willingly believe that there are in
philosophy great teachers, so profound and sagacious,
that, in order to arrive at truth, we have only to learn
their thoughts, to understand their writings. There
is a peculiar interest which men feel ia dealing with
the thoughts of their fellow-meir, rather than with
brute matter. Matter feels and excites no sympa-
thies ; in seeking for mere laws of nature, there is
nothing of mental intercourse with the great spirits
of the past, as there is in studying Aristotle or Plato.

THE COMMENTATORIAL SPIRIT. 267

Moreover, a large portion of this employment is of
a kind the most agreeable to most speculative
minds, consisting 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 iner^
haustible 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 vigour and hope
of men's minds are enfeebled by civil and political
changes. Accordingly S 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
vigour in the Museum, are likely to be, at all times,
the leading propensities of similar academical insti-
tutions.

How natural it is to select a great writer as
a paramount authority, and to ascribe to him ex-
traordinary profiindity and sagacity, we may see,
in the manner in which the Greeks looked upon
Homer ; and the fancy which detected in his poems
traces of the origin of all arts and sciences, has, as
we know, found favour even in modem times. To
pass over earlier instances of this feeling, we may

* Degerando. Hist, des Syst. de Philos. iii. p. 134.

268 PHYSICAL SCIENCE IN THE MIDDLE AGES.

observe, that Strabo begins his Geography by saying
that he agrees with Hipparchus, who had declared
Homer to be the first author of our geographical
knowledge : and he does not confine the application
of this assertion to the various and curious topogra-
phical information which the Iliad and Odyssey
contain, concerning the countries surrounding the
Mediterranean ; but in phrases which, to most per-
sons, 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*, when Homer speaks of
the sun "rising from the soft and deep-flowing
ocean," of his " splendid blaze plimging in the ocean;"
of the northern constellation

"Alone imwashen by the ocean ware;**

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.

2. Character of Commentators. — ThiB spirit of
commentation, as has already been suggested, turns
to questions of taste, of metaphysics, of morals, v^dth
far more avidity than to physics. Accordingly,
critics and grammarians were peculiarly the growth
of this school ; and, though the commentators some-
times chose works of mathematical or physical

• Strabo. i. p. 5.

THE COMMENTATORIAL SPIRIT. 269

science for their subject (as Proclus, who commented
on Euclid's Geometry, and Simplicius, on Aris-
totle's Physics,) these commentaries were, in fact,
rather metaphysical than mathematical. It does not
appear that the commentators have, in any instance,
illustrated the author by bringing his assertions of
facts to the test of experiment. Thus, when Sim-
plicius comments on the passage concerning a
vacuum, which we formerly adduced, he notices the
argument which went upon the assertion, that a
vessel full of ashes would contain as much water as
an empty vessel ; and he mentions various opinions
of different authors, but no trial of the fact. Eu-
demus 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'.

The commentator's professed object is to explain,
to enforce, to illustrate. He endeavours to adapt
the work on which he employs himself to the state
of information and of opinion in his own time ; to
elucidate obscurities and technicalities; to supply
steps omitted in the reasoning; but he does not
seek to obtain additional truths or new generaliza-
tions. He undertakes only to give what is virtually
contained in his author; to develope, but not to
create. He is a cultivator of the thoughts of others :
his labour is not spent on a field of his own ; he
ploughs but to enrich the granary of another man.

' Simplicius, p. 170.

270 PHYSICAL SCIENCE IN THE MIDDLE AGES.

Thus he does not work as a freeman, but as one
in a serrile condition ; or rather his is a menial,
and not a productiye service : his office is to adorn
the appearance of his master, not to increase his
wealth.

Yet though the commentator^s employment is
thus subordinate and dependent, he is easily led to
attribute to it the greatest importance and dignity.
To elucidate good books is» indeed, a useful task ;
and when those who undertake this work execute
it well, it would be most unreasonable to find fault
with them for not doing more. But the critic, long
and earnestly employed on one author, may easily
underrate the relative value of other kinds of mental
exertion. He may ascribe too large dimensions to
that which occupies the whole of his own field of
vision. Thus he may come to consider such study
as the highest aim, and best evidence of human
genius. To understand Aristotle, or Plato, may
appear to him to comprise all that is possible of
profundity and acuteness. And when he has
travelled over a portion of their domain, and satisfied
himself that of this he too is master, he may look
with complacency at the circuit he has made, and
speak of it as a labour of vast effort and difficulty.
We may quote, as an expression of this temper,
the language of Sir Henry Savile, in concluding
a course of lectures on Euclid, delivered at Oxford*.

* Exolvi per Dei gratiam, Domini auditores, promissum ;
liberayi fidem meam; expHcayi pro meo modulo, definitiones,

THE COMMENTATORIAL SPIRIT. 271

« 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 defi-
nitions, postulates, axioms, and first eight proposi->
tions 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 of the
commentator ; for undoubtedly, in many instances,
a comment 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 labours of learned men
in the stationary period, which came under this
description, belong to another class.

3. Greek Commentators on Aristotle. — ^The com-«
mentators or disciples of the great philosophers did
not assume at once their servile character. At first
their object was to supply and correct, as well as to
explain their teacher. Thus among the earlier com-
mentators 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 syllo-
gisms. He also, not only collected much informa-
tion concerning animals, and natural events, which

petitiones, communes sententias, et octo priores propositiones
Elementorum Euclidis. Hie, annis essus, cyclos artemque
repoDO.

272 PHYSICAL SCIENCE IN THE MIDDLE AGES.

Aristotle had omitted, but often differed wiiii his
master ; as, for instance, oonceming Hie 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*, who flourished in the third
century, wrote a book on the PredicaiieSf which was
found to be so suitable a complement to the Predi-
caments 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 modem times.
The Predicables are the five steps which the gradations
of generality and particularity introduce; — -gemtSi
spedes^ differmcey indimdncd^ accident; — ^the Categories
are the ten heads under which assertions or predi-
cations may be arranged ; — ^namely, substance^ qwm--
iHtyy relation^ qtiality, place^ time^ position^ habity action^
passion.

At a later period, the Aristotelian commentators
became more servile, and followed the author step
by step, explaining, according to their views, his
expressions and doctrines; often, indeed, with ex-
treme prolixity, expanding his clauses into sentences,
and his sentences into paragraphs. Alexander
Aphrodisiensis, who lived at the end of the second
century, is of this class ; " sometimes usefal," as one
of the recent editors of Aristotle says'; " but by the
prolixity of his interpretation, by his perverse itch

* Buhle, Arist. i. 284. « Bulile, i. 288.

THE COMMENTATORIAL SPIRIT. 273

for liimself discussing the argument expounded by
Aristotle, for defending his opinions, and for refuting
or reconciling those of others, he rather obscures
than enlightens." At various times, also, some of
the commentators, and especially those of the Alex-
andrian school, endeavoured 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 Alex-
andrian philosophers ^ as Alexander, Ammonius, and
others, employed themselves in the futile task of
reconciling the doctrines of the Pythagoreans, of the
Eleatics, of Plato, and of the Stoics, with those of
Aristotle. Boethius* entertained the design of
translating into Latin the whole of Aristotle's and
Plato's works, and of showing their agreement ; a
gigantic plan, which he never executed. Others
employed themselves in disentangling the confusion
which such attempts produced, as John the Gramma-
rian, surnamed Philoponus, "the labour-loving;" who,
towards the end of the seventh century, maintained
that Aristotle was entirely misunderstood by Por-
phyry and Proclus ', who had pretended to incorporate
his doctrines into those of the New Platonic school, or
even to reconcile him with Plato himselfon the subject
of ideas. Others, again, wrote epitomes, compounds,
abstracts; and endeavoured to throw the works
of the philosopher into some simpler and more

"^ BuHle, i. 311. • Degerando. Hist, des Syst. iv. 100.

. • lb. iv. 155.
VOL. I. T

274 PHYSICAL SCIENCE IN THE MIDDLE AGES.

obviously regillal* fomi, as John of DaHiascud^ in the
middle of the eighth century, who made abstracts of
some of Aristotle's works, and introduced the study
of the author into theological education. These two
tmters lived under the patronage of the Arabs J the
former was favoured by Amrou, the conqueror of
Egypt ; the latter was at first secretary to the Caliph,
but afterwards withdrew to a monastery ^•.

At this period the Arabs became the fosterei*s alid
patrons of philosophy rather than the Greeks. Jus-
tinian had, by an edict, closed the school of Athens^
the last of the schools of heathen philosophy. Ledj
the Isaurian, who was a zealous Iconoclast^ abolished
also the schools where general knowledge had been
taught, in combination with Christianity^*; yet the
line of the Aristotelian commentators was continued^
though feebly, to the later ages of the Greek empire^
Anna Comnena^' mentions a Eiistratus who em-
ployed himself upon the dialectic aiid moral treatises,
and whom she does not hesitate to elevate above
the Stoics and Platonists, for his talent in philoso-
phical discussions. Nicephorus Blemmydes wrote
logical and physical epitomes for the use of John
t)ucasj George Pachymeus 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

'' Beg. iv. 150. '' lb. iv. 163 ^» lb. 167.

THE COMMENTATORIAL SPIRIT. 275

Physics, on the Soul, the Heavens'*, &c. Fabricius
states that this writer has a chapter, the object of
which is to prove, that all philosophers, and Aristotle
and Plato in particular, have disdained the authority
of their predecessors. He could hardly help re-
marking, in how different a spirit philosophy had
been pursued since their time.

8. Greek Commentators of Plato and others. — I
have spoken principally of the commentators of
Aristotle, for he was the great subject of the com-
mentators 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 doc-
trines 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 multi-
plied itself Porphyry, who commented on Aristotle,
was commented on by Ammonius ; Plotinus's En-
neads were commented on by Proclus and Dexippus.
Psellus^* the elder was a paraphrast of Aristotle;
Psellus the younger, in the eleventh century, at-
tempted to restore the New Platonic school. The
former of these two writers had for his pupils two
men, the emperor Leo, sumamed the Philosopher,
and Photius the patriarch, who exerted themselves
to restore the study of literature at Constantinople.

18

Deg. ir. 168. " lb. ir. 169.

T 2

276 PHYSICAL SCIENCE IN THE MIDDLE AGES.

We still possess the Collection of Extracts of Photius,
which, like that of Stobseus and others, shows the
tendency of the age to compilation, abstracts, and
epitomes, — ^the extinction of philosophical vitality.

4. Arabian Commentators of Aristotle.— The reader
might perhaps have expected, that when the philo-
sophy of the Greeks was carried among a new race
of intellects, of a different national character and
condition, the chain of this servile tradition would
have been broken ; that some new thoughts would
have started forth ; that some new direction, some
new impulse, would have been given to the search
for truth. It might have been anticipated that we
should have had schools among the Arabians which
should rival the Peripatetic, Academic and Stoic
among the Greeks ; — ^that they would preoccupy the
ground on which Copernicus and Galileo, Lavoisier
and Linnaeus, won their fame; — ^that they would
make the next great steps in the progressive sciences.
Nothing of this, however, happened. The Arabians
cannot claim, in science or philosophy, any really
great names; they produced no men and no dis-
coveries which have materially influenced the course
and destinies of human knowledge; they tamely
adopted the intellectual servitude of the nation
which they conquered by their arms ; they joined
themselves at once to the string of slaves who were
dragging the car of Aristotle and Plotinus. Nor,
perhaps, on a little further reflection, shall we be
surprised at this want of vigour and productive

THE COMMENTATORIAL SPIRIT. 277

power, in this period of apparent natural youth.
The Arabs had not been duly prepared rightly to
enjoy and use the treasures of which they thus
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 philo-
sophy without having passed through those grada-
tions of ardent curiosity and keen research, of ob-
scurity brightening into clearness, of doubt succeeded
by the joy of discovery, by which the Greeks had
had their minds enlarged and exercised. Nor had
the Arabs ever enjoyed, as the Greeks had, the in-
dividual consciousness, the independent volition, the
intellectual freedom, arising from the freedom of poli-
tical institutions. They had not felt the contagious
mental activity of a small city ; the elation arising
from the general sympathy in an admiration of specu-
lative pursuits dijffused through an intelligent and
acute audience ; in short, they had not had a national
education such as fitted them to be disciples of Plato
and Hipparchus. Hence, their new literary wealth
rather encumbered and enslaved, than enriched and
strengthened them : in their want of taste for intel-
lectual 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

278 PHYSICAL SCIENCE IN THE MIDDLE AGES.

Koran also. Thus the Arabians, though they never
translated the Greek poetry, translated, and merely
translated, the Greek philosophy ; they followed the
Greek philosophers without deviation, or, at least,
without any philosophical deviations. They became
for the most part Aristotelians ; — studied not only
Aristotle, but the commentators of Aristotle ; and
themselves swelled the vast and unprofitable herd*

The philosophical works of Aristotle had, in some
measure, made their way in the east, before the
growth of the Saracen power. In the sixth century,
a Syrian, Uranus'*, encouraged by the love of philo^
JKjphy manifested by Cosroes, had translated some
of the writings of the Stagirite; about the same
time, Sergius had given some translations in Syriac.
In the seventh century, Jacob of Edessa translated
into this language the Dialectics, and added Notes to
the work. Such labours 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 philo-
sopher a tinge of opinions borrowed from another
source, which I shall have to speak of under the
name of mysticism. But they are, for the most
part, sufficiently strong examples of the peculiar

'' Deg. iv. 196.

THE COMMBNTATORIAI4 SPIRIT. 279

spirit of compientatiou, to make it fitting to notice
thPW here. At the head of them stands '• Alkindi,
who 9;ppears 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,
aatrojiomy, medicine and philosophy. Born in an
elevated rank, and possessed of a rich patrimony, he
led an austere life, and devoted himself altogether
to study and meditation. He employed himself
particularly in unfolding the import of Aristotle's
treatise on the Soul, Avicenna'^ (Ebn Sina) was at
once the Hippocrates and the Aristotle of the Arar
bians; and certainly the most extraordinary man
that the nation produced. In the course of an un-r
fortunate and stormy life, occupied by politics and
by pleasures, he produced works which \vere 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 Montpellier,
till the end of the seventeenth century, at which
period they fell into an almost complete oblivion.
Avieenna is conceived, by some modem writers '^ to
have shown some power of original thinking in his
representations of the Aristotelian Logic and Meta-

»• Deg. It. 187. '^ lb. iv. 205.

^« lb. ir. 206.

280 PHYSICAL SCIENCE IN THE MIDDLE AGES.

physics. Averroes (Ebn Roshd) of Cordova, was
the most illustrious of the Spanish Aristotelians, and
became the guide of the schoolmen'*, 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 Commenkttor ; and he deserves this title by the
servility with which he maintains that Aristotle*'
carried the sciences to the highest possible degree,
measured their whole extent, and fixed their ulti-
mate and permanent boundaries ; although his works
are conceived to exhibit a trace of the New Plato-
nism. Some of his writings are directed against
an Arabian sceptic, 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 main-
tained it, their philosophy went further than a
system of mere commentation, and became a system
of dogmatism ; we must, therefore, in another chap-
ter, say a few words more of the Aristotelians in
this point of view, before we proceed to the revival
of science ; but we must previously consider some
other features in the character of the Stationary
Period.

*• Deg. iy. 247. Ayerroes died a. d. 1206. " Deg. iy. 248.

281

CHAPTER HI.

Op the Mysticism of the Middle Ages.

It has been already several times hinted, that a new
and peculiar element was introduced into the Greek
philosophy which occupied the attention of the
Alexandrian school ; and that this element tinged a
large portion of the speculations of succeeding ages.
We may speak of this peculiar element as mysticism ;
for, from the notion usually conveyed by this term,
the reader will easily apprehend the general cha-
racter of the tendency now spoken of; and espe-
cially 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
connexion and causation, men attempted to reduce
such occurrences under spiritual and supersensual
relations and dependencies ; they referred them to
superior intelligences, to theological conditions, to
past and ftiture events in the moral world, to states
of mind and feelings, to the creatures of an imagi-
nary mythology or demonology. And thus their
physical science became magic, their astronomy be-
came astrology, the study of the composition of
bodies became alchemy, mathematics became the
contemplation of the spiritual relations of number
and figure, and philosophy became theosophy.

282 PHYSICAL SCIENCE IN THE MIDDLE AGES.

The examination of this feature in the history of the
human mind is important for us^ in consequence of its
influence upon the employments and the thoughts
of the tunes now under our notice. This tendency
materially affected both men's speculations and
their labours in the pursuit of knowledge. By its
direct operation, it gave rise to the newer Platonic
philosophy among the Greeks, and to corresponding
doctrines among the Arabians ; and by calling into
a prominent place astrology, alchemy, and magic, it
long occupied most of the real observers of the
material world. In this manner it delayed and 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 misdireo-
tion of their efforts, than it gained by any increase of
zeal arising from the peculiar hopes and objects of
the mystics.

It is not to 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 ten-
dencies of thought which accompanied the retrogra-
dation of inductive science. And of these, the lead-
ing feature which demands our notice is that already
alluded to ; namely, the practice of referring things
and events, not to clear and distinct relations, obvi-
ously applicable to such cases ;-r-not to general rules
capable of direct verification ; but to notions vague,
distant, and vast, which we cannot bring into con-

THEIB MYSTICISM. 283

taet 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 spiri-
tual 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. Neophionic Theosophy. — The Newer Plor
tonism is the first example of this mystical philo-
sophy which I shall consider. The main points
which here require our notice are, the doctrine of an
intellectual world resulting from the act of the
Divine Mind, as the only reality ; and the aspiration
after the union of the human soul with this Divine
Mind, as the object of human existence. The
*' ideas" of Plato were forms of our knowledge ;
but among the Neoplatonists they became really
existing, indeed the only really existing, objects;
and the inaccessible scheme of the universe which
these ideas constitute, was offered as the great sub-
ject of philosophical contemplation. The desire of
the human mind to approach towards its Creator
and Preserver, and to obtain a spiritual access to Him,
leads to an employment of the thoughts which is well
worth the notice of the religious philosopher ; but
such an effort, even when founded on revelation and
well regulated, is not a means of advance in physics :

284 PHYSICAL SCIENCE IN THE MIDDLE AGES.

and when it is the mere result of natural enthu-
siasm, it may easily obtain such a place in men's
minds as to unfit them for the successful prosecution
of natural philosophy. The temper, therefore, which
introduces such supernatural communion into the
general course of its speculations, may be properly
treated as mystical, and as one of the causes of the
decline of science in the Stationary Period. The
Neoplatonic philosophy requires our notice as one
of the most remarkable forms of this mysticism.

Though Ammonius Saccas, who flourished at the
end of the second century, is looked upon as the
beginner of the Neoplatonists, his disciple Plo-
tinus is, in reality, the great founder of the school,
both by his works, which still remain to us, and by
the enthusiasm which his character and manners in-
spired among his followers. He lived a life of medi-
tation, gentleness, and self-denial, and died in the
second year of the reign of Claudius (a. d. 270.)
His disciple, Porphyry, has given us a Life of him,
from which we may see how well his habitual man-
ners were suited to make his doctrines impressive.
" Plotinus, the philosopher of our time," Porphyry
thus begins his biography, " appeared like a person
ashamed that he was in the body. In consequence
of this disposition, he could not bear to talk con-
cerning his family, or his parents, or his country.
He would not allow himself to be represented by a
painter or statuary ; and once^ when AureUus en-
treated him to permit a likeness of him to be taken,

THEIR MYSTICISM. 285

he said, * Is it not enough for us to carry this image
in which nature has enclosed us, but we must also try
to leave a more durable image of this image, as if it
were so great a sight V And he retained the same
temper to the last. When he was dying, he said,
* I am trying to bring the divinity which is in us to
the divinity which is in the universe.' " He was
looked upon by his successors with extraordinary
admiration and reverence ; and his disciple Porphyry
collected from his lips, or from fragmental notes, the
six Enneads of his doctrines (that is, parts each
consisting of nhie books,) which he arranged and
annotated.

We have no difficulty in finding in this remark-
able work examples of mystical speculation. Besides
the general tendency of the doctrines, the intelli-
gible world of realities or essences corresponds to
the world of sense ^ in the classes of things which it
includes. To the intelligible world, man's mind
ascends, by a triple road which Plotinus figuratively
calls that of the musician, the lover, the philo-
sopher*. The activity of the human soul is identi-
fied 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

^ vi Ennead iii. 1. ' ii E. ii. 2.

286 PHYSICAL SCIENCE IN THE MIDDLE AGES.

the sphere revolres about its centre, the soul
revolves about God through its affections^'*

The conclusion of the work is", as might be sup-
posed, upon the approach to, union with, and fruition
of God. The author refers again to the analogy
between the movements of the soul and those of
the heavens. " We move round him like a choral
dance; even when we look from him we revolve
about him ; we do not always look at him, but when
we do, we have satisfaction and rest, and the har-
mony which belongs to that divine movement. In
this movement, the mind beholds the fountain of
life, the fountain of mind, the origin of being, the
cause of good, the root of the soul*." ** There will
be a time when this vision shall be continual ; the
mind being no more interrupted, nor suflfering any
perturbation from the body. Yet that which be-
holds is not that which is disturbed ; and when this
vision becomes dim, it does not obscure the know-
ledge which resides in demonstration, and faith, and
reasoning ; but the vision itself is not reason, but
greater than reason, and before reason*."

The fifth book of the third Ennead, has for its
isubject the Daemon which belongs to each man. It
is entitled " Concerning Love ;" and the doctrine ap-
pears 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*." These

« vi Enn. ix. 8. * lb. 9. ' lb. 10.

' Ficinus, Comm. in y. Enn. iii.

THEIR MYSTICISM. 287

deemons were, however, (at least by later writers,) in-
vested with a visible aspect and with a personal cha-
i*aeter, including a resemblance of human passions and
inbtives. 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 ima-
gination soon produced pretensions to the power of
Inaking these daemons or genii visible ; and the Trea-
tise on the Mysteries of the Egyptians, which is attri-
buted to lamblichus, 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 at-
tempts to claim a high antiquity for this system^
knd to make Orpheus, the poet, the first promulgator
of its doctrines. The system, like all mystical sys*-
terns, assumed the character rather of a religion than
of a theory. The opinions of its disciples materially
influenced their lives. It gave the world the spec-
tacle of an austere morality, a devotional exaltation,
combined With the grossest superstitions of Paganism.
The successors of lamblichus appeared rather to
hold a priesthood, than the chair of a philoso-
phical schools They were persecuted by Constan-
tino and Constantius, as opponents of Christianity.

' Deg. iii. 407.

288 PHYSICAL SCIENCE IN THE MIDDLE AGES.

Sopater, a Syrian philosopher of this school, was
beheaded by the former emperor, on a charge that
he had bound the winds by the power of magic'.
But Julian, who shortly after succeeded to the
purple, embraced with ardour the opinions of lam-
blichus. Proclus (who died A. D. 487,) was one of the
greatest of the teachers of this school"; and was,
both in his Ufe and doctrines, a worthy successor of
Plotinus, Porphyry, and lamblichus. We possess a
biography, or rather a panegyric of him, by his dis-
ciple Marinus, in which he is exhibited as a repre-
sentation of the ideal perfection of the philosophic
character, according to the views of the Neopla^
tonists. His virtues are arranged as physical,
moral, purificatory, theoretic, and theurgic. Even
in his boyhood, Apollo and Minerva visited him in
his dreams : he studied oratory at Alexandria, but it
was at Athens that Plutarch and Lysianus initiated
him in the mysteries of the New Platonists. He
received a kind of consecration at the hands of the
daughter of Plutarch, the celebrated Asclepigenia,
who introduced him to the traditions of the Chal-
deans, and the practices of theurgy; he was also
admitted to the mysteries of Eleusis. He became
celebrated for his knowledge and eloquence; but
especially for his skill in the supernatural arts which
were connected with the doctrines of his sect. He
appears before us rather as a hierophant than a
philosopher. A large portion of his life was spent in

• Gibbon, iii. 352. • beg. iii. 419.

THEIR MYSTICISM. 289

evocations, purifications, fiistings, prayers, hjnmns, in-
tercourse with apparitions, and with the gods, and in
the celebration of the festivals of Paganism, especially
those which were held in honour 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 in
the world. Accordingly, he composed hymns in
honour of all the divinities of Greece, Rome, Egypt,
Arabia ; — ^Christianity alone was excluded from his
favour.

2. Mystical Aritiimetic. — It is unnecessary further
to exemplify, from Proclus, the general mystical
character of the school and time to which he be-
longed; but we may notice more specially one of the
forms of this mysticism, which very frequently offers
itself to our notice, especially in him ; and which we
may call mystical arithmetic. Like all the kinds of
mysticism, this consists in the attempt to connect
our conceptions of external objects by general and
inappropriate notions of goodness, perfection, and
relation to the divine essence and government; in-
stead of referring such conceptions to those appro-
priate ideas, which, by diie attention, become per-
fectly distinct, and capable of being positively ap-
plied 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 qjore naturally than any
other. For number is really applicable to moral

VOL. I. u

290 PHYSICAL SCIENCE IN THE MIDDLE AGES.

notions, — ^to emotions and feelings, and to their ob-
jects, — 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 unex-
pectedly, that numerical relations were closely con-
nected with sounds which could hardly be distin-
guished f5pom 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, when men were willing to follow
them into darkness and vagueness; which it is
precisely the mystical tendency to do. Accord-
ingly, this kind of speculation appeared very early,
and showed itself first among the Pythagoreans,
as we might have expected, from the attention
which they gave to the theory of harmony: and
this, as well as some other of the doctrines of
the Pythagorean philosophy, was adopted by the
later Platonists, and, indeed, by Plato himself, whose
speculations concerning number have decidedly a
mystical character. The mere mathematical propor-
tions of numbers,-^s odd and even, perfect and im-
peri^ect, abundant and defective,--.were, by a willing
submission to an enthusiastic bias, connected with
the notions of good and beauty, which the terms
suggested ; and principles^resulting from such a con-
nexion were woven into a wide and complex system.

THEIR MYSTICIgM. 291

It is not necessary to dwell long on this subject; the
mere titles of the works which treated of it show its
nature. Archytas** is said to have written a treatise
on the number ten: Telauge, the daughter of Pytha-
goras, wrote on the number four. This number,
indeed, which was known by the name of the 7V-
tractys, was very celebrated in the school of Pytha-
goras. It is mentioned in the " Golden Verses,"

«

which are ascribed to him: the pupil is conjured to
be virtuous,

Nai jxib Tov afierepa '^^v'x^a irapahovra T€rpa)(rvv
Ilarfav Aevvdov (jyvaeat)^

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

In Plato's works, we have evidences of a similar
belief in religious relations of number ; and in the
New Platonists, this doctrine was established as a
system. Proclus, of whom we have been speaking,
founds his philosophy, in a great measure, on the
relation of unity and multiple ; from this, he is led
to represent the causality of the Divine Mind by
three triads of abstractions ; and in the developement
of one part of this system, the number seven is
introduced * *. " The intelligible and intellectual gods
produce all things triadically; for the monads in
these are divided according to number; and what
the monad was in the former, the number is in the
latter. And the intellectual gods produce all things

** Mont. ii. 123. " Procl. v. 3., Taylors Translation.

U 2

292 PHYSICAL SCIENCE IN THE MIDDLE AGES.

•

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 geometrical properties being associated
with such physical and metaphysical notions as
vague thought and lively feeling could anyhow
connect with them. We may consider, as an ex-
ample of this^', Plato's opinion concerning the par-
ticles of the four elements. He gave to each kind
of particle one of the five regular solids, about which
the geometrical speculations of himself and his
pupils had been employed. The particles of fire
were pyramids, because they are sharp, and tend
upwards ; those of earth are cubes, because they are
stable, and fill space ; the particles of air are octahe-
dral, as most nearly resembling those of fire ; those
of water are icositetrahedron, as most nearly spheri-
cal. The dodecahedron is the figure of the element
of the heavens, and shows its influence in other
things, as in the twelve signs of the zodiac; we see

i«

Stanley, Hist. Phil.

THEIR MYSTICISM. 293

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 Bungo and Kircher, who have written De
Mysteriis Numerorum. Bungo treats of the mysti-
cal 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^', 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 calr
culators, or with reference to Judaical Sabbatarian
notions.

3. Astrology. — Of all the forms which mysticism
assumed, none was cultivated more assiduously
than astrology. Although this art prevailed most
universally and powerfully during the stationary
period, its existence, even as a detailed technical
system, goes back to a very early period. It pro-
bably had its origin in the East ; it is universally
ascribed to the Babylonians and Chaldeans; the
name Chaldean was, at Rome, synonymous with
mathematictis^ or astrologer ; and we read repeatedly
that this class of persons were expelled from Italy

^^ Montucla, i. 511.

294 PHYSICAL SCIENCE IN THE MIDDLE AGES.

by a decree of the senate, both during the times of
the republic and of the empire^*. The recurrence
of this act of legislation shows that it was not effec-
tual ; " It is a class of men," says Tacitus, " which,
in our city, will always be prohibited, and will alM'ays
exist." In Greece, it does not appear that the state
showed any hostility to the professors of this art.
They undertook, it would seem, then, as at a later
period, to determine the course of a man's character
and life from the configuration of the stars at the
moment of his birth. We do not possess any of
the speculations of the earlier astrologers ; and we
cannot therefore be certain that the feelings 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 ori-
ginally suggested by mythological belief. The Greeks
spoke of the influences or effliuves {airoppota^;) which
proceeded from the stars ; but the Chaldeans had
probably thought rather of the powers which they
exercised as deities. In whatever manner the sun,
moon, and planets came to be identified with gods
and goddesses, it is clear that the characters ascribed
to these gods and goddesses regulate the virtues
and powers of the stars which bear their names.
This association, so manifestly visionary, was retained,

** Tacit. Ann. ii. 32. xii. 52. Hist. I. 22, II. 62.

THEIR MYSTICISM. 295

amplified, and pursued, in an enthusiastic spirit,
instead of being rejected for « more distinct and
substantial connexions ; and a pretended science
was thus formed, which bears the obvious stamp
mysticism.

That common sense of mankind which teaches
them that theoretical opinions are to be calmly tried
by their consequences and their accordance with
facts, appears to have counteracted the prevalence
of astrology in the better times of the human mind.
Eudoxus, as we are informed by Cicero^*, rejected the
pretensions of the Chaldeans; and Cicero himself
reasons against them with arguments as sensible and
intelligent as could be adduced by a writer of the pre-
sent day ; such as the different fortunes and charac-
ters of persons born at the same time ; and the failure
of their predictions, in the case of Pompey, Crassus,
Caesar, to whom they had foretold glorious old age
and peaceful death. He also employs an argument
which the reader would perhaps not expect from
him ; — the very great remoteness of the planets as
compared with the distance of the moon. ** What
contagion can reach us," he asks, " from a distance
almost infinite ?"

Pliny argues on the same side, and with some of
the same arguments ^•. " Homer," he says, " tells
us that Hector and Polydamas Were born the same
night ; — ^men of such different fortune. And every

" Cic. de Dir. ii. 42. '' Hist. Nat. vii. 49.

296 PHYSICAL SCIENCE IN THE MIDDLE AGES.

hour, in every part of the world, are bom lords and
slaves, kings and beggars."

The impression made by these arguments is
marked in an anecdote told concerning Publius
Nigidius Figulus, a Roman of the time of Julius
Caesar, whom Lucan mentions as a celebrated astro-
loger. It is said, that when an opponent of the art
urged as an objection the different fetes of persons
bom in two successive instants, Nigidius bade him
make two contiguous marks on a potter's wheel,
which was revolving rapidly near them. On stop-
ping 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 argu-
ment, says St. Augustine, who gives us the narra-
tive, 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*^ 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 their predictions, by

'"^ Ann. vi. 22.

THEIR MYSTICISM. 297

the ignorance of those who profess the art ; and that
thus the art is unjustly blamed, confirmed as it is by
noted examples in all ages." The occasion which
gives rise to these reflections of the historian is the
mention of Thrasyllus, the favourite astrologer of
the Emperor Tiberius, whose skill is exemplified in
the following narrative. Those who were brought
to Tiberius on any important matter, were admitted
to an interview in an apartment situated on a lofty
cliff in the island of Caprese. They reached this place
by a narrow path, accompanied by a single freedman
of great bodily strength ; and on their return, if the
emperor had conceived any doubts of their 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 examined the aspect of the stars, and
while he did this, as the narrative states, showed
hesitation, alarm, increasing terror, and at last de-
clared 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 of practical energy,
naturally had a more complete sway among the spe-

298 PHYSICAL SCIENCE IN THE MIDDLE AGES.

culatlve but unstable minds of the later philosophi-
cal schools of Alexandria, Athens, and Rome. We
have a treatise on astrology by Proclus, which will
serve to exemplify the mystical principle in this
form. It appears as a commentary on a work on
the same subject called " Tetrabiblos," ascribed to
Ptolemy ; though we may reasonably doubt whether
the author of the " Megale Syntaxis" was also the
writer of the astrological work. A few notices of
the commentary of Proclus will suffice '^ The
science is defended by urging hotv powerful we
know the physical effects of the heavenly bodies to
be. " The sun regulates all things on earth ; — ^the
birth of animals, the growth of fruits, the flowing
of waters, the change of health, according to the
seasons ; he produces heat, moisture, dryness, cold,
according to his approach to our zenith. The moon,
which is the nearest of all bodies to the earth, gives
out much influence ; and all things, animate and in-
animate, sympathize with her ; rivers increase and
diminish according to her light ; the advance of the
sea, and its recess, are regulated by her rising and
setting ; and along with her, fruits and animals wax
and wane, either wholly or in part." It is easy to
see that by pursuing this train of associations (some
real and some imaginary) very vaguely an^ very
enthusiastically, the connexions which astrology
supposes would receive a kind of countenance.
Proclus then proceeds to state ^' the doctrines of the*

" L 2- '' I. 4.

t I' »f f '• • w

Irr

THEIR MYSTICISM. 299

f

science. " The sun," he says, " is productive of
heat and dryness; this power is moderate in its
nature, but is more sensible 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 vapours 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 heat-
ing power of the sun, and the moist vapours of the
eaitb. -His cold, however, is most prevalent, his
dryness is more moderate. Both he and the rest
receive addi'tional powers from the configurations
which they make with respect to the sun and moon."
In jij^e same manner it is remarked that Mars is dry
mid caustic, from his fiery nature, which, indeed, his
colour 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 malefic effect of these
stars. Heat and moisture are generative and crea-
tive 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 connexions. Some are masculine,

300 PHYSICAL SCIENCE IN THE MIDDLE AGES.

and some feminine : the moon and Venus are of
the latter kind ; this appears to be merely a mytho-
logical or etymological association. Some are diurnal,
some nocturnal; the moon and Venus are of the
latter kind, the sun and Jupiter of the former;
Saturn and Mars are both.

The fixed stars, also, and especially those of the
zodiac, had especial influences and subjects assigned
to them. In particular, each sign was supposed to
preside over a particular part of the body; thus
Aries had the head assigned to it, Taurus the neck,
and so on.

The most important part of the sky in the astro-
loger'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 home ; the whole circuit of the heavens
being divided into twelve houses, in which life and
death, marriage and children, riches and honours,
friends and enemies were distributed.

We need not attempt to trace the progress of
this science. It prevailed extensively among the
Arabians, as we might expect from the character of
that nation. Albumasar, of Balkh in Khorasan,
who fl,ourished in the. ninth century, who was one of
their greatest astronomers, was also a great astro-
loger ; and his work on the latter subject, " De
Magnis Coiyunctionibus, Annorum Bevolutionibus
ac eorum Perfectionibus," was long celebrated in
Europe. Aboazen Haly (the writer of a treatise

THEIR MYSTICISM. 301

De Judiciis Astronom.) who lived in Spain in the
thirteenth century, was one of the classical authors
on this subject.

It will easily be supposed that when this apoteles-
matic or Judicial astrology obtained firm possession of
men's minds, it would be pursued into innumerable
subtle distinctions and extravagant conceits; and
the more so, as experience could offer little or no
check to such exercises of fancy and subtlety. For
the correction of rules of astrological divination by
comparison with known events, though pretended to
by many professors of the art, was far too vague and
fallible a guidance to be of any real advantage.
Even in what has been called natural astrology, the
dependence of the weather on the heavenly bodies,
it is easy to see what a vast accumulation of well-
observed facts is requisite to establish any true rule;
and it is well known how long, in spite of facts,
false and groundless rules (as the dependence of the
weather on the moon) may keep their hold on men's
minds. When the facts are so loose and many-sided
as human characters, passions, and happiness, it was
hardly to be expected that even the most powerfiil
minds should be able to find a footing suflBiciently
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 connexion of the stars with human
persons and actions was, for a long period, undis-
puted. The vague, obscure, and heterogenous cha-

302 PHYSICAL SCIENCE IN THE MIDDLE AGES.

racter of such a connexion, and its unfitness for any
reallj scientific reasoning, could, of course, never be
got rid of: and the bewildering feeUng of earnest-
ness and solemnity, with which the connexion of the
heavens with man was contemplated, never died
away. In other respects, however, the astrologers
fell into a servile commentatorial spirit; and em*
ployed themselves in annotating and illustrating the
works of their predecessors to a considerable extent,
before the revival of true science.

It may be mentioned, that astrology has long been,
and probably is, an art held in great esteem and
admiration among other eastern nations besides the
Mohammedans : for instance, the Jews, the Indians,
the Siamese, and the Chinese. The prevalence of
vague, visionary, and barren notions among these
nations, cannot surprise us ; for we have no evidence
from them, as from Europeans w6 have, that they
are capable, on subjects of physical speculation, of
originating sound and rational general principles.
The arts may have had their birth in all parts of the
globe ; but it is only Europe, at particular favoured
periods of its history, which has ever produced
sciences.

We are, however, now speaking of a long period,
during which this productive energy was interrupted
and suspended. During this period Europe de-
scended, in intellectual character, to the level at
which the other parts of the world have always stood.
Her science wfis then a mixture of art and mysticism ;

THEIR MYSTICISM. 803

we have considered several forms of this mysticism,
but there are two others which must not pass
unnoticed, alchemy and magic.

We may observe, before we proceed, that the
deep and settled influence which astrology had ob-
tained among men, 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,
Brahe, Francis Bacon, are examples of this. These,
or most of them, rejected all the more obvious and
extravagant fallacies with which the subject had
been loaded ; but still conceived that some real and
valuable truth remained when all these were re-
moved. Thus Campanella", whom we shall have to
speak of as one of the first opponents of Aristotle,
wrote an " Astrology purified from all the Supersti-
tions of the Jews and Arabians, and treated physio-
logically."

4. Alchemy. — Like other kinds of mysticism,
alchemy seems to have grown out of the notions of
moral, personal, and mythological qualities, which
men associated with terms, of which the primary
application was to physical properties. This is the
form in which the subject is presented to us in the
earliest writings which we possess on the subject of

■^ Bacon, De Aug. ill. 4.

304 PHYSICAL SCIENCE IN TH& MIDDLE AGES.

chemistry ; — thos^ of G^er" of S^^yiUe, wixp-i^ -SHp-
posed to have lived in the eighth, or .pi^th, qcfatjiry.
The very titles of Giber's wprks shaw the iiQ^^cffia
on which his pretended SQience prweetdpi . T3iey -arex
«0f the. Search of Perfpctigji ;" "Of .tllft.^^i^f
Perfection, pr of the Perfect Magistery ; ' ," Of .^^
Invention of Verity, or Perfp^tion,". The basis, <rf
this phraseology is the distinction of me^Qjis>in^Q more,
or less perfect ; gold being the mo«t p^rfqct, aa;be{Qg
the most, valuable, most beautiful, most purei.i!!)j5st
durable ; silver the next ; and so on. The " S^soreh
of Perfeption," was, therefore^ tlie at|;eq[ipt;to.cpn^i^^
other metals into gold; and doctrines, were a^Qpted
\f hich repifesented the metids as aU coinpoupded of.
the ^am^ elementSi so that this w^ts theoretiiCaHy
po^iWe.. But the myst^ic^ trwjs of. asscfciation w€a«-
pursued, loiuch j&iri^er. than this ; gpld a^d silveiJ were
hpld to be the most n^Aie of metals ^ gold was th^
king, and silver their /quieen. My thcJogical . associa-
tipns w^e wUbii^ siid pf Ibeiie'feiideB^ a« had. been
dpne in. astrology.. Gqld.MlasBpl, the sun; tilvenwas.
Luna, the m(>on ; jeoppeor, iron^ tint,, load, were assigned
to Venusi M^rs^Juipiter^i Satujrn. The processes of
mixture and heat were spoken of a$ personal aetions
and relations, struggles and victpriqs. iSome ele*-
ments were conquerors, som^e . conquered ; there. «x<^
isted preparations which possessed the power of
changing the whole of a body into a substance of

•^ Thoflnaons Hist, of Chem. i. II7.

THEIR MYSTICISM. 805

another kind : these were called magisterie$*\ 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 chemi«
cal operations were described in phraseology of this
sort, the enthusiasm of the fancy would be added to
that of the hopes, and observation would not be per-
mitted to correct the delusion, or to suggest sounder
and more rational views.

The exaggeration of the vague notion of perfec
tion and power in the object of the alchemist's
search, was carried further still. The same prepa-
ration which possessed the faculty of turning baser
jnetals 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 philosopAers^ stone was finally in-
vested with every desirable efficacy which the fimcy
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 sci-
ence is founded, if they had not been animated by
the hopes and the energy which the delusive art
inspired. To judge whether this is truly said, we
must be able to estimate the degree of interest
which men feel in purely speculative truth, and in
the real and substantial improvement of art to

** Boyle. Thomson's Hist. Ch. i. 25. Carolus Musitanus.
VOL. I. X

806 PHYSICAL SOIENCB IN THE KIDDLE AGES.

which it leads. Since the fell of alchemy, and thc^
progress of real chemistry, these motiyes have be^i
powerfid enough to engage in the study of the science»
a body fitr larger than the alchemists ever were^ and
no less zealous. There is no apparent reason why tiie
result should not have been the same, if the progress
of true science had begun sooner. Astronomy was
long cultivated without the bribe of astrology. But,
perhaps, we may justly say this ;~*>that, in the station*
aiy period, men's minds were so far enfeebled and
degraded, that pure speculative truth had not its ftill
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 con-
dition, is perpetually directed to something above the
mere objects of sense and appetite ^^-^-Or contrivance
of compensation, as it were, in the intellectual and
spiritual constitution of man.

5. illf<z^f(;.«— Magical arts, so &r as they were be-
lieved in by those who professed to practise them,
and so &r as they have a bearing in science, stand
on the same footing as astrology; and, indeed, a
close alliance has generally been maintained between
the two pursuits. Incapacity and indisposition to
perceive natural and philosophical causation, an en-
thusiastic imagination, and such a faith as can devise
and maintain supernatural and i^lritual connexion)^
are the elements of this, as of other forms of mysti-
cism. And thus that temper which led men to aim

THBim MYSTICISM. 80?

at the magician's supposed authority over the ele-
ments, is an additional exemplification of those habits
of thought which prevented the progress of real
science, and the acquisition of that command over
nature which is founded on science, during the iU'^
terval 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 emi*
nent for great speculative or practical knowledge, is
a feature of those times, which shows how extensive
and complete was the inability to apprehend the
nature of real science. In cultivated and enligh«
tei^ed periods, such bb those of ancient Greece, or
modem 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,how-
eveif high the philosopher may be raised above the
multitude, they can catch glimpses of the interven-
ing path, and see that it is open to all, and that
elevation is the reward of energy and labour. 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

X2

308 PHYSICAL SC3ENCS IN THE MIDDLE AGES.

with the learned man: they see him above them^
but know not how he is raised or supported : he
beoomes an olject of aversion and envy, of vague
susjHcion and terror ; and these emotions are emr-
bodied and confirmed by association with the &ncies
and dogmas of superstition. To consider sup^or
knowledge as magic, and magic bb 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 &me, 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 Ma-
gicians, 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, Baymund Lully, Arnold
de Villa Nova, Peter of Apono, and Paracelsus, had
incurred the black suspicion as physicians or alche-
mists* Thomas Aquinas, Roger Bacon, Michael
Scot, Picus of Mirandula, and Trithemius, had nat
escaped it, though ministers of religion. Ev^i dig-
nitaries, such as Robert Grosteste, bishop of Lincohi,
Albertus Magnus, bishop of Ratisbon, Popes Syl-
vester the Second, and Gregory the Seventh, had
been involved in the wide calumny. In the same
way in which the vulgar confounded the eminent
learning and knowledge which had appeared in recent
times, with skill in dark and supernatural arts, they

THfilR MYSTICISM. 809

converted into wizards all the best-known names in
the rolls of fame; as Aristotle, Solomon, Joseph,
Pythagoras ; and, finally, the poet Virgil was a power-
fill and skilful necromancer, and this fancy was ex-
emplified 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
promliient features in the intellectual character of
the world, for a long course of centuries. The
theosophy and theurgy of the Neoplatonists, the
mystical arithmetic of the Pythagoreans and their
successors, the predictions pf the astrologers, the
pretences of alchemy and magic, represent, not un-
fairly, the general character and disposition of men's
thoughts, with reference to philosophy and science.
That there were stronger minds, which threw off in
a greater or less degree this train of delusive and
unsubstantial ideas, is true ; as, on the other hand,
mysticism, among the vulgar or the foolish, often
went to an extent of extravagance and superstition,
of which I have not attempted to convey any con-
ception. The lesson which the preceding survey
teaches us is, that during the stationary period,
mysticism, in its various forms, was a leading cha-
racter, both of the common mind, and of the specu-
lations of the most intelligent and profound reasoners;
and that this mysticism was the opposite of that
habit of thought which we have stated science to
require; namely, clear ideas, distinctly employed to

SIQ PHYSICAL SCIENCB IN THE MIDDLE AGES.

conneot weU-«scertained facts ; inadmuch asrthe ideas
in which it dealt were vague and unstable, and the
temper in which they were contemplated was an
urgent and aspiring enthu8ia«n» which could not
submit to a calm conference with experience upon
even terms. The fervour of thought in some degree
supplied the place of reason in producing belief;
but opinions so obtained had no enduring value;
they did not exhibit a permanent record of old truths^
nor a firm foundation for new. Experience collected
her stores in vain, or ceased to collect them, when
she had only to pour them into the flimsy folds of
the lap of mysticism ; who was, in truth, so much
absorbed in looking for the l3*easures which were to
&11 from the skies, that she heeded little how scan<-
tily she obtained, or how loosely she held, such riches
as might be found near her.

311

CHAPTER IV.

Of the Dogmatssim of the Stationary Period.

In speaking of the character of the age of commen*
tator^, we noticed principally the ingenious servility
which it displays ;**^the acuteness with which it finda
ground for speculation in the expression of other
men's thoughts ;-^the want of all vigour and fertility
in acquiring any real and new truths* Such wa3
the character of the reasoners of the stationary
period from the first; hut, at a later day^ this
character, from various causes, was modified hy new
features. The servility which had yielded itself to
the yoke, insisted upon forcing it on the necks of
others; the subtlety which foimd all the truth it
needed in certain accredited writings, resolved that
no one should find there, or in any other region, any
other truths ; speculative men became tyrants with-
out ceasing to be slaves ; to their character of com-
mentators they added that of dogmatists.

1. Origin of the Scholastic Philosophj/. — ^The causes
of this change have. been very happily analysed and
described by several modern writers \ The general
nature of the process may be briefly stated to have
been the following.

* Dr. Hampden, in the Life of Thomas Aquinas, in the Encyc.
Metrop. Degerando, Hist. Compar^e, vol. iv. Also Tennemann,
Hist, of Phil. vol. viii. Introduction.

312 WmSIVAL 80IENQB IH THE MIDDLE AQtEM.

The tendeEcies of the later times of the Boman
raapire to a ocMiimeiitiiig literatofe, and a seoond*
hand phQosophy, have ahready been noticed. The
loss of the dignity of political fireedom, tiie want of the
chearfulness of advancing proq)eiity^ and tibie substi-
tution of the unphilosophical Latin language fw the
delicate intellectual mediianism of the Greek ; fixed
and augmented the preTalent feebleness and barren*
ness of intellect. Men forgot, or feared, to consult
tiature^ to seek for hew truths, to do what the great
discoiFerers of other times had done; they weid
content to consult libraries, to study and defend
old (^pinions, to talk of what great geniuses had said.
They sought their philos<^hy in accredited treatise^
iuid 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 Tarious anta-
gonist principles of opinion, which seem alike tb
baye their root in tiie intellectual constitution of
man, and whidi are maintained and developed by
opposing sects^ when the intellect is in vigorous
action. Such principles are, for instance^— -*th6
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 sceptical
turn of thought. Such oppositions of doctrine were
found in writers of the greatest fame ; and two of
those, who most occupied the attention of students.

DOGMATISM OF TBE aTATTONABY PESEtlOD* SIS

Plato and Aristotle, vmre, on several points of this
nature^ very diverse from each other in their ten-
dency. The attempt to reconcile these philosophers
by BoSthins and others, we have already noticed ;
and the attempt was so far successful, that it 1^ on
men's minds the belief in the possibility of a great
philosophical system which should be based on these
writers, and have a claim to the assent of all sobw
speculators.

But, in the mean time, the Christian religion had
become the leading subject of men's thoughts; and
divines had put forward its claims to be, not merely
the guide of men's lives, and the means of reconciling
them to their heavenly Master; but also to be a
philosophy in the widest sense in which the term had
been used ; — a consistent speculative view of man's
condition and nature, and of the world in whidh he
is placed.

These daims had been acknowledged; and, un-
fortunately, from the intellectual condition of the
times,^th no due apprehenrion (rf the necessaiy
ministry of observation, and rewon dealing with
observation, by which alone such a system can be em-
bodied. It was held, without any regulating principle,
that the philosophy which had been bequeathed to the
world by the great geniuses of heathen antiquity, and
the philosophy which was deduced fit)m, and implied
by, the revelations made by God to man, must be
identical ; and therefore, that theology is the only true
philosophy. Indeed, the Neoplatonists had already

814 PHYSICAL SCISNCB IN THE MIDDLE AGES,

arriyed, by other roads, at the same conviction. John
Scot £rigena» in the reign of Alfred, and consequently
before the existence of the scholastic philosophy,
properly so called, had reasserted this doctrine*.
Anselm, in the deyenth century, a^n brought it
forward'; and Bernard de Chartres, in the thirteenth\

This view was confirmed by the opinion which
prevailed, concerning the nature of philosophical
truth ; a view supported by the theory of Plato, the
practice of Aristotle, and the general propensities of
the human mind: I mean, the opinion that all
science may be obtained by the use of reasoning
alone ;«~that by analysing and combining the notions
which common language brings before us, we may
learn all that we can know. Thus logic came to
include the whole of science ; and accordingly this
Abdard expressly maintained'. I have already ex*
plained, in some measure, the fallacy of this belief,
which ooninsts, as has been well said% ^ in mistaking
the universality of the theory of language for the
generalisation of ftcts*" 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 tru&

Thus a universal science was established, with the
authority of a religious creed. Its universality rested
on erroneous views of the relation of words and
truths ; its pretensions as a science were, admitted

*Deg.iY.351. »Ib.iY.388. * lb. iv. 418.

* lb. iv. 407. • Enc. Met. 807.

DOGMATISM OF THE STATIONARY PERIODt 815

by the servile temper of men's intellects ; and its
religious authority was assigned it, by making all
truth part of religion. And as religion claimed
assent within her own jurisdiction under the most
solemn and imperative sanctions, philosophy shared
in her imperial power, and dissent from their doctrines
was no longer blameless or allowable. Error became
wicked, dissent became heresy; to reject the re*
ceived human doctrines, was nearly the same as to
doubt the Divine declarations. The Scholastic PhU
lasophy claimed the assent of all believers*

The external form, the details, and the text o(
this philosophy, were taken, in a great measure,
from Aristotle; though, in the spirit, the general
notions, and the style of interpretation, Plato and the
Platonists had no inconsiderable share. Various
causes contributed to the elevation of Aristotle to
this distinction. His logic had early been adopted
as an instrument of theological disputation ; and his
spirit of systematieation, of subtle distinction, and
of analysis of words, as well as the disposition to
argumentation, afforded the most natural and gratefid
employment to the commentating propensities;
Those principles which we formerly noted as the
leading points of his physical philosophy, were s^
lected and adopted; and these, presented in a moat
technical form, and applied in a systematic manner,
constitute a large portion of the philosophy of which
we now speak, so far as it pretends to deal with
physics.

016 PHYSICAL mmm m the mm^E miss.

2. SchclasHe I)ogm(zs.^^But before the oomplete
ascendency of Aristotle was thus established,
when sometWng of an intellectual waking took
place after the darkness and sleep of the nintl^
and tenth centuries, the Platonic doctrines seem
to have had, at first, a strong attraefcion for
men's minds, as better falling in with the n^ystical
speculations and contemplative piety which belong
to the times. John Scot Erigena^ may be looked
upon as the reviver of the New Platonism in the
tenth century. Towards the end of the deventh,
Peter Damien% in Italy, reproduced, involved in a
theological discussion, some Neoplatonic ideas. Ooder-
froy* also, censor of St. Victor, has left a treatise,
entitled Microcosmus ; this is founded on a mystical
analogy, often afterwards again brought forward,
between man and the universe. ** Philosophers and
theologians,*' says the writer, *^ agree in considering
man as a little world ; and as the world is composed
k>f four elements, man is endowed with four foculties,
the senses, the imagination, reason, and understand-
ing.*' Bernard of Chartres*^ in his Megascosmus
iand Microcosnms, 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 psycholo^ his special study**. He says the
Acuities of the mind are " the senses, the imaginar

'Deg. iv. 35. »Ib. iv. 367. » lb. iy. 413

'' lb. iv. 419. '' lb. iy. 415.

DOGKATISM OP THE STATIONARY PERIOD* 317

tion» the reason, the memory, the undearstanding,
and the intelligence."

Physics does not originally and properly form any
prominent part of the scholastic philosophy, which
consists mainly of a series of questions and determi-
nations 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 Senten«
tiarum ;" 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 concealing 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, s^
in. many of the writers of this time^ the nature of
angels is considered in detail, and the order? of^their
hierarchy, of which there weue held, to be nine.
The: physical discussions enter only a^ bearing uppn
the revealed history of the creation^ and cannot be
taken as a specimen of the work ; but I may observe,
that in speaking of the division of the waters above
the firmament from the waters under the firmament,
he gives one opinion, that of Bede, that the former
waters are the solid crystalline heavens in which the
stars are fixed ^*, "for crystal, which is so hard and

^' Lib. ii. Distinct, sir.

318 PHYSICAL 8CIEN0E IN THE HIDraJS A018.

transpai^nt, is made of water.'' But he mentions also
the opinion of St. Augustine, and adds that the waters
above the heavens are there in a state of vapour
(vaporaliter) and in minute drops ; ^' if» then^ water
can, as we see in clouds, be so minutelj divided tiiat
it may be thus supported as vapour on air, which is
naturally lighter than water ; why may we not be-
lieve that it floats above that lighter celestial element
in still minuter drops and still lighter vapours ? But
in whatever manner the waters are there, we do not
doubt that they are there."

The celebrated •* Summa Theologise" of Thomafir
Aquinas is a woric of the same kind ; and anything
which has a physical bearing forms an equally small
part of it. Thus, of the 512 Questions of the
gumma, there is only one (Part I., Quest- 116) "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 Ohris-
tian phflosophers, are adduced as authority, Aristotle
is referred to in a peculiar manner as " the philoso-
pher." This is noticed by John of Salisbuiy, ai^
attracting attention in his time; (he died a. P.

DOGMATISM OF THE GPTATIONARY PIBRIOD; 319

1 182.) *' The various masters of Dialectic,'* says he *%
'* shine, each Mith his peculiar mei}t; but all are
proud to worship the footsteps of Aristotle; so
much so, indeed, that the name of phthMpker^ which
belongs to them all, has been pre-eminently appro«
priated to him. He is called the philosopher aut(h
nomatice^ that is, by excellence."

The Question oonceming Corporeal Action, in
Aquinas, is divided into six Articles ; and the oonclu*
sion delivered upon the first, is ^\ that *^ 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 larger body is more
difficult to move. The author replies, that " quan«<
tity does not prevent corporeal form from action
altogether, but prevents it from being a universal
agent inasmuch as the form is individualized, which,
in matter subject to quantity, it is. Moreover, the
illustration deduced from the ponderousness of bodies
is not to the purpose ; first, because the addition of
quantity is hot the cause of gravity, as is proved in the
fourth book, De Ccelo and De Mundo" (we see that
he quotes familiarly the physical treatises of Aris-»
totle); ^^ second, because it is false that ponderous-
ness makes motion slower; on the contrary, in
proportion as anything is heavier, the more does it
move with its proper motion ; thirdly, because action

18

Metalogicus, lib. ii. cap. 16. ^* Summee, P. i. Q. 115. Art. 1.

320 PHY0ICAX. .905)109 IN. fTH^ .mpmjir A8K8.

does not take place by loe^ .mot]iOii>(M..D0iiioeritu0
aaserted ; but by tbj% th^ i^m^buig !» diMvuftiam
power into act." . , ? ; :' ./p.;

It does not belong to 0X^ piirpoig^ to ;a>n0id^
dither the theologieal -or. tbei m^jiixymeel dMf rines
wludx form so large a portim of tb^ tceCtlBes/«{<lhe
schoolmen. Pedxaps it 9iay : b^ioiift^r . sappefby tlu^t
some light is thrown on, ^omp.tofihe/qp^ptiom nMsk
have occupied metaphysiQiaASe io nil ages^ .by \thftt
examination of the bistoiiy of the j^xogtoBm^.^mifxe^
in which we are now eugage4; but.tUl W€|. aco'^ble
to analyse the leading controversies pf this jkpu^ it
would be of. little serviice to speak of jthem ip 4etaU.
It may be noticed5 bowe veri that nia^y q£, t}x» mj[>st
prominent of them rpfej: to . tlti^ groat que^n,-^
<* What is the . relati w between aetu^ ^if^g^ '^^
general te;rnp^s?'' Perhaps in. mpdejr^ tUuc^ tbe
actual things would ,be more epnimonly taken a^.tbe
point to start from ; mi men wou)ld; beg^ by eon-*
sidering how classes apid univ W9^ ape pbtained fron;
individuals. Bu,t the sc^OQtlm^« fpundii^g tl^^ic
speculations on the recedved mpdefii of ppni^denng
such subjects, to which both iVristotle and Platp had
contributed, travelled in the pppoi^ite dire^tion^ and
endeavoured to discover how individuals were de-;
duced from genera and species; — ^what was ^Uhe
principle of individuation." This was variously
stated by different reasoners. Thus Bonaventura**

15

Deg. ir. 673.

150»»rA*tl8ll'^F TH* BTAtlONARY PERIOD. 321

mhre» %h6 diifiettlty fe^rthe aid tf the AristotcHan
distHbotkm of -mattei^ and form. The individual
derives from the form the property of being some-^
Mng^'tBOid fttnn th^ matter the property of being
that pofttihuhr Jhinq. ' Duiis Seotus'*, the great ad-
ve^stery of Thomai^ Aqninas in theology, placed the
{Mriliciple of individuation in ^^ a certain positive de-
tenhiniiig entity,'- which his school called Hacceityt
or thkne^s. *' Tliitti' Peter is an individual, because
his kMumity is combined with Petreity.*" The force
of abstract terms is a curious question, and some
remarkable experiments in their use had been made
by the Latin Aristotelians before this time. In the
same way in which we talk of the quaniiit/ and qiuditg
of a thing, they spoke of its quiddity^\

We may consider the teign of mere disputation
as fully established at the time of which we are now
speaking; and the only kind of philosophy hence-
forth studied was one in which no sound physical
science had or could have a place. The wavering
abstractions, indistinct generalisations, and loose
classifications of common language, which we have
already noted as the fountain of the physics of the
Greek schools of philosophy, were also the only
source from which the schoolmen of the middle ages
drew their views, or rather their arguments: and
though these notional and verbal relations were in-
vested with a most complex and pedantic techni-

»« Deg. iy. 523. /^ lb. iv. 404.

VOL. I. Y

322 PHYSICAL SCIENCE IN THE MIDDLE AGES.

cality, they did not, on that account, become at all
more precise as notions, or most likely to lead to a
single real truth. Instead of acquiring distinct ideas,
they multiplied abstract terms ; instead of real gene^
ralisations, they had recourse to verbal distinctions.
The whole course of their employments tended to
make them, not only ignorant of physical truth, but
incapable of conceiving its nature.

Having thus taken upon themselves the task of
raising and discussing questions by means of abstract
terms, verbal distinctions, and logical rules alone,
there was no tendency in their activity to come to
an end, as there was no progress. The same ques-
tions, the same answers, the same difficulties, the
same solutions, the same verbal subtleties, — sought
for, admired, cavilled at, abandoned, reproduced, and
again admired, — ^might recur without limit. John of
Salisbury** 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. Hal-

•

^' He stadied logic at Paris, at St. Geneyiere, and then left
them. ^^ Duodecennium mihi elapsitm est dirersis studiis oc*-
cupatum. Jucundmn itaque yisum est yeteres qnos TeUqueram,
et quos adhuc Dialectica detinebat in monte, (Sanctse GenoTe£e)
revisere socios, conferre cum eis super ambiguitatibus pristinis ;
ut nostrum invicem collatione mutua commetiremur profectum.
Inventi sunt, qui fuerant et ubi; neque enim ad palmam risi
sunt processisse ad qussstiones pristinas diiimendas, neque pro-
positiunculam unam adjeceiant. Quibus uigebant stimulis
eisdem et ipsi urgebantur." &c. Metalogicus^ Kb. li. cap. 10.

DOGMATISM OF THE STATIONARY PERIOD* 823

lam remarks '% ^^ was equally applicable to the period
of centuries." The same knots were tied and un-
tied ; the same clouds were formed and dissipated.
The poet's censure of " the Sons of Aristotle," is as
just as happily expressed : —

They stand
Locked up together hand in hand ;
Eyery 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
pf the thirteenth, fourteenth, and fifteenth centuries.
We may suppose it to have been, during the interme-
diate time, such as it was at first and at last. An
occasion to consider its later days will be brought
before us by the course of our subject. But, even
during the most entire ascendency of the scholastic
doctrines, the elements of change were at work.
While the doctors and the philosophers received all
the ostensible homage of men, a doctrine and a phi-
losophy of another kind were gradually forming : the
practical instincts of man, their impatience of tyranny,
the progress of the useful arts, the promises of alchemy,
were all disposing men to reject the authority and
deny the pretensions of the received philosophical
creed. Two antagonist forms of opinion were in
existence, which for some time went on detached,

»• Middle Ages, iii. 537-

y 2

324 PHYSICAL SCIENCE IN THE MIDDLE AGES^

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
£urope.

3. Scholastic Physics. — ^It is difficult to give briefly
any appropriate examples of the nature of the Aris-
totelian 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 ". " Zabarella maintains that
the proximate cause of the motioxi of elements is
atxeform, in the Aristotelian sense of the term : but
to this sentence we," says Keckerman, "cannot
agree; for in all other things the form is the proxi-
mate cause, not of the ad, but of the power or faculty
from which the act flows. Thus in man, the rational
soul is not the cause of the act of laughing, but of
the risible faculty or power." Keckerman*s system
was at one time a work of considerable authority :
it was published in 1614. By comparing and
systematising what he finds in Aristotle, he is led
to state his results in the form of definitions . 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 in-
termediate element, cold and moist." The first
theorem concerning water is, " The moistness of

»* Keckerman, p. 1428.

DOGMATISM OP THE STATIONARY PERIOD. 325

water is controlled by its coldness, so that it is less
than the moistness of the air ; though, according to
the sense of the vulgar, water appears to moisten
more than air." It is obvious that the two proper-
ties of fluids, to have their parts easily moved, and
to wet other bodies, are here confounded. I may,
as a concluding specimen of this kind, mention those
propositions or maxims concerning fluids, which were
so firmly established, that, when Boyle propounded
the true mechanical principles of fluid action, he
was obliged to state his opinions as " hydrostatical
'paradowesr Theise were, — ^that fluids do not gravi-
tate in proprio loco ; that is, that water has no gravity
in or on water, since it is in its own place ; that air
has no gravity on water, since it is above water,
which is its proper place ; that earth in water tends
to descend, since its place is below water ; — ^that the
water rises in a pump or siphon, because nature
abhors a vacuum ; — ^that some bodies have a positive
levity in others, as oil in water ; and the like.

4. Authority of Aristotle among the Schoolmen. — >
The authority of Aristotle, and the practice of mak-
ing 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, how-
ever, without its fluctuations. Launoy has traced
one part of its history, in a book " On the various
Fortune of Aristotle in the University of Paris."
The most material turns of this fortune depend on
the bearing which the works of Aristotle were sup-

326 PHYSICAL SCIENCE IN THE MIDDLE AGES.

posed to have upon theology. Several of Aristotle's
works, and more especially his metaphysical writings,
had heen translated into Latin, and were explained in
the schools of the University of Paris, as early as the
beginning of the thirteenth century**. At a council
held at Paris in 1209, they were prohibited, as having
given occasion to the heresy of Almeric (or Amauri),
and because "they might give occasion to other
heresies not yet invented." The Logic of Aristotle
recovered its credit some years after this, and was
publicly taught in the University of Paris, in the
year 1215 ; but the Natural Philosophy and Meta-
physics 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 Arabic, certain books of
Aristotle, and of other ancient sages ; and we have
a letter of Peter de Vineis, in which they are recom-
mended to the attention of the University of Bo-
logna: probably the same recommendation was
addressed to other Universities. Both Albertus
Magnus and Thomas Aquinas wrote commentaries
on Aristotlelb works ; and as this was done soon
after the decree of Gregory the Ninth, Launoy is
much perplexed to reconcile the fact with the ortho-
doxy of the two doctors- Campanella, who was one
of the first to cast off the authority of Aristotle,
says, " We are by no means to think that St. Thomas

** Mosheinii iii. 167-

DOGMATISM OF THE STATIONARY PERIOD. 327

aristotdized ; he only expounded Aristotle, that he
might correct his errors ; and I should conceive he
did this with the license of the Pope." This state-
ment, however, by no means gives a just view of
the nature of Albertus's and Aquinas's commentaries.
Both have followed their author with profound de-
ference ". For instance, Aquinas " attempts to defend
Aristotle's assertion, that if there were no resistance,
a body would move through a space in no time ; and
the same defence is given by Scotus.

We may imagine the extent of authority and
admiration which Aristotle would attain, when thus
countenanced, both by the powerful and the learned.
In universities, no degree could be taken without a
knowledge of the philosopher. In 1452, Cardinal
Totaril established this rule in the University of
Paris". When Ramus, in 1543, published an attack
upon Aristotle, it was repelled by the power of the
court, and the severity of the law. Francis the
First published an edict, in which he states that he
had appointed certain judges, who had been of
opinion", " que le dit Ramus avoit ete temeraire
an'ogant et impudent ; et que parcequ'en son livre des
animadversions il reprenait Aristotle, estait evidem-
ment connue et manifesto son ignorance.'^ The
books are then declared to be suppressed. It was
often a complaint of pious men, that theology was
corrupted by the influence of Aristotle and his com-

8S

Dcg. N. 475. " F. Piccolomini, ii. 835.

»* Launoy, p. 108, 128. " Launoy, p. 132.

328 PHYSICAL SCIENCE IN THE HIDPLE AGES.

mentator&k Petrarch says*% that one of. the Italian
learned men conversing ^'it)i him» ^iter e^^pressing
much contempt for the apostles and jhtbers, ex-
claimed, ^^Utinam tu Averroen pati .posses» ut
videres quanto ille tuis his nugatoribns major ^t!""

When the revival of letters began to take pfeyee,
and a number of men of ardent and elegant minds,
susceptible to the impressions of beauty of style and
dignity of thought, were brought in cont^t Mith
Greek literature, Plato had naturally greater charms
for them. A powerful school of Platonists i(not
Neoplatonists) was formed . in Italy, including some
of the principal scholars and men of genius of the
time ; as Picus of Mirandula in the middle, Marsir
lius Ficinus at the end, of the fifteenth century. At
pne time, it appeared as if the ascendency of Aria*
totle was about to be overturned ; but, in physics at
least, his authority passed unshaken through this
trial. It was not by disputation that Aristotle could
be overthrown ; and the Platonists were not persona
whose doctrines led th^m to use the only decisive
method in such cases, the observation and unfettei^ed
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 tho
scholastic philosophy on general theoretical grounds
of various kinds. Such examples of insurrection
against the dogmatism which we have been review*

»• Halhun, M. A., in. 536.

DOOMAtrSM OF THE STATIONARY PERIOD. 329

ing, are extremely interesting events in the history
of the philosophy of science. Bnt, 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 iipon that philo-
sophy 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 accotmt of the stationary period, and to
enter upon the great subject of the progress of physi-
cal science in modem times.

5. Subjects omitted. Civil Law. Medicine. — My
object has been to make my way, as rapidly as pos-
sible, to this period of progress ; and in doing this, I
have had to pass over a long and barren tract, where
almost all traces of the right road disappear. In
exploring this region, it is not without some difficulty
that he who is travelling with objects such as mine,
continues a steady progress in the proper direction ;
for many curious and attractive subjects of research
come in his way: he crosses the track of many a
controversy, which in its time divided the world of
speculators, and of which the results may be traced,
even now, in the conduct of moral, or political, or
metaphysical discussions ; or in the common associa-
tions of thought, arid forms of language. The wars
of the Nominalists and Realists ; the disputes con-
cerning the foundations of morals, and the motives
of human actions ; the controversies concerning pre-
destination, free will, grace, and the many other

330 PHYSICAL SCIENCE IN THE MIDDLE AGES.

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
upon each other, and upon society ; and many other
subjects ; — ^might be well worth examination, if our
hope of success did . not reside in pursuing, steadily
and directly, those inquiries in which we can look
for a definite and certain reply. We must even
neglect two of the leading studies of those times,
which occupied much of men's time and thoughts,
and had a very great influence on society ; the one
dealing with notions, the other with things; the
one employed about moral rules, the other about
material causes, but both for practical ends ; I mean,
the study of the Civil Law, and of Medicine. The
second of these studies will hereafter come before
us, as one of the principal occasions which led to the
cultivation of chemistry ; but, in itself, its progress
is of too complex and indefinite a nature to be ad-
vantageously 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, there-
fore, be useful to consider it, if we should, in the
sequel, have to examine how feir there can exist an
analogy between moral and physical science. But,
after a few more words on the middle ages, we must
return to oujp task of tracing the progress of the latter.

831

CHAPTER V.

Progress of the Arts in the Middle Ages.

1. Art and Science. — ^I shall, before I resume the
history of science, say a few words on the subject
described in the title of this chapter, both because
I might otherwise be accused of doing injustice to
the period now treated of; and also, because we shall
thus have, brought under our notice, some circum-
stances which were important as the harbingers of
the revival of progressive knowledge.

The accusation of injustice to the state of science
in the middle ages, if we were to terminate our
survey of them with what has hitherto been said,
might be urged from obvious topics. How do we
recognise, it might be asked, in a picture of mere
confusion and mysticism of thought, of servility and
dogmatism of character, the powers and acquirements
to which we owe so many of the most important in-
ventions which we now enjoy ? Parchment and paper,
printing and engraving, improved glass and steel,
gunpowJler, clocks, telescopes, the mariner's compass,
the reformed calendar, the decimal notation, algebra,
trigonometry, chemistry, counterpoint, which was
equivalent to a new creation of music ; — ^these are
all possessions which we inherit from that which has
been so disparagingly termed the stationary period.

»■•

■*>*,

332 PHYSICAL SCIENCE IN THE MIDDLE AGES.

Above all, let us look at the monuments of arehi-
tectnre of this period; — ^the admiration and the
despair of modem architects, not onlj for their
beauty, but for the skill disclosed in their construc-
tion. With all these evidences before us, how can
we avoid allowing that the masters of the middle
ages not only made some small progress in astronomy,
which has, grudgingly as it would seem, been ad-
mitted 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
c^ the advanced state of our physical philosophy ; — ^if
our steam-engines, our gas-illumination, our build-
ings, our navigation, our manufiictures, are cited as
triumphs of science; — shall not prior inventions, made
under fer heavier disadvantages, — shall not greater
works, produced in an earlier state of knowledge,
also be admitted as witnesses that the middle ages
had their share, and not a small or doubtfol one, of
science?

To these questions I answer, by distinguishing
between art, and science in that sense of general
inductive systematic truth, which it bearff 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 suf-
ficiently obvious. Art is practical, science is specu-

^

PROGJtESS OF TKB ARTS* 333

lative : the fonner i^ 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 ^ch other^s pressure, though he may neyer
haVQ applied his knowledge in a single easa

Npw the remark which. I have to make is this :-^
in all cases the arts are prior to the related acienoes.
Art is the parent, not the progeny, of science ; the
realization of principles in practice forms part of
the pi^elude, as well as of the sequBl, of theoretical
discoyeiy. And thus the inventions of the middle
ages, which have been above eniunerated, though at
the present day they may be portions of our sciencess
are no evidence that the sciences th^ existed ; but
only that those powers of practical obs^vation and
practical skill were ^t work, which prepare, the way
fo;* theoretic^ views and sci^ntifio discoveries*

It may be urged, that the great works of art do
virtiially take for granted principles of science ; and
that, therefore, it is unreasonable to deny science to
great artists. It may be said^ that the. grand struct
tures of Cologne, or Amiens, or Canterbury, could
not have been erected without a profound knowledge
of mechanical principles.

To this we reply, that ^uck knowledge is rnani^
festly not of the nt^ture.pf that which we call science^

334 PHYSICAL SCIEMrCE IN THB MIDDLE AGES.

If the beautiful and skilful structures of the middle
ages prove that mechanics then existed as a science,
mechanics must have existed as a science also among
the builder? of the Cyclopean walls of Greece and
Italy, or of our own Stonehenge ; for the masses which
are there piled on each other, could not be raised
without considerable mechanical skill. But we may
go much further. The actions of every man who
raises and balances weights, or walks along a pole, take
for granted the laws of equilibrium ; and even animals
constantly avail themselves of such principles. Are
these, then, acquainted with mechanics as a science ?
Again, if actions which are performed by taking
advantage of mechanical properties prove a know-
ledge of the science of mechanics, they must also
be allowed to prove a knowledge of the science of
geometry, when they proceed on geometrical pro-
perties. But the most familiar actions of men and
animals do this. The Epicureans held, as Proclus
informs us, that even asses knew that two sides of a
triangle are greater than the third. They may be said
to have a practical knowledge of this ; but they have
not, therefore, a science of geometry. And in like
manner among men, if we consider the matter strictly,
a practical assimiption of a principle does not imply a
speculative knowledge of it.

We may, in another way also, show how inadmissi-
ble 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

PROGRESS OF THE ARTS. 835

histoTy, such as we are here endeavouring to write.
We are employed in tracing the progress of such
general principles as constitute each of the sciences
which we are reviewing ; and no fitcts or subordinate
truths belong to our scheme, except so fer 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 such pro-
cesses of aH as those which we have referred to, as
the inventions of the middle ages, let us ask, what
principle each of them illustrates ? What chemical
doctrine rests for its support on the phenomena of
gunpowder, or glass, or steel ? What new harmoni-
cal 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 in-
ventions 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 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 scien-
tific eminence, the arts of the middle ages should
not be received as proof of theirs ; we must reply

836 PHYSICAL SCIENCE IN THE MIDDLE AGES.

to it, by giving up some of the pretensions which
are often put forwards on behalf of the science of
our times. The perfection of the mechanical and
other arts among us proves the advanced condition
of our sciences, only in so far as these arts have
b«o pe*o^ b/u.e .pplictioa 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 prin-
ciple is illustrated by the beautiful manufactures of
porcelain, or steel, or glass ? A chemical view of
these compounds, which would explain the condi-
tions of success and &ilure 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 prac
tised.

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 dis-
tinction has been recognised by others, it has hardly
been rigorously adhered to, in consequence of the
indistinct notion of science which has commonly
prevailed. Thus Gibbon, in speaking of the know-

< FSt06BXfi» OP THE ARTB. 337

l^iAge-of tfaa period ^ no^- under (mr -notice^ says\
<^Muelt useful experience had been acquired in th6
ptoactiee^ofr aits and manufa<^ures ; bui the scieike
o£' eheaasttytmB^ its^ JOrigin ' ajid^ improvement to
the;* indourtrjr <xP the iSafrac^s. . They,** he adds,
^^ first iniieiited and'iiiaided'the alembic for the puiv^
poses iof distiUation^ :4malysed the' substances of the
three kiogdems jof nfltute, tried the . distlncrtronr and
aflinitieenof' aloatis and acid$, and converted the
poiso|i6usi tsadfieat^lS'into BOfbmidt salutary medidnes;^'
The fotcmaiion and realisation of the notions of cmoh^
lyms and oS. affimtjfy were important steps in ehe-»:
mioid science^ n^hicfa, as Ishali^hereafter endeavour
to diow^ it.TemainJad for the chemists of Eurk)pe to
nid.ke«t a much later period. If the Arabis(ns ^d*
dffioie this^ thej might* with justice have been eblled-
the Btttiiors {Of the science' of chemistry; but^ no'
doctrineai cto be« ■ adduced^ firom their works wMeh •
give: .them any title tP' this ^^nii^ntdistinctionv
Their, claims aror dissipated atrtmce. by the application'
of the maxim above stated. What analysis of theirs'
tended(tQf«[St9)bliidi iaiQ^irectived primdpleof cheniis-
tiy? H^^ikrfitrueido^ineoaaG^imig the differences
and affinities ctf acids and bjHaUis: did they teach ? We
need not wonder if Gifobon,wbo^e views of the boun-
daries of scientific chemistry » were probably very wide
and indistinct, could include the arts of tiie Arabians
within its domain; but they* cannot pass the frontier of
science if philosophitcallydefined, and steadily guarded.

' * Decline and Fall, vdl. x. p: 43.

VOL. I. Z

338 PHYSICAL SCIENCE IN THE MIDDLE AGES.

The judgment which we are thus led to form
respecting the chemical knowledge of the middle
ages, and of the Arabians in particular, may serve
to measure the condition of science in other depart-
ments ; for chemistry has justly been considered one
of their strongest points. In botany, anatomy,
zoology, optics, acoustics, we have still the same
observation 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 astro-
nomy and pure mathematics, we have already

3. Experimental Philosophy of the Arabians.''^
The estimate to which we have thus been led, of
the scientific merits of the learned men of the
middle ages, is much less exalted than that which
has been formed by many writers ; and, among the
rest, by some of our own time. But I am persuaded
that any attempt to answer the questions just asked,
will expose the imtenable nature of the higher
claims which have been advanced in favour of the
Arabians. We can deliver no just decision, except
we will consent to use the terms of science in a
strict and precise sense': and if we do this, we shall

* If I might take the liberty of criticising an author who has
given a very interesting view of the period in question (Maho-
metanism Unveiled^ by the Rev. Charles Forster, 1829), I would
remark, that in his work this caution is perhaps too little ob-

JPEOGRSSS OF THE ABTS. 339

find little, » either in the particular discoveries or
general methods of the Arabians, which is important
in the history o^ the inductive sciences.

The credit due to the Arabians for improvements
in the general methods of philosophising, 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 commenta«
tion. They followed their Greek leaders, for the
most part, with abject servility, and with only that
kind of acuteness and independent speculation which
the commentator's vocation implies. And in their
choice of the standard subjects of their studies, they
fixed upon those works, the Physics of Aristotle,
which have never promoted the progress of science^

served. Thus, lie says, in speaking of Alhazen (vol. ii. p. 270),
^'the theory of the telescope maj be found in the work of this
astronomer;" and of another, ^^ the uses of magnifjing glasses
and telescopes, and the principle of their construction, are ex-
plained in the great work of (Roger) Bacon, with a truth and
clearness which hare commanded universal admiration." Such
phrases would he 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 principles
of all meaning.

Z 2

340 PHYSICAL SCIENCE IN THE MIDDLE AGES.

except so far as they incited men to refutp them ; an
effect which they never produced on the Arabians.
That the Arabian astronomers made some advances
beyond the Greeks, we have already stated: the
two great instances are, the discovery of the motion
of the sun's apogee by Albategnius, and the dis-
covery (recently brought to light) of the existence
of the moon's second inequality, by Aboul Wefiu
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 &r as we can judge, to fall
into neglect and oblivion : so little were the learned
Arabians prepared to take their lessons from obser-
vation as well as books. That in many subjects
they made experiments, may easily be allowed:
there neyer was a period of the earth's history, and
least of all a period of commerce and manu&ctures,
luxury and art, medicine and engineering, in which
were not going on innumerable processes, which
may be termed experiments; and, in addition to
these, the Arabians adopted the pursuit of alchemy,
and the love of exotic plants and animals. But
they seem to have been so far from being, as has
been ipaintained", a people whose "experimental

' Mahometanism Unveiled, ii. 271.

PROGRESS OF THE ARTS. 341

intellect" fitted them to form sciences which the
"abstract intellect" of the Greeks failed in pro-
ducing, that the case appears rather to be, that
several of the sciences which the Greeks had founded,
were never even comprehended by the Arabians.
I do not know any evidence that these pupils ever
attained to understand the real principles of me-
chanics, 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 Ara-
bian name which any one has thought of interposing
between Archimedes the ancient, aiid Stevinus and
Galileo the modems.

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 asser-
tion 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 vmters, there can be no
doubt ; for they were in his time the repositories of
all traditionary knowledge. But that he derived
from them his disposition to shake off the authority
of Aristotle, to maintain the importance of experi-
ment, and to look upon knowledge as in its infancy.

342 PHYSICAL SCIENCE IN THE MIDDLE AGES.

I cannot believe, because I have not myself hit
upon, nor seen quoted by others, any passages in
which Arabian writers express such views. 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 impres-
sions. We have already seen that Aristotle asserts,
as distinctly as words can express, that all know-
ledge must depend on observation, and that science
must be collected from fistcts by induction. We
have seen, too, that the Roman writers, and Seneca
in particular, speak with an enthusiastic confidence
of the progress which science must make in the
course of ages. When Roger Bacon holds similar
language in the thirteenth century, the resemblance
is probably rather a sympathy of character, than a
matter of direct derivation ; but I know of nothing
which proves even so much of connexion with
Arabian philosophers.

A good deal has been said of late^ of the coin-
cidences between his views, and those of his great
namesake in later times, Francis Bacon \ The re-
semblances consist mainly in such points as I have
just noticed ; and we cannot but acknowledge, that
many of the expressions of the Franciscan fifiar
remind us of the large thoughts and lofty phrases
of the philosophical chancellor. How f^r the one
can be considered as having anticipated the method

* Hallam's Middle Ages, iii. 539. Forster's Mahom. U. ii.
313.

PROGRESS OP THE ARTS. 343

of the other, we shall examine more advantageously,
when we oome to consider what the character and
effect of Francis Bacon's works really are.

5. Architecture of the Middle Ages. — But though
we are thus compelled to disallow several of the
claims which have been put forwards in support of
the scientific character of the middle ages, there are
two points in which we may, I conceive, really trace
the progress of scientific ideas among them; and
which, therefore, may be considered as the prelude
to the period of discovery. I mean their practical
architecture, and their architectural treatises.

In a previous chapter of this book, we have en-
deavoured to explain how the indistinctness of ideas,
which attended the decline of the Roman empire,
appears in the forms of their architecture ; — ^in the
disregard, which the decorative construction exhibits,
of the necessary mechanical conditions of support.
The original scheme of Greek ornamental architec-
ture, had been horizontal masses resting on vertical
columns; when the arch was introduced by the
Romans, it was concealed, or kept in state of sub-
ordination ; and the lateral support which it required
was supplied latently, masked by some artifice. But
the struggle between the mechanical and the deco-
rative construction*, ended in the complete disorga-
nisation of the classical style. The inconsistencies
and extravagancies, of which we have noticed the

* See Mr. Willis's admirable Remarks on the Architecture cf
the Middle Ages^ chap. ii.

344 PHYSICAL SCIENCE IN THE MIDDLE AGES.

the occurrence, were results and indications of the
fall of good architecture. The elements of the
ancient system had lost all principle of connexion
and regard to rule. Building became not only a
mere art, but an art exercised by masters without
skill, or feeling for real beauty.

When, after this deep decline, architecture rose
again, as it did in the twelfth and succeeding cen-
turies, in the exquisitely beautiftil and skilful forms
of the Gothic style, what was the nature of the
change which had taken place, so far as it bears upon
the progress of science ? It was this : — ^the idea of
true mechanical relations in an edifice had been
revived in men's minds, as far as was requisite for
the purposes of art and beauty : and this, though a
very different thing from the possession of the idea
as an element of speculative science, was the proper
preparation for that acquisition. The notion of
support and stability in the decorative construction
again became conspicuous and universal in the forms
of building. The eye which, looking for beauty in
definite and significant relations of parts, is never
satisfied except the weights appear to be duly sup-
ported', was again gratified. Architecture threw off
its barbarous characters : a new decorative construc-
tion was matured, not thwarting and controlling, but
assisting and harmonizing with the mechanical con-

• Willis, p. 15 — 21. I have throughout this description of
the formation of the Gothic style ayailed myself of Mr. Willis's
well-chosen expressions.

PROGRESS OF THE ARTS. 345

struction. All the ornamental parts were made to
enter into the apparent construction. Every mem-
ber, almost every moulding, became a sustainer of
weight; and by the multiplicity of props assisting
each other, and the consequent subdivision of weight,
the eye was satisfied of the stability of the structure,
notwithstanding the curiously-slender forms of the
separate parts. The arch and the vault, no longer
trammelled by an incompatible system of decoration,
but favoured by more tractable forms, were only
limited by the skill of the builders. Everything
showed that, practically at least, men possessed and
applied, with steadiness and pleasure, the idea of
mechanical pressure and support.

The possession of this idea, as a principle of art,
led, in the course of time, to its speculative deve-
lopement as the foundation of a science ; and thus
architecture prepared the way for mechanics. But
this advance required several centuries. The in-
terval between the admirable cathedrals of Salisbury,
Amiens, Cologne, and the mechanical treatises of
Stevinus, is not less than three hundred years.
During this time, men were advancing towards
science, but in the meantime, and perhaps from
the very beginning of the time, art had begun to
decline. The buildings of the fifteenth century,
erected when the principles of mechanical support
were just on the verge of being enunciated in general
terms, exhibit those principles with a far less im-
pressive simplicity and elegance than those of the

349 PHYSICAL SCIENCE IN THE MIDDLE AGES.

thirteenth. We inay hereafter inquire whether we
find my other examples to countenance the belief,
that the formation of science igf commonly accon^-*
panied by the decline of art

The leading principle of the style of the Gothic
edifices was, not merely that the weights were sup-
ported, 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 dis-
played. 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 elevates them
above the character of barbarous architecture. Their
masses are broken into innumerable members, with'-
out subordination or meaning, and suggested appa-
rently by caprice and the love of the marvellous.
<^In the construction of their mosques, it was a
favourite artifice of the Arabs to sustain immense
and ponderous masses of stone by the support of
pillars so slender, that the incumbent weight seeined,
as it were, suspended in the air by an invisible
hand^" This pleasure in the contemplation of ap-
parent impossibilities is a very general disposition
among mankind ; but it appears to belong to the
infancy, rather than the maturity pf intellect The

'^ Mahometemism XJnveiled^ ii* 255,

PROGRESS OF THE ARTS, 347

pleasure in the contemplation of what is clear, the
craving for a thorough insight into the reasons of
things, which marks the European mind, is the
temper which leads to science.

6, TreoHsm 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 remarkably
connected and definite artificial system. Nor can
we doubt that it was exercised by a class of artists
who formed themselves by laborious study and prac-
tice, and by communication with each other. There
must have been bodies of masters and of scholars,
discipline, traditions, precepts of art. How these
associated artists diffused themselves over Europe,
and whether history enables us to trace them in a
distinct form, I shall not here discuss. But the
existence of a course of instruction, and of a body of
rules of practice, is proved beyond dispute by the
great series of European cathedrals and churches, so
nearly identical in their general arrangements, and
in their particular details. The question then occurs,
have these rules and this system of instruction any-
where 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 ?

348 PHYSICAL SCIENCE IN THE MIDDLE AGES.

We are not to be surprised, if, during the most
flourishing and vigorous period of the art of the
middle ages, we find none of its precepts in books.
Art has, in all ages and countries, been taught and
transmitted by practice and verbal tradition, not by
writing. It is only in our own times, that the
thought occurs as fstmiliar, of committing to books
what we wish to preserve and convey. And, even
in our own times, most of the arts are learned far
more by practice, and by intercourse with practi-
tioners, than by reading. Such is the case, not only
with manufectures and handicrafts, but with the fine
arts, with engineering, and even yet, Avith that art,
building, of which we are now speaking.

We are not, therefore, to wonder, if we have no
treatises on architecture belonging to the great
period of the Gothic masters ; — or if it appears to
have required some other incitement and some other
help, besides their own possession of their practical
skill, to lead them to shape into a literary form the
precepts of the art which they knew so well how to
exercise: — or if, when they did write on such subjects^
they seem, instead of delivering their own sound
practical principles, to satisfy themselves with pur-
suing some of the frivolous notions and speculations
which were then current in the world of letters*

Such appears to be the case. The earliest treatises
on architecture come before us under the form which
the commentatorial spirit of the middle ages inspired.
They are translations of Vitruvius, with annotations.

PROGRESS OF THE ARTS. 349

In some of these, particularly that of Cesare Cesa-
riano, published at Como, in 1521, we see, in a very
curious manner, how the habit of assuming that, in
every department of literature, the ancients must
needs be their masters, led these writers to subordi-
nate the members 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
cinqtie cento by the Italians, of the renaissance by the
French, and which is commonly included in our
Elizabethan. But in the early architectural works,
besides the superstitions and mistaken erudition
which thus choked the growth of real architectural
doctrines, another of the peculiar elements of the
middle ages comes into view ; — ^its mysticism. The
dimensions and positions of the various parts of
edifices and of their members, are determined by
drawing triangles, squares, circles, and other figures,
in such a manner as to bound them : and to these
geometrical figures were assigned many abstruse
significations. The plan and the front of the Cathe-
dral 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 evi-
dence of a fanciful and mystical turn of thought ^

^ The plan which he has given, fol. 14, he has entitled
^' Ichnographia Fundamenti sacrse ^dis baricephalae, Oermanico

360 PHYSICAL SCIENCfi IN THE MIDDLE AGES.

We thus find eradition and mysticism take the
place of much of that developement of the architec-
tural principles of the middle ages which would be
so interesting to us. Still, however, these works
are by uo means without their value. Indeed many
of the arts appear to flourish not at all the worse, for
being treated in a manner somewhat mystical ; and
it may easily be, that the relations of geometrical
figures, for which fantastical reasons are given, may
really involve principles of beauty or stability. But
independently of this, we find, in the best works of
the architects of all ages (including engineers), 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 these arts could not be successfully exercised
if it were not so. Hence the writings of architects
and engineers during the middle ages do really form
a prelude to the writers on scientific mechanics.
Vitruvius, in his Architecture^ and Julius Frontinus,
who, under Vespasian, wrote On Aqueducts^ of
which he was superintendent, have transmitted to

more, a Trigono ac Pariquadrato perstructa, uti etiam ea quad
nunc Milani videtur."

The work of Cesariano was translated into German by
Gualter Eirius, and published at Nuremberg, in 1548, under
the title of Yitruyius Teutsch, with copies of the Italian dia-
grams. A few years ago, in an article in the Wiener Jahr-
biicher (Oct. — Dec, 1821), the reviewer maintained, on the
authority of the diagrams in Rivius's book, that Gothic archi-
tecture had its origin in Germany, and not in England.

PROGRESS OF THE ARTS. 351

US the principal part of What we know respecting
the practical mechanics and hydraulics of the Ro-
mal In modem time, the series is resumed.
The early writers on architecture are also writers on
engineering, and often on hydrostatics: for ex-
ample, Leonardo da Vinci wrote on the equilibrium
of water. And thus we are led up to Stevinus of
Bruges, who was engineer to Prince Maurice of
Nassau, and inspector of the dykes in Holland;
and in whose work, on the processes of his art, is
contained the first clear modem statement of the
scientific principles of hydrostatics.

Having thus explained both the obstacles and the
prospects which the middle ages offered to the
progress of science, I now proceed to the history of
the progress, when it was once again resumed.

BOOK V.

HISTORY

OF

FORMAL ASTRONOMY

AFTER THE STATIONARY PERIOD.

VOL. I. 2 A

• • • Cjclopum edncta caminifl

MfBDia conqdcio, atqne adverBO fomice portas.

Hia demum exactis, perfecto mnnere Diysd,
Devenere looos Isetos et amflena yireta
Fortimatonim nemomm sedesqne beatas.
TsjTgioT hie campos sether et lumine vestit
Fmpureo : solemque sauni, sua sidera noront.

Virgil, JEn. vL 630.

They leave at length the nether gloom, and stand

Before the portals of a better land :

To happier plains they come, and £Edrer groves,

The seats of those whom heaven, benignant, loves ;

A brighter day, a bhier ether, spreads

Its lucid depths above their fsivonred heads ;

And, pniged from mists that veil our earthly skies.

Shine sons and stars unseen by mortal eyes.

Introduction.

Of Formal and Physical AstroMmy.

We have thus rapidly traced the causes of the ahnost
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 steadi-
ness of intellectual action. This mental declension
produced a senile admiration for the genius of the
better times, and thus, the spirit of commentation :
Christianity established the clain) of truth to govern
the world; and this principle, misinterpreted and
combined with the ignorance and servility of the
times, gave rise to the dogmatic system : and the
love of speculation, finding no secure and permitted
path on solid ground, went off into the regions of
mysticism.

The causes which produced the inertness and
blindness of the stationary period of human know-
ledge, began at last to yield to the influence of the
principles which tended to progression. The indis-
tinctness of thought, which was the original feature
in the decline of sound knowledge, was in a measure
remedied by the steady cultivation of pure mathe-
matics and astronomy, and by the progress of inven-

2 A 2

356 INTRODUCTION.

tions in the arts, which call out and fix the distinct-
ness of our conceptions of the relations of natural
phenomena. As men's minds became clear, they
became less servile : the perception of the nature of
truth drew men away from controversies about mere
opinion ; when they saw distinctly the relations of
things^ they ceased to give their whole attention to
what had been said concerning them ; and thus, as
science rose into view, the spirit of commentation
lost its sway. 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 im-
pose opinions upon them. When they threw off
their blind admiration for the ancients, they were
disposed to cast away also their passive obedience to
the ancient system of doctrines. When they were
no longer inspired by the spirit of commentation,
they were no longer submissive to the dogmatism of
the schools. When they began to feel that they
could discover truths, they felt also a persuasion of a
right and a growing will so to do.

Thus the revived clearness of ideas, which made
its appearance at the revival of letters, brought on a
struggle with the authority, intellectual and civil, of
the established schools of philosophy. This clearness
of idea showed itself, in the first instance, in astro-
nomy, 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 oui: present business to trace

INTRODUCTION. 357

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 pro-
ceeds ; and, therefore, I neglect subordinate persons
and occurrences, in order to bring into view the
leading features of great changes. Now in the in-
troduction 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 consi-
deration of this system with reference to its causes ; —
the formal SLiid the phj/sical ss]^ect of the theory ; — ^the
relations of space and time, and the relations of force
and matter. These two divisions of the subject were
at first not clearly separated ; and, indeed, 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 conditions of
the universe, the relations of space and time ; but
Kepler, Galileo, and others, were led, by controversies
and other causes, to give a gradually increasing
attention to the physical relations of the heavenly
bodies ; an impulse was given to the study of me-
chanics, (the doctrine of motion,) which became very
soon an important and extensive science ; and in no
long period, the discoveries of Kepler, suggested by

358 INTRODUCTION.

a vague but intense belief in the physical connexion
of the paxts of the universe, led to the decisive and
sublime generalizations of Newton.

The distinction of formal and physical astronomy
thus becomes necessary, in order to treat clearly of
the discussions which the propounding of the Coper-
nican theory occasioned. But it may be observed
that, besides this great change, astronomy made very
great advances in the same path which we have
already been tracing, namely, the determination of
the quantities and lavrs of the celestial motions, in so
far as they were exhibited by the ancient theories, or
might be represented by obvious modifications of
those theories. I speak of new inequalities, new
phenomena, such as Copernicus, Galileo, and Tycho
Brahe discovered. As, however, these were very
soon referred to the Copemican rather than the
Ptolemaic hypothesis, they may be considered as
developements rather of the new than of the old
theory ; and I shall, therefore, treat of them, agree-
ably to the plan of the former part, as the sequel of
the Copemican induction.

859

CHAPTER I.

Prelude to the Inductive Epoch of

Copernicus.

The doctrine of Copernicus, that the sun is the true
centre of the celestial motions, depends primarily
upon the consideration that such a supposition ex-
plains very simply and completely all the obvious
appearances of the heavens. In order to see that it
does this, nothing more is requisite than a distinct
conception of the nature of relative motion, and a
knowledge of the principal astronomical phenomena.
There was, therefore, no reason why such a doctrine
might not be discovered^ that is, suggested as a theory
plausible at first sight, long before the time of
Copernicus; or rather, it was inevitable that this
guess, among others, should be propounded as a solu-
tion 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 succeed-
ing 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 opi-
nion, having in our minds, as we unavoidably have.

360 HISTORY OF FORMAL ASTRONOMY.

the clear and irresistible considerations by which
the Copemican doctrine is established for us, it is
difficult for us not to attribute superior sagacity and
candour to those who held that side of the question,
and to imagine those who clung to the Ptolemaic
hypothesis to have been blind and prejudiced ;— in-
capable of seeing the beauty of simplicity and sym-
metry, or indisposed to resign established errors,
and to accept novel and comprehensive truths. Yet
in judging thus, we are probably ourselves influenced
by the prejudices of the knowledge and received opi-
nions of our own times. For is it, in reality, clear
that, before the time of Copernicus, the heliocentric
theory (that which places the centre of the celestial
motions in the sun,) had a claim to assent so de-
cidedly superior to the geocentric theory, which
places the earth in the centre ? What is the basis
of the heliocentric theory ? — ^That the relative mo-
tions are the same^ on that and on the other suppo-
sition. So fer, therefore, the two hypotheses are
exactly on the same footing. But, it is urged, on
the heliocentric side we have the advantage of sim-
plicity : — ^true ; but we have, on the other, the testi-
mony of our senses ; that is, the geocentric doctrine
is the obvious and spontaneous interpretation of the
appearances. Both these arguments, simplicity on
the one side, and obviousness on the other, are
vague, and we may venture to say, both indecisive.
We cannot establish any strong preponderance of
probability in favour of the former doctrine, without

PRELUDE TO THE EPOCH OF COPERNICUS. 361

going much further into the arguments of the
question.

Nor, when we speak of the superior simplicity of
the Copemican 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 under-
takes 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 epicyles
of its predecessor, and, in some parts, with increased
machinery. The heliocentric theory, without these
appendages, would not approach the Ptolemaic, in
the accurate explanation of facts ; and as those who
placed the sun in the centre had never, till the time
of Copernicus, shown how the inequalities were to
be explained on that supposition, we may assert that
after the promulgation of the theory of eccentrics
and epicycles on the geocentric hypothesis, there
was no published heliocentric theory which could
bear a comparison with it.

It is true, that all the contrivances of epicycles, and
the like, by which the geocentric hjrpothesis was made
to represent the phenomena, were susceptible of an
easy adaptation to a heliocentric method, when a
good mathematician had once proposed to himself the
problem; and this was precisely what Copernicus
undertook and executed. But, till the appearance
of his work, the heliocentric system had never come

362 HISTORY OF FORMAL ASTRONOMY.

before the world except as a hasty and imperfect
hypothesis; which bore a favourable comparison
with the phenomena, so long as their general features
only were known ; but which had been completely
thrown into the shade by the labour and intelligence
bestowed upon the Hipparchian or Ptolemaic theories
by a long series of great astronomers of all countries.

But, though the astronomers who, before Coper-
nicus, held the heliocentric opinion, cannot, on any
good grounds, be considered as much more enlight*-
ened than their opponents, it is curious to trace the
early and repeated manifestations of this view of the
universe. Its distinct assertion among the Greeks is
an evidence of the clearness of their thoughts, and
the vigour of their minds ; and it is a proof of the
feebleness and servility of intellect in the stationary
period, that, till the period of Copernicus, no one
was found to try the fortune of this hypothesis,
modified according to the improved astronomical
knowledge of the time.

The most ancient of the Greek philosophers to
whom the ancients ascribe the heliocentric doctrine,
is Pythagoras ; but Diogenes Laertius makes Philo-
laus, one of the followers of Pythagoras, the first
author of this doctrine. We learn from Archimedes,
that it was held by his contemporary, Aristarchus.
" Aristarchus of Samos," says he \ " makes this sup-
position, — ^that the fixed stars and the sun remain at

^ Archim Arenarius.

PRELUDE TO THE EPOCH OF COPERNICUS. 363

rest, and that the earth revolves round the sun in a
circle." Plutarch* asserts that this, which was only
a hypothesis in the hands of Aristarchus, was proved
by Seleucus ; but we may venture to say that, • at
that time, no such proof was possible. Aristotle
had recognised the existence of this doctrine by
arguing against it. " All things," says he', " tend to
the centre of the earth, and rest there, and there-
fore 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 Mer-
cury and Venus revolve about the sun, as does Mar-
tianus Capella at a later period ; and Seneca says*,
it is a worthy subject of contemplation, whether the
earth be at rest or in motion : but at this period, as
we may see from Seneca himself, that habit of in-
tellect which was requisite for the solution of such
a question, had been succeeded by indistinct views,
and rhetorical forms of speech. If there were any
good mathematicians and good observers at this
period, they were employed in cultivating and veri-
fying the Hipparchian theory.

Next to the Greeks, the Indians appear to have

* Quest. Plat. Delamb. A. A. vi.
' Copemic. i. 7* * Quest. Nat. vii. 2.

364 HISTORY OF FORMAL ASTRONOMY.

possessed that original vigour and clearness of
thought, from which true science springs. It is
remarkable that the Indians, also, had their heliocen-
trie theorists. Ar7abatta^ (a.d. 1322), and other
astronomers of that country, are said to have advo-
cated the doctrine of the earth's revolution on its
axis ; which opinion, however, was rejected by sub-
sequent philosophers among the Hindoos.

Some jmters have thought that the heliocentric
doctrine was derived by Pythagoras and other Euro-
pean 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 anything which the oriental
nations could teach ; and that each astronomer was
induced to adopt or reject it, not by any informa-
tion which a master could give him, but by his love
of geometrical simplicity on the one hand, or the
prejudices of sense on the other. Real science, de-
pending on a clear view of the relation of phenomena
to general theoretical ideas, cannot be communicated
in the way of secret and exclusive traditions, like
the mysteries of certain arts and crafts. If the
philosopher do not see that the theory is true, he is
little the better for having heard or read the words
which assert its truth.

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

PRELUDE TO THE EPOCH OF COPERNICUS. 365

It is impossible, therefore, 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 arrange-
ments of the Ptolemaic system, was so much more
obvious than any other, that it must necessarily
come first, iii order to form an introduction to the
Copemican.

The true foundation of the heliocentric theory for
the ancients, was, as we have intimated, its perfect
geometrical consistency with the general features of
the phenomena, and its simplicity. But it was
unlikely that the human mind would be content to
consider the subject under this strict and limited
aspect alone. In its eagerness for wide speculative
views, it naturally looked out for other and vaguer
principles of connexion and relation. Thus, as it
had been urged in favour of the geocentric doctrine
that the heaviest body must be in the centre, it was
maintained, as a leading recommendation of the
opposite opinion, that it placed the fire, the noblest
element, in the centre of the universe. The autho-
rity of mythological ideas was called in on both sides
to support these views. Numa, as Plutarch* in-

* De Facie in Orbe Lunae. 6.

366 HISTORY OF FOBMAL ASTRONOMY.

fonns us, btiilt a circular temple over the ever-burn-
ing fire of Vesta ; typifying, not the earth, but the
universe, which, according to the Pythagoreans, has
the fire seated at its centre. The same writer, in
another of his works, makes one of his interlocutors
say, "Only, my Mend, do not bring me before a
court of law on a charge of impiety ; as Cleanthes
said, that Aristarchus the Samian ought to be tried
for impiety, because he removed the homestead of
the universe." This, however, seems to have been
intended as a pleasantry.

The prevalent physical views, and the opinions con-
cerning the causes of the motions of the parts of the
universe, were scarcely more definite than those con-
cerning 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 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 ac-
cording to the state of the science of motion before
Copernicus, all reasonings from such principles were
utterly vague and obscure.

PRELUDE TO THE EPOCH OF COPERNICUS. 367

We must not omit to mention a modem who
preceded Copernicus, in the assertion at least of the
heliocentric doctrine. This was Nicholas de Cusa,
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
Ignorantia," propounded the doctrine of the motion
of the earth ; more, however, as a paradox than as
a reality. We cannot consider this as any anticipa-
tion of a profound and consistent view of the truth.

We shall now examine further the promulgation
of the heliocentric system by Copernicus, and its
consequences.

368

CHAPTER II.

Induction op Copernicus. — ^The Heliocentric
Theory asserted on formal grounds.

It will be recollected that ihe formal are opposed to
the physical grounds of a theory ; the fonner tenn
indicating that it gives a satisfectory 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 refer to the causes
of the motions, the laws of force and matter. The
strongest of the considerations by which Copernicus
was led to invent and adopt his system of the universe
were of the former kind. He was dissatisfied, he says,
in his preface addressed to the Pope, with the want of
symmetry in the eccentric theory, as it prevailed in
his days ; and weary of the uncertainty of the mathe-
matical traditions. He then sought through all the
works of philosophers, whether any had held opinions
concerning the motions of the world, different from
those received in the established mathematical
schools. He found, in ancient authors, accounts of
Philolaus and others, who had asserted the motion
of the earth. " Then," he adds, " I, too, began to
meditate concerning the motion of the earth : and
though it appeared an absurd opinion, yet since I

INDUCTION OP COPERNICUS. 369

knew that, in previous times, others had been allowed
the privilege of feigning what circles they chose, in
order to explain the phenomena, I conceived that I
also might take the liberty of trying whether, on the
supposition of the earth's motion, it was possible to
find better explanations than the ancient ones, of
the revolutions of the celestial orbs.

" Having then assumed the motions of the earth,
which are hereafter explained, by laborious and long
observation I at length found, that if the motions of
the other planets be compared with the revolution
of the earth, not only their phenomena follow from
the suppositions, but also that the several orbs, and
the whole system, are so connected in order and
magnitude, that no one part can be transposed with-
out 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 sym-
metry of the system, were the grounds on which
Copernicus adopted his theory ; as the craving for
these qualities was the feeling which led him to seek
for a new theory. It is manifest that in this, as in
other cases of discovery, a clear and steady possession
of abstract ideas, and an aptitude in comprehending
real facts under these general conceptions, must have
been leading characters in the discoverer's mind.
He must have had a good geometrical head, and
great astronomical knowledge. He must have seen,
with peculiar distinctness, the consequences which

VOL. I. 2 B

370 HISTORY OF FORMAL ASTRONOMY.

flowed from his suppositions as to the relations of
space and time, — the apparent motions which re-
sulted from the assumed real ones; and he must
also have known well all the irregularities of the
apparent motions for which he had to account. We
find indications of these qualities in his expressions.
A steady and calm contemplation of the theory is
what he asks for, as the main requisite to its recep-
tion. If you suppose the earth to revolve and the
heaven to be at rest, you will find, he says, ** si serio
animcdverlas^^ if you think steadily, that the apparent
diurnal motion will follow. And after alleging his
reasons for his system, he says^ " 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 diflSicult and almost inconceivable,
and against the opinion of the majority, yet, in the
sequel, by God's favour, 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 hypothesis ascribed to the planets those
motions which were apparent only, and which really

' De Ber. p. 9.

INDUCTION OP COPERNICUS. 871

arose from the motion of the earth round the sim in
the new hypothesis, the latter must much simplify the
planetary theory. Kepler' enumerates eleven motions
of the Ptolemaic system, which are at once extermi-
nated and rendered unnecessary by the new system.
Still, as the real motions, both of the earth and the
planets, are unequable, it was requisite to have some
mode of representing these inequalities ; and, accord-
ingly, the ancient theory of eccentrics and epicycles
was retained, so far as was requisite for this purpose.
The planets revolved round the sun by means of a
deferent, and a great and small epicycle ; or else by
means of an eccentric and epicycle, modified from
Ptolemy's, for reasons which we shall shortly men-
tion. This mode of repr^enting the motions of the
planets continued in use, till it was expelled by the
discoveries of Kepler.

Besides the daily rotation of the earth on its axis,
and its annual circuit about the sun, Copernicus
attributed to the axis a " motion of declination," by
which, during the whole annual revolution, the pole
was constantly directed towards the same part of
the heavens. This constancy in the absolute direc-
tion of the axis, or its moving parallel to itself, may
be more correctly viewed as not indicating any
separate motion. The axis continues in the same
direction, because there is nothing to make it change
its direction ; just as a straw, lying on the surface of

■ Myst. Cosm. cap. 1.

2 B 2

372 HISTORY OF FORKAL ASTRONOMY.

a cup of water, continues to point nearly in the same
direction when the cup is carried round a room.
And this wa« noticed by Copemicus's adherent,
Rothman', a few years after the publication of the
work De Revolutionibus. " There is no occasion,"
he says, in a letter to Tycho Brahe, " for the triple
motion of the earth : the annual and diurnal motions
suffice." This error of Copernicus, if it be looked
upon as an error, arose from his referring the position
of the axis to a limited space, which he conceived
to be carried round the sun along with the earth,
instead of referring it to . fixed or absolute space.
When, in a planetarium, 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 paral-
lelism. A similar confusion of geometrical concep-
tion, 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 no.

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 diflFer-
ence. Copernicus erroneously supposes the preces-
sion to be unequable ; and his method of explaining

• Tycho. Epist. i. p. 184, a. d. 1590.

INDUCTION OP COPERNICUS. 373

this change, which is simpler than that of the
ancients, becomes more simple still, when applied to
the true state of the facts.

The tendencies of our speculative nature, which
carry us onwards in pursuit of symmetry and rule,
and which thus produced the theory of Copernicus,
as they produce all theories, perpetually show their
vigour by overshooting their mark. They obtain
something by aiming at much more. They detect
the order and connexion which exist, by imagining
relations of order and connexion which have no
existence. Real discoveries are thus mixed with
baseless assumptions ; profound sagacity is combined
with fanciful conjecture; not rarely, or in peculiar
instances, but commonly, and in most cases; pro-
bably in all, if we could read the thoughts of the
discoverers as we read the books of Kepler. To try
wrong guesses is apparently the only way to hit upon
right ones. The character of the true philosopher
is, not that he never conjectures hazardously, but that
his conjectures are clearly conceived and brought
into rigid contact with facts. He sees and compares
distinctly the ideas and the things, — ^the relations of
his notions to each other and to phenomena. Under
these conditions it is not only excusable, but ne-
cessary 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

874 HISTOEY OP FORMAL ASTRONOMY.

spirit. The axiom that the celestial motions must
be circular and uniform, appeared to him to have
strong claims ; and his theory of the inequalities of
the planetary motions is fashioned upon it. His
great desire was to apply it more rigidly than
Ptolemy had done. The time did not come for
rejecting the ajdom, till the observations of Tycho
Brahe and the calculations of Kepler had been
made.

I shall not attempt to explain, in detail, Copemi-
cus'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 epi-
cycles : but we must observe that Copernicus was
aware of some of the discrepancies which belonged to
that theoryas it had, up to that time, been propounded.
In the case of Mercury, which is more eccentric than
the other planets, he makes suppositions which are
complex indeed, but which show his perception of
the imperfection of the common theory; and he
proposes a new theory of the moon, for the very
reason which did at last overturn the doctrine of
epicycles, namely, that the ratio of their distances

INDUCTION OF COPEBNICUS. 375

from the earth at diiferent times was inconsistent
with the circular hypothesis*.

It is obvious, that, along with his mathematical
clearness of view, and his astronomical knowledge,
Copernicus must have had great intellectual bold-
ness and vigour, to conceive and fiiUy develope a
theory so different as his .was, from all received doc-
trines. His pupil and expositor, Rheticus, says to
Schener, " I beg you to have this opinion concern-
ing 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, Ael KiKevBipov

elvat T§ yyoifitj rov fiiWovra <f>iXo(TO<f>€2v» * 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 tem-
per," 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 reject-
ing the opinions of ancient philosophers, except for
weighty reasons and irresistible fiusts, through any
love of novelty. His years, his gravity of character,
his excellent learning, his magnanimity and noble*

* De Rev. iv, c, 2.

376 HISTORY OF FORMAL ASTRONOMY.

ness of spirit, are very fiur £5pom haying any liability
to such a temper, which belongs either to youth, or
to ardent and light tempers, or to those r&v iieya
<l>povovvTcifv iirl Oetopia fiixp^y ^ who think much of them-
selves and know little,' as Aristotle says/' Undoubt-
edly this deference for the great men of the past,
joined with the talent of seizing the spirit of their
methods when the letter of their theories is no
longer tenable, is the true mental constitution of
discoverers.

Besides the intellectual energy which was requi-
site in order to construct a system of doctrines so
novel as those of Copernicus, some courage was
necessary to the publication of such opinions; certain,
as they were, to be met, to a great extent, by rejec-
tion and dispute, and perhaps by charges of heresy
and mischievous tendency. This last danger, how-
ever, must not be judged so great as we might infer
from the angry controversies and acts of authority
which occurred in Galileo's time. The dogmatism
of the stationary period, which identified the cause
of philosophical and religious truth, had not yet dis-
tinctly felt itself attacked by the advance of phy-
sical knowledge; and therefore had not begun to
look with alarm on such movements. Still, the
claims of Scripture and of ecclesiastical authority
were asserted as paramount on all subjects ; and it
was obvious that many persons would be disquieted
or offended, with the new interpretation of many
scriptural expressions, which the true theory would

INDUCTION OF COPERNICUS. 377

make necessary. This evil Copernicus appears to
have foreseen ; and this and other causes long with-
held him from publication. He was himself an
ecclesiastic ; and, perhaps by the patronage of his
maternal uncle, was prebendary of the church of
St. John at Thorn, and a canon of the church of
Frawenturg, in the diocese of Ermeland*. He was
a student at Bologna, a professor of mathematics at
Rome in the year 1500, and afterwards pursued his
studies and observations at Fruemburg, at the mouth
of the Vistula*. His discovery of his system must
have occurred before 1607, for in 1543 he informs
Pope Paulus the Third, in his dedication, that he had
kept his book by him for four times the nine years
recommended by Horace, and then only published it
at the earnest entreaty of his friend Cardinal Schom-
berg, whose letter is prefixed to the work. "Though
I know," he says, " that the thoughts of a philosopher
do not depend on the judgment of the many, his
study being to seek out truth in all things as far as
that is permitted by God to human reason: yet
when I considered," he adds, " how absurd my doc-
trine would appear, I long hesitated whether I should
publish my book, or whether it were not better to
follow the example of the Pythagoreans and others,
who delivered their doctrines only by tradition and
to friends." It will be observed that he speaks here
of the opposition of the established school of astro-

^ Rheticus, Nar. p. 94. ' Riccioli.

378 HISTORY OF FORMAL ASTRONOMY.

nomerSy not of divines. The latter, indeed, he
appears to consider as a less formidable danger. " If
perchance," he says at the end of his preface, " there
be fmraioXoyoii vain babblers, who knowing nothing
of mathematics, yet assume the right of judging on
account of some place of Scripture perversely
wrested to their purpose, and who blame and attack
my undertaking ; I heed them not, and look upon
their judgments as rash and contemptible," He
then goes on to show that the globular figure of the
earth (which was, of course, an undisputed point
among astronomers,) had been opposed on similar
grounds by Lactantius, who, though a writer of credit
in other respects, had spoken very childishly in that.
In another epistle prefixed to the work (apparently
from another hand, and asserted by Kepler^ to be by
Andreas Osiander), the reader is reminded that the
hjrpotheses of astronomers are not necessarily as-
serted to be true, by those who propose them, but
only to be a way of representing facts. This salvo,
indeed, appears to be still the orthodox Catholic
mode of avoiding the supposed theological diflicul-
ties which are involved in admitting the motion of
the earth ; for it is the language used by the Jesuit
editors of Newton. They prefix to the third book
of the " Principia" a declaration that they admit the
motion of the earth only as a hypothesis, professing
to obey the decrees of the popes against the motion

' See the motto to Kepler's De Stella Martis.

INDUCTION OP COPEBNICUS. 370

of the earth : — ^^ Latis a summis pontificibus contra
telluris motum decretis nos obsequi profitemur." We
may observe that, in the time of Copernicus, when
the motion of the earth had not been connected
with the physical laws of matter and motion, it
could not be considered so distinctly real as in after
times.

The delay of the publication of Copemicus's work
brought it to the end of his life : he died in the
year 1543, in which it was published ^ His system
was, however, to a certain extent, promulgated, and
his fame diffused before that time. Cardinal Schom-
berg, 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 honour. 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 remains immoveable and
fixed." He then proceeds to entreat him earnestly
to publish his work. The book appears to have been
written in 1539', and is stated to have been sent in
1540 by Achilles P. Gessarus of Feldkirch to Dr.

^ De Revolutionibus Siderura. • Maestlin.

380 HISTORY OF FORMAL ASTRONOMY.

Vogelinus of Constance, as a palingenesis, or new
birth of astronomy. At the end of the De Revo-
lutionibus is the " Narratio" of Rheticus, already
quoted. Rheticus, it appears, went to Copernicus
for the purpose of studying his theory, and spealcs
of his " Preceptor" with strong admiration, as we
have seen. " He appears to me," says he, " more to
resemble Ptolemy than any other astronomer." This,
it must be recollected, was selecting the highest
known subject of comparison.

881

CHAPTER III.

Sequel to Copernicus. — ^The Reception and Db-
velopement op the copernican theory.

Sect 1. — First Reception of the Copemican Theory.

The theories of Copernicus made their way among
astronomers, in the manner in which true 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
these doctrines was to be looked for, from the agree-
ment of these tables with observation, through a
sufficient course of time. The work " De Revolu-
tionibus" contains such tables. In 1551 Beinhold
improved and republished tables founded on the
principles of Copernicus. " We owe," he says in his
preface, "great obligations to Copernicus, both for
his laborious observations, and for restoring the doc-
trine of the Motions. But though his geometry is
perfect, the good old man appears to have been, at
times, careless in his numerical calculations. I have,
therefore, recalculated the whole, from a comparison
of his observations with those of Ptolemy and others,
following nothing but the general plan of Copemi-

382 HISTORY OF FORMAL ASTRONOMY.

cus's demonstrations." These Prutenic tables were
republished in 1571 and 1585, and continued in re-
pute for some time ; till superseded by the Rudolph-
ine tables of Kepler in 1627. The name Pru-
tenic, or Prussian, may be considered as a tribute
to the feme of Copernicus, for it shows that his dis-
coveries had inspired his countrymen with the ambi-
tion of claiming a place in the literary community of
Europe. In something of the same spirit, Rheticus
wrote an " Encomium Borussise," which was published
along with his " Narratio."

The tables founded upon the Copemican system
were, at first, much more generally adopted than the
heliocentric doctrine on which they were founded.
Thus Magin published at Venice, in 1587, " New
Theories of the Celestial Orbits, agreeing with the
Observations of Nicholas Copernicus." But in the
preface, after praising Copernicus, he says, " Since,
however, he, either for the sake of showing his talents,
or induced by his own reasons, has revived the opinion
of Nicetas, Aristarchus, and others, concerning the
motion of the earth, and has disturbed the established
constitution of the world, which was a reason why
many rejected, or received with dislike, his hypothe-
ses, 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 fevour by many persons, even before

SEQUEL TO COPERNICUS. 888

its general publication. We have already seen the
enthusiasm with which Rheticus, who was his 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 Copemican
system, who adopted it before the controversy on the
subject had attracted attention, I shall only add
Maestlin, and his pupil, Kepler. Maestlin published
in 1588 an " Epitome Astronomiae," in which the
immobility of the earth is asserted ; but in 1596 he
edited Kepler's " Mysterium Cosmographicum," and
the " Narratio" of Rheticus ; and in an epistle of his
own, which he inserts, he defends the Copemican
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 Tiibingen,
attending to Michael Maestlin, being disturbed by
the manifold inconveniences of the usual opinion
concerning the world, I was so delighted with Coper-
nicus, of whom he made great mention in his lec-
tures, 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 Copemi-

384 HISTORY OF FORMAL ASTRONOMY.

can system, of which we thus see traces, led to a
controversy of some length and extent. This con-
troversy turned principally upon physical considera-
tions, which were much more distinctly dealt with
by Kepler, and others of the followers of Copernicus,
than they had been by the discoverer himself. I
shall, therefore, give a separate consideration to this
part of the subject. It may be proper, however, in
the first place, to make a few observations on the
progress of the doctrine, independently of these phy-
sical speculations.

Sect. 2. — Diffusion of the Copemican Theory.

The diffusion of the Copemican opinions in the
world did not take place rapidly at first. Indeed, it
was necessarily some time before the progress of
observation, and of theoretical mechanics, gave the
heliocentric doctrine that superiority in argument,
which now makes us wonder that men should have
hesitated when it was presented to them. Yet there
were some speculators of this kind, who were at-
tracted at once by the enlarged views of the universe
which it opened to them. Among these was the
unfortunate Giordano Bruno of Nola, who was burnt
as a heretic at Rome in 1600. The heresies which
led to his unhappy fate were, however, not his astro-
nomical opinions, but a work which he published in
England, and dedicated to Sir Philip Sydney, under
the title of " Spaccio della Bestia Trionfante,"

SEQUEL TO COPERNICUS. 385

and which is understood to contain a bitter satire of
the Catholic 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 em-
braced the Copernican opinions at an early period,
and connected with them the belief in innumerable
worlds besides that which we inhabit ; as also cer-
tain metaphysical or theological doctrines, which he
called the Nolan philosophy. In 1591 he published
*' De innumerabilibus Mundis et infigurabili, sen de
Universe et Mundis," in which he maintains that
each star is a sun, about which revolve planets like
our earth ; but this opinion is mixed up with a large
mass of baseless verbal speculations.

Giordano Bruno is a disciple of Copernicus on
whom we may look with peculiar interest, since he
probably had a considerable share in introducing the
new opinions into England \ He visited this coun-
try in the reign of Queen Elizabeth, and speaks of
her and of her councillors in terms of praise, which
appear to show that his book was intended for
English readers ; though he describes the mob which
was usually to be met with in the streets of London,
with expressions of great disgust : '^ Una plebe la
quale in essere irrespettevole, incivile, rozza, rustica,
selvatica, et male allevata, non cede ad altra che

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

VOL. I. 2 C

886 HISTOKY OF FOBHAL ASTBONOMT.

pasoev possa la terra nel suo Beno'." The work
to which I refer is '^La Cena de le Cenere/'
and narrates what took place at a eupper held on
the evening of Ash Wednesday (about 1588, see
p. 146)9 at the house of Sir Fulk Greville, in order
to give " H Nolano" an opportunity of defending his
peculiar opinions. His principal antagonists are two
*< Dottori d' Oxonia," whom Bruno calls Nundinio and
Torquato. The subject is not treated in any very
masterly manner on either side ; but the author makes
himself have greatly the advantage not only in argu-
ment, but in temper and courtesy : and in support of
bis representations of *^ pedantesca» ostinatissima
ignoranza et presumdone, mista con una rustica inci-
vilita, che farebbe prevaricar la pazienza di Giobbe,"
in his opponents, he refers to a public disputation
which he had held at Oxford with these doctors of
theology, in presence of Prince Alasco, and many of
the English nobility".

Among the evidences of the diificulties which still
lay in the way of the reception of the Copemican
system, we may notice Bacon, who, as is well known,
constantly refused his assent to it. It is to be ob-
served, however, that he does not reject the opinion
of thd 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

• Opere di Giordano Bruno, vol. 1. p. 146. ■ voL I. p. 179-

SEQUEL TO OOPERNICUS. 387

appears to us the mor^ true opinion)." And in his
tract *• On the Cause of the Tides," he says, -« If the
tide of the sea be the extreme and dimished limit ef
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 Intelleotualis" he gives his
reasons for not accepting the heliocentric theory.
" In the system of Copernicus there are many and
grave difficulties: for the threefold motion with
which he encumbers the earth is a serious incon-
venience ; and the separation of the sun from the
planets, with which he has so many affections ip
common, is likewise a harsh step: and the intro-
duction 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 other things which he as*
sumes, are proceedings which mark a man who
thinks nothing of introducing fictions of any kind
into nature, provided his calculations turn out well."
We have already explained that, in attributing three
motions to the earth, Copernicus had presented his
system encumbered with a complexity not really
belonging to it. But it will be seen shortly, that
Bacon's fundamental objection to this system'was his
wish for a system which could be supported by sound
physical considerations ; and it must be allowed, that
at the period of which we are speaking, this had not yet

2 c 2

388 HifirroRY of formal asttronomt.

been done in feyour of the Copermcan hypothesis.
We maj add, however, that it is not quite clear that
Bacon was in full possession of the details of the
astronomical systems which that of Copernicus was
intended to supersede ; and that thus he, perhaps, did
not see how much less harsh were these fictions^ as he
called them, than those which were the inevitable
alternatives. Perhaps he might even be liable to a
little of that indistinctness, with respect to strictly
geometrical conceptions, which we have remarked in
Aristotle. We can hardly otherwise account for his
not seeing any use in resolving the apparently irre-
gular motion of a planet into separate regular mo-
tions. Yet he speaks slightingly of this important
step*. " The motion of planets, which is constantly
talked of as the motion of regression, or renitency,
from west to east, and which is ascribed to the
planets as a proper motion, is not true; but only
arises from appearance, from the greater advance
of the starry heavens towards the west, by which
the planets are left behind to the east." Un-
doubtedly those who spoke of such a motion of
regression, were aware of this ; but they saw how
the motion was simplified by this way of conceiving
it, which Bacon seems not to have seen. Though,
therefore, we may admire Bacon for the stedfastness
with which he looked forwards to physical astronomy
as the great and proper object of philosophical inte-
rest, we cannot give him credit for seeing the ftdl

* Thema CoeH, p. 246.

SEQUEL TO COPERNICUS. 389

value and meaning of what had been done, up to his
time, in Formal Astronomy.

Bacon's contemporary, Gilbert, whom he fre-
quently praises as a philosopher, was much more
disposed to adopt the Copemican opinions, though
even he does not appear to have made up his mind
to assent to the whole of the system. In his work,
" De Magneta," (printed 1600,) he gives the prin-
cipal arguments in favour of the Copernican system,
and decides that the earth revolves on its axis*. He
connects this opinion with his magnetic doctrines ;
and especially endeavours 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 Philosophia
Nova,") he appears to hesitate between the systems
of Tycho and Copernicus*. Indeed, it is probable
that at this period many persons were in a state of
doubt on such subjects. Milton, at a period some<-
what later, appears to have been still undecided.
In the opening of the eighth book of the Paradise
Lost, he makes Adam state the difficulties of the
Ptolemaic hypothesis, to which the archangel Ra-
phael opposes the usual answers; but afterwards
suggests to his pupil the newer system :

. . . . What if seyenth to these

The planet earth, so stedfast though she seem,

Insensihly three different motions move ?

P. L. b. Till.

* Lib. vi. cap. 3, 4. • Lib. ii. cap. 20.

S90 HISTOBT OF FORMAL A8TB0N0MY.

Milton's leaning) however, seems to have been for
the new system; we can hardlj believe that he
would otherwise have conceived so distinctly, tad
described with such obvious pleasure, the motion of
the earth :

Or she from west her silent course advance
With hio£fetlftite pace, that spinning sleeps
On her soft axle, while she paces ey^H,
And bears thee soft with the smooth air along.

P. L. b. viii.

Perhaps the works of the celebrated Bishop Wil-
kins tended more than any others to the difl^lsion of
the Copemican system in England, since even their
extravagancies drew a stronger attention to them.
In 1638, when he was only twenty-four years old, he
published a book entitled " The Discovery of a New
World ; or, a Discourse tending to prove that it is
probable there may be another habitable World in
the Moon ; with a Discourse concerning the possi-
hUity 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 after-
wards, 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 favour of the heliocentric system ; and
explained away the opposite arguments, especially
those drawn from the supposed declarations of Scrip-
ture* Probably a good deal was done for the esta-

SEQUEL TO COPERNICUS4 391

blishment of those opinions by Thomas Salusbury,
who was a wann admii^er of Galileo, and published,
in 1661^ a translation of several of his works bearing
upon this subject. The mathematicians of this
coimtry, in the seventeenth century, as Napier and
Briggs, Horrox and Crabtree, Oughtred and Ward,
Wallis and Wren, were probably all decided Coper-
nicans. Kepler dedicates one of his works to
Napier, and Ward invented an approximate method
of solving Kepler's problem, still known as "the
simpld elliptical hypothesis." Horrox wrote, and
wrote well, in defence of the Copemican opinion, in
his " Keplerian Astronomy defended and promoted,"
composed (in Latin) probably about 1636, but not
published till 1678, 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 intro-
ductory address, "being, for subject and design,
intended chiefly for gentlemen, I have been as care-
less of using a studied pedantry in my style, as
careful in contriving a pleasant and beautifiil im-
pression." In order, however, to judge of the
advantage under which the Copernican system now
came forwards, we must consider the additional
evidence for it which was brought to light by
Galileo's astronomical discoveries.

392 HISTORY OF FORMAL ASTRONOMY.

Sect. 3.— -7%^ Hdiocenbric ITieorjf confirmed hy Facts.
GaWeds Astronomical Discoveries.

The long interval which elapsed between the last
great discoveries made by the ancients and the first
made by the modems, had afforded ample time for
the developement of all the important consequences
of the ancient doctrines. But when the human
mind had been thoroughly roused again into acti-
vity, this was no longer the course of events. Dis-
coveries crowded on each other ; one wide field of
speculation was only just opened up, when a richer
promise tempted the labourers away into another
quarter. Hence the history of this period contains
the beginnings of many sciences, but exhibits none
fully worked out into a complete or final form. Thus
statics, soon after its revival, was eclipsed and over-
laid by dynamics ; and the Copernican system, con-
sidered 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 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 dis-
covery of the satellites of Jupiter, and of the ring of

SEQUEL TO COPERNICUS. 393

Saturn. These discoveries excited at the time the
strongest interest ; both from the novelty and beauty
of the objects they presented to the sense ; from the
way in which they seemed to gratify man's curiosity
with regard to the remote parts of the universe ; and
also from that of which we have here to speak, their
bearing upon the conflict of the old and the new
philosophy, the heliocentric and geocentric theories.
It may be true, as Lagrange and Montucla say, that
the laws which Galileo discovered in mechanics
implied a profounder genius than the novelties he
detected in the sky: but the latter naturally attracted
the greater share of the attention of the world, and
were matter of keener discussion.

It is not to our purpose to speak here of the details
and occasion of the invention of the telescope ; it is
well known that Galileo constructed his about 1609,
and proceeded immediately to apply it to the heavens.
The discovery of the satellites of Jupiter was almost
immediately the reward of this activity : and these
were announced in his Nuncius Sidereus, published
at Venice in 1610. The title of this work will best
convey an idea of the claim it made to public notice :
" The Sidereal Messenger^ annoimcing great and very
wonderful spectacles, and oflering them to the con-
sideration of every one, but especially of philosophers
and astronomers; which have been observed by
Galileo Galilei, &c. &c., by the assistance of a per-
spective glass lately invented by him; namely, in
the face of the moon, in innumerable fixed stars

394 Hi&rroitT of fobmal AflrniONOMY.

in the milkjr way^ in nebulous stafs, but especiallj
in foul* planets which reyolte round Jupiter at Ai$*
ferent intervals and periods with a wonderful cele-^
litf; which, hitherto not known to any one^ the
author has recently been the first to detect, and has
decreed to call the Medicean stars'^

The interest this discovery excited was intense:
and men were at this period so little habituated to
accommodate their convictions on matters of science
to newly-observed facts, that several of " the paper-'
philosophers," as Galileo termed them, appear to have
thought they could get rid of these new objects by
writing books against them. The effect which the
discovery had . upon the reception of the Copemican
system was immediately very considerable* It
showed that the real universe was very different
from that which ancient philosophers had imagined,
and suggested at once the thought that it contained
mechanism more various and more vast than had
yet been coiyectured. And when the system of
the planet Jupiter thus offered to the bodily eye a
model or image of the solar system according to the
views of Copernicus, it supported the belief of such
an arrangement of the planets, by an analogy all but
irresistible. It thus, as a writer^ of our own times
has said, ^' gave the hMing turn to the opinions of
mankind respecting the Copemican system." We
may trace this effect in Bacon, even though he does

^ Sir J. Hersehel.

SEQUEL TO COPERNICUSi 395

not adsent to the motion of the earth. *^ We afi&rm,"
he s&ysS ^^the mn^fcUowing arrangement (solisequiuxn)
of Veaus and Mercury ; since it has be^n found by
Galileo that Jupiter also has attendants."

The " Nuncius Sidereus" contained other dis-
coveries 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 irl'egular. This,
though perhaps not bearing directly upon the ques-
tion 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 giyen an abundant quantity of reasons
for the visible marks on her surface, all proceeding
on these preconceived views. Others of his dis-
coveries produced 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 communicate, bearing more decidedly
on the Copernican controversy. This intelligence was
indeed decisive with regard to the motion of Venus
itbout the sun ; for he found that that planet, in the
course of her revolution, assumes the same succession
of phases ti'hich the moon exhibits in the course of
a month. This he expressed by a Latin verse :

CjAthitt figuras aBinulatur mater amoruln :

The ^ueen of lore like Cjruthia shapes her forms :

^ Thema Cceli, ix. p^ S53.

396 HISTORY OF FORMAL ASTRONOMY.

transposing the letters of this Une in the pubUshed
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 fsucts.

It had always been a formidable objection to the
Copemican theory that this appearance of the planets
had not been observed. The author of that theory
had endeavoured to account for this, by supposing
that the rays of the sun passed freely through the
body of the planet, and Galileo takes occasion to
praise him for not being deterred from adopting
the system which, on the whole, appeared to agree
best with the phenomena, by meeting with some
which it did not enable him to explain*. Yet while
the fate of the theory was yet undecided, this could
not but be looked upon as a weak point in its defences.

The objection, in another form also, wa* embarrass-
ing alike to the Ptolemaic and Copernican systems.
Why, it was asked, did not Venus appear four times
as large when near her perigee, as when near her apo-
gee ? The author of the epistle prefixed to Coperni-
cus's work had taken refdge in this argument from
the danger of being supposed to believe in the reality
of the system ; and Bruno had attempted to answer
it by saying, that luminous bodies were not governed
by the same laws of perspective as opaque ones.
But a more satisfactory answer now readily offered

• L. U. K. Life of Galileo, p. 35.

SEQUEL TO COPERNICUS. 397

itself. Venus does not appear four times as large
when she is four times as near, because her briglU
part is not four times as large, though her visible
diameter is ; and as she is too small for us to see
her shape, we judge of her size only by the quantity
of light.

The other great discoyeries made in the heavens
by means of telescopes, as that of Saturn's ring and
his satellites, the spots in the sun, and others, belong
to the further progress of astronomy. But we may
here observe, that this doctrine of the motion of
Mercury and Venus about the sun was further con-
firmed by Kepler's observation of the transit of the
former planet over the sun in 1631. Our country-
man Horrox was the first person who, in 1639, had
the satisfaction of seeing a transit of Venus.

These events are a remarkable instance of the
way in which a discovery in art, (for at this period,
the making of telescopes must be mainly so con-
sidered,) may influence the progress of science. We
shall soon have to notice a still more remarkable
example of the way in which two sciences (astro-
nomy and mechanics) may influence and promote
the progress of each other.

Sect 4. — The Copemican System opposed on

Theological Grounds.

We have seen that the doctrines promulgated by
Copernicus excited no visible alarm among the
theologians of his own time ; and we have assigned

308 Hi&rroRT op formal astronomy.

as a reason for this, that those who were disposed to
assert the sway of authority in all matters of belief,
had not yet been roused and ruffled by the aggres-
sions of innovators in philosophy and religion, as
they soon afterwards were. Probably, also, we ought
to take into account the different temper and cir-
eumstances of the ultramontane and Italian learned
men. The latter, liying under the immediate shadow
of the papal chair, were necessarily less bold in their
speculations, and less open in their promulgation of
any opinions which might have a taint of heresy.
This influence operated less strongly in Poland and
Germany ; and we find no evidence which leads us
to deny to these countries the glory of having re*
oeived the Copemioan system of the world, from the
first, with satis&ction, and without bigoted oppo-
sition. The great religious reform which had its
rise in Germany about the time of the promulgation
.of the Copemican system, showed sufficiently that
that was the land where opinions would assert their
freedom ; and where authority could not, with pru-
dence, urge superfluous claims.

But in Italy the church entertained the persuasion
that her authority could not be upheld at all, with-
out uMrmtaining it to be supreme ou all poiiits. The
spirit of dogmatism of the middle ages, which we
have already endeavoured to characterize, had de-
scended upon the ecclesiastical institutions of the
seventeenth ^etitury ; and in consistency with that
spirit, it was criminal to disturb received doctrines,

SBQUEL TO 00PERNICU8. 890

or to separate philosophy from religion. The tenet
of the earth being at rest in the centre of the uni<«
verse, was not only a part of the established school-*
philosophy, but was also, it was conceived, sanctioned
by Scripture. The Copemican system, therefore, so
lar as it came into view, was looked at with sus^
picion and aversion. But though this system is
afterwards, in the official condemnation of it, spoken
of as " entertained by many," it never came under
the notice of the spiritual judges in any conspicuous
manner, till it had been illustrated by Galileo's
discoveries, and recommended by his writings.

The story of the condemnation of Galileo by the
Inquisition, for asserting the motion of the earth,
and of his formal renunciation of this doctrine in
the presence of his judges, has been so often told,
that I need not here repeat the details. It rather
belongs to our purpose to consider what lessons may
be gathered from it with regard to the progress of
science.

One reflection which occurs is, that both Galileo's
behaviour and that of his judges, appear to disclose
some Italian traits of character. The assumption of
supreme authority in all matters of opinion, an
assumption unsuited to the powers and condition of
man, had led, it would seem, to a kind of artificial
state of compromise, in which men's published opi-
nions were treated as a point of decorum only, the
truth being left out of consideration. Thus Galileo
seems to have expected that the flimsiest veil of

B

400 HISTORY OP FORMAJL AfimtONOBCY.

professed submissioH in his b^ef would enable his
arguments in fiivour of the Gop^mioan dootrine to
pass unidsited; and the inquisitors were satisfied
with a renunciation which they eouM not beUeve to
be sincere. TMs artificial state, again, was probably
one occasion of the furtive mode of insinuating his
doctrines, so mudi employed by Galileo, which some
of his historians admire as subtle irony, and others
blame as insincerity. Nor do we see anything to
lead us to believe tiiat Galileo was not at all times
roady to make such submissions as the spiritual tri-
bunals roquirod ; although undoubtedly he was also
very desirous of promoting the cause of what he
conceived to be philosophical truth. The same
absence of earnestness appears on the other side, in
the courtesy and indulgence with which, as is now
almost universally allowed, Gralileo .was treated
throughout the course of the proceedings against
him. For his being confined in the dungeons of the
Inquisition, as his lot has sometimes been desisribed,
appears to have consisted principaUy in his being
placed under some slight rostrictions, firsts in the
house of Nicolini, the ambassador of his own sove-
reign, the Duke of Tuscany, and afterwards in the
country-fieat of Archbishop Piecolomini, one of his
own warmest friends. It appears to be not going
too £str to suppose that the extravagant assumptions
of the churdi of Borne, which it was impossible
sincerely to allow, and necessary to evade by arti-
fice, generated in the philosophers of Italy an

SEQUEL TO COPERNICUS. 401

acuteness and subtlety^ but also a suppleness and
servility very different from the vigorous independent
habits of thought of Germany and England.

But there remains something more to be attended
to in the case of Galileo; for though the >See of
Rome might exaggerate the claims of religious
authority, there is a question of no small real diffi->
culty, 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 di-
lenmia, — ^that doctrines, established by a scientific use
of reason, may seem to contradict the declarations of
revelation according to our view of its meaning; — and
yet, that we cannot, in consistency with our religious
views, make reason a judge of the truth of revealed
doctrines. In the case of astronomy, on which
Galileo was called in question, the general sense of
cultivated and sober-minded men has long ago drawn
the distinction between religious and physical tenets
which is necessary to resolve this dilemma. On
this point, it is reasonably held, that the phrases
which are employed in Scripture respecting astro-
nomical 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 accomplished without

VOL. I. 2D

402 HISTORY OF FOkHAli AfltBOKOMY.

long and diBti*e8skig cont2y)ver8ie8. Nol*» if Wd Wish
to include all cages in which the fiatne dilemma may
again come into play, is it easy to lay down an ade*
quate canon for the purpose, l^ot 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 generalise
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 genera*
tion 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 be-
lieve to be rationally probable. And the new inter-
pretation, which the new philosophy requires, and
which appears to the older school to be a fetal
violence done to the authority of religion, is accepted
by their successors without the dangerous results
which Were apprehended. When the language of
Scripture, invested with its new meaning, has be-
come familiar to men, it is found that the ideas

SfiCtUEL TO COPEltNIOUB. 405

WMich it fealls upi are quite as reconcileable as the
f6rthei* ohes Wei*^, ^^th the soundest religious views.
And the worid then Iboks back with surprise at the
6i*tti» df thosej who thoU^t that the esseuce df retd*
lation was involved in their own arbitrary version of
some collateral circumstance. At the present day
we can hardly conceive how reasonable men should
have imagined that religious reflections on the sta-
bility of the earth, and the beauty and use of the
luminaries which revolve round it, would be interfered
With by its beiiig Acknowledged that thifil test and
tadtidh are aj)parent ohly.

In the next place, w^ tnay observe that those who
thU!^ adhere tenaciously to the tt^ditionary or arbi-
trary mode of understaudilig Scriptural expressions
df physical stents, ai*e always strongly condemned
hy suceefeding genefAtidns. They are looked upon
with feonteUipt by the 'world at Mrgd, who cartnot
enter Into thd obsolete difficulties With which they
encumbered theUiselveS 5 fend with pity by the more
fedUsiddiAtd and serious, whd know how much saga-
City and right-mindedness Jli*e requisite for the con*-
dufet df philoi^ophers and religious men on such
occasions ; but who know also hoW weak fend vain
is the attempt to get rid of the difficulty by merely
denouncing the new tenets as inconsistent with
religious belief, and by visiting the promulgators of
them with severity such as the state of opinions and
institutions may allow. The prosecutors of Galileo
fere still held up to the scorn and aversion of man-

2 D 2

404 HISTORY OF FORMAL ASTRONOMY.

kind ; although^ as we have seen^ they did not act
till it seemed that their position compelled them to
do SO, and then proceeded with all the gentleness
and moderation which were compatible with judicial
forms.

Sect. 5. — The Heliocentric THteory confirm^ on Phy-
sical cofisiderations. — {Prdude to Kepler^s Astroruh
micd Discoveries.)

By physical views, I mean, as I have already said,
those which depend on the causes of the motions of
matter, as, for instance, the oonsidefation of the
nature and laws of the force by which bodies fall
downwards. Such considerations were necessarily
and immediately brought under notice by the exa-
mination of the Copernican theory ; but the loose
and inaccurate notions Fhich prevailed respecting
the nature and lawa of force, prevented, for som^
time, all distinct reasoning on this subject, aad gave
truth little advantage ovev error. . The fonnation of
a new science, the science of m^otion BSkA. its causes,
was requisite, before the helioc^oitric system could
have justice done it with regard . to this part of the
subject.

This discussion was at first carried on, as was to
be expected, in terms of the received^, that, is, the
Aristotelian doctrines. Thus, Copernicus says that
terrestrial things appear to be at r^st when they
have a motion according to nature, tiiat is, a circular

SEQUEt t6 COPbRNlCUS. 405

motion ; and ascend or descend when they have, in
addition to this, a rectilinear motion by which they
endeavour 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 Maestlin, " is that heavy bodies
are said to move to the centre of the universe, and
light bodies from the centre. But I would ask,
where do we get this experience of heavy and light
bodies ? and how is our knowledge on these subjects
extended so far that we can reason with certainty
concerning the centre of the whole universe? Is
not the only residence and home of all the things
which are heavy and light to us, the earth and the
air which surrounds it ? and what is the earth and
the ambient air with respect to the immensity of the
universe ? It is a point, a punctule, or something,
if there be anything, still less. As our light and
heavy bodies tend to the centre of our earth, it is
credible that the sun, the moon, and the other lights,
have a similar affection, by which they reniain found
as we see them, but none of these centres is neces-
sarily 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, fialls exactly at the foot of the tower ? since
the tower bein^ carried from west to east by the

406 HISTORY OF FORMAL ASTRONOMY.

diurnal revolution of the earth, the stone must bei
left behind to the west of the place fron^ which it
was let fall. The proper answer to this was, thfit
the motion which the falling body received from its
tendency downwards w9J3 compotmded witli thp mo^
tion which, before it fell, it had in virt\je of the
earth's rotation : but this answer* cqu14 not be ^leswrly
made or apprehended, till Gralileo find his pupi}^ had
established the laws of such copipositions of motion
arising from different forces. Bothmaai, Kepler, and
other defenders of the Copemioan system, g^ve tJiaip
reply somewhat at a venture, when they asserted
that the motion of the earth was conn^unicated to
bodies at its surface. Still, the iacts which indicate
and establish this truth are obyipT^fl, when the siibject
is steadily considered; and the Copernic£i.i|d mon
found that they had the superiority of argument on
this point as well as others. The attacks upon the
Copemican system by Durrat, Moiin, Riocioli, and
the defewe of it by GnUle^ Lanaheig, Gafiae»di ^\
left ou all caadid jeasQuerft a oleai* impresiicai m
feyour of the system. Morin attempted to atop the
motiQU of the earth, which he oalled breal^ng^ ite
wings ; his Ake Term Froi^ was publiihed ia 1€48»
and aaaweved by Gbifiaacqdi. And Rieeidii m late
as 16^, in his Almageatum Novum, emsmemted
fifty-seven Copeimoan arguments, and pretended to
reltite them all : but such reaaoniags now made na

10

Pel. A. M. a, 504.

8EQ.UEli TO COPERNICUS. 407

converts ; md by this time the mechanical objections
to the motion of the earth were generally seen to be
baaeleasi m we shall relate when we come to speak
of the progress of mechanics aa 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, reftised their assent to it. Thus Riccioli, the
last of its considerable opponents, allows its supe^
riority in these respects ; and acknowledges (in 1658)
that the Gopemican belief appears rather to increase
than diminish under the condemnation of the de-i
ereea of the Cardinals. He applies to it the lines
of Horace'^!

Per danma per oeBdes, ab ipso
Sumit opes aaimumque ferro.

Untamed its pride, unchecked its course,
Froia fben w4 wounds it gathers force.

We have spoken of the influence of the motion of
the earth on the motions of bodies at its surfkee ; but
the notion of a physical connexion among the parts
of the universe was taken up by Kepler in another
point of view, which would probably have been con-
sidered as highly fantastical, if the result had not been,
that it led to by far the most magnificent and most
certain train of truths which the whole expanse of
human knowledge can show. I speak of the peiv
suasion of the existence of numerical and geometrical

408 HISTORY OF FORMAL ASTRONOMY.

laws connecting the distances, times, and forces of
the bodies which revolve about the central sun. That
steady and intense conviction of this governing prin-
ciple, which made its developement 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 con-
nected, though dimly and obscurely, with the notion
of a central agency or influence of some sort, ema«
nating from the sun, cannot be doubted. Kepler in
his first essay of this kind, the Mysterium Cosmogra-
phicum, 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 endeavours to make out some relation
between the distances of the planets from the sun
and their velocities. The inveterate yet vague
notions of forces which preside in this attempt, may
be judged of by such passages as the following : —
" We must suppose one of two things : eith^
that the moving spirits, in proportion as they are
more removed from the sun, are more feeble; or
that there is one moving spirit in the centre of all
the orbits, namely, in the sun, which urges each body
the more vehemently in proportion as it is nearer ;
but in more distant spaces languishes in consequence
of the remoteness and attenuation of its virtue."

We must not forget, in reading such passages, that
they were written under a belief that force was re-

SEQUEL TO COPERNICUS. 409

quisite to keep up, as well as to change the motion
of each planet ; and that a body, moving in a circle,
would stop when the force of the central point
ceased, instead of moving off in a tangent to the
circle, as we now know it would do. The force
which Kepler supposes is a tangential force, in the
direction of the body's motion, and nearly perpen-
dicular to the radius ; the force which modem phi-
losophy 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 connexion between the cause of motion and the
distance from the centre ; not only was his know-
ledge imperfect in all particulars, but his most gene-
ral 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 endeavoured to detect
numerical and geometrical relations among the parts
of the solar system. After extraordinary labour,
perseverance, and ingenuity, he was eminently suc-
cessful in discovering such relations ; but the glory
and merit of interpreting them according to their
physical meaning, was reserved for his greater suc-
cessor, Newton.

410 HISTORY op FOBMAL ASTRONOMY.

CHAPTER IV.

INPUCnVB EPOCH OF KilFLER.

Sect. 1. — InteUedual Character of Kepler.

Several persons*, especially in recent times, who
have taken a view of the discoveries of Kepler,
appear to have been surprised and somewhat dis-
contented that conjectures, apparently so fenclftil
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 fkntastical and self-willed, and violating in his
conduct, 2A they conceived, all right rule and sound

* Laplaoe, Precis de PHist. d'Ast. p. 94. <^ II eat affiigeant potur
Teiiprit bumaiii de iw e^ gra^d homme m^e« daQ« s^ d^nii^if^
auyn^ea, se compl^ire avec delicea dana ses chiin^ri<juQa speoiU^i-
tions, et les regarder CQmme Tame et la yie de rastronomiQ."

Hist, of A»t., L. U. K., p. 53. " This success []of Kepler]
may well inspire with dismay those who are aeoastoined to
consider experiment and rigorous induction as the only means
to interrogate nature with success."

life of Kepler, L. U. K., p. 14, « Bad philosophy." P. 15,
'^ Kepler's miraculous good fortune in seizing truths across the
wildest and most absurd theories." P. 5^ ^^ The danger of
attempting to follow his method in the pursuit of truth."

inductive; epoch of kbpleb, 411

philosophy, is rewarded with the most signal tri.
umphs. Perhaps one or two reflections may in some
measure reooncile us to this result. In the first
place, we may observe th«i.t the leading thought
which suggested and animated all Kepler's attempts
^as true, and we may add, sagacious and philosot
phical ; namely, that there must be ^ome numerical
or geometrical relations among the times, distances,
md velocities of the revolving bodies of the solar
system. This settled and constant conviction of an
important truth regulated all the coi\jectures, ap«
parently so capricious and fanciful, which he made
and examined, respecting particular relations in the
siystem.

In the next place, we may venture to ^y, that
advances in knowledge are not commonly made witht*
put (he previous exercise of some boldness and license
in guessing. The discovery of new truths requires,
undoubtedly, minds careftil and scrupulous in examin**
ing what is suggested ; but it requires, no less, such as
are quick and fertile in suggesting. What is inven*
tion, 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 inadr
missible suppositions, they are quickly forgotten by
mast persons ; and few think it necessary to dwell
on these discarded hypotheses, and on the process
by which they were condemned, as Kepler has dona
But all who disi^over truths must have reasoned
upon many errors, to obtain each truth; Qveiy

412 HISTORY OP FORMAL ASTRONOMY.

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 dis-
coverers have been. Discovery is not a " cautious"
or "rigorous" process, in the' sense of abstaining
from such suppositions. But there are great dif-^
ferences in different cases, in the £Etcility 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 remark-
able for the labour which he gave to such self-refu-
tations, and for the candour and copiousness with
which he narrated them ; his works are in this way
extremely curious and amusing ; and are a very in-
structive exhibition of the mental process of dis-*
covery. But in this respect, I venture to believe^
they exhibit to us the usual process (somewhat
caricatured) of inventive minds : they mther exem--
plify the rule of genius than (as has genendly been
hitherto taught,) the eaeeptiosfu We may add^ that
if many of Kepler^s guesses now appear fimcifiil and
absurd, because time and observation have reftited
them, others, which were at the time equally gra*
tuitous, have been confirmed by sueeeeding diseo^
veries in a manner which makes them appear
marvellously sagacious ; as for instance^ his assertion
of the rotation of the sun on his axis, beforo the
invention of the telescope, and his opinion that the
obliquity of the ecliptic was decreasing, but would,

INDUCTIVE EPOCH OF KEPLER. 413

after a long-continued diminution, stop, and then
increase again". Nothing can be more just, as well
as more poetically happy, than Kepler's picture of
the philosopher's pursuit of scientific truth, conveyed
by means of an allusion to Virgil's shepherd and
shepherdess :^-

Malo ne Cblatea petit, lascira puella
Et fiigit ad salioes et se cupit ante videri.

Ooy yet inTittng, Galatea lores
To sport in sight, then plunge into the grores ;
The challenge given, she darts along the green,
"Will not be caught, yet woidd not run unseen.

We may notice aa another peculiarity of Kepler's
reasonings, the length and laboriousness of the pro-
cesses by which he discovered the errors of his first
guesses. One of the most important talents requi-
site for a discoverer, is the ingenuity and skill which
devises means for rapidly testing false suppositions
as they offer theansdves. This talent Kepler did
not possess : he was not even a good arithmetical
calculator, often making mistakes, some of which he
detected and laments, while others escaped him to
the last. But his defects in this respect were com-
pensated by his courage and perseverance in under-
taldng and executing such tasks ; and, what was still
more admirable, he never allowed the labour he had
spent upon any conjecture to produce any reluctance
in abandoning the hypothesis, as soon as he had

* Bailly, A. M. ui. 175. ;

414 HISTOBT OF FOttMAt AfiTTEONOMY.

evidence of its inaccuracy* The only way in which
he reWftMed himaelf for his ti^ubl^ Was by d^
Scribitlgf to the world, in his lively mAtmet, Mn
ichetnes, ekertions, and feelings;

The mtfstical parts df Kepler's t^inioAs^ aji hiii
belief in astrology, his persuasion that the earth WM
an animal, and many of the loose moral and spiritual
as well as sensible analyses by which he rej^tesented
to himself the powers which he supposed to prevail
in the uuivei^e, do not appear to have Interfered
with his discovery, but rather to have stimulated
his invention, and animated his exertions. Indeed,
Where there ai*e cleat* scientific ideaa on one subject
in the rnind^ it does not appeal! that mysticism on
others is at all unfavourable to the successful prose<
cution of research.

It appears, then, that We may eonsidet Kepler's
character as containing the general features of the dltt*
Iticter of a scientific discoverer^ though some of the
features are exaggerated, and some too feebly mat^ked*
His spirit of invention was undoubtedly very l^ile
and ready, and this and his pers^erance B&ffeA to
remedy his deficiency in mathematical artifice and
method. But the peculiar physiognomy is giVett to
his intellectual aspect by his dwelling in a mdit
prominent manner on those erroneous ttidns df
thought which other persons conceal from the
worlds and often themselves forget, because they
find means of stopping them at the outset. In
the beginning of his book {Arffummta Capiium)

INbUCTlVfi EPOCH OP KEPLER. 416

h(§ mp^ " if Christophei» Columbus, if Magellan, if the
Pdrtugfuese when they narrate their Wanderings, are
not only excusedj but if we do not wish these pas-
sages omitted, and should lose much pleasure if they
Wer^, let no one blame me for doing the same.**
Kepter's talents were a kindly and fertile soil, which
h^ cultivated with abundant toil and vigour; but
With great scantiness of agricultural skill and imple-
ments. Weeds and the grain throve and flourished
side by side almost undistinguished ; and he gave a
peculiar appearance to his harvest, by gathering and
preserving the one class of plants with as much care
and diligence as the other.

Sect 2. — Kepler's Discovery of his Third Lata*

I sriALL now give some account of Kepler's specula-
tions and discoveries. The first discovery which hd
attempted, the relation among the successive dis**
tances of the planets from the sun, was a fkilure;
his doctrine being without any solid foundation,
although propounded by him with great triumph,
in a work which he called " Mysterlum Cosmogra-
phlcum,*' and which was published in 1596. The
account which he gives of the train of his thoughts
on this subject, viz. the various suppositions assumed,
examined, and rejected, is curious and instructive, for
the reasons Just stated ; but we shall not dwell upon
th^se essays, since they led only to an opinion now
entirely abandoned. The doctrine which professed to

416 HISTORY OF FORMAL ASTRONOMY.

give the true relation of the orbits of the different
planets, was thus delivered'. ^* The orbit of the earth
is a circle ; round the sphere to which this circle be-
longs describe a dodecahedron ; the sphere including
this will give the orbit of Mars. Bound Mars describe
a tetrahedron ; the circle including this will be the
orWt of Jupiter. Describe a cube round Jupiter's
orbit ; the circle including this will be the orbit of
Saturn. Now inscribe in the earth's orbit an icosar
hedron ; the circle inscribed in it will be^ the orbit
of Venus. Inscribe an octahedron in the orbit of
Venus ; the circle inscribed in it will be Mercury's
orbit. This is the reason of the number of the
planets." The five kinds of polyhedral bodies here
mentioned are the only " regular solids."

But though this part of the " Mysterium Cosmo-
graphicum" was a failure, the same researches con-*
tinned to occupy Kepler^s mind; and twenty-two
years later led him to one of the important rules
known to us as "Kepler's laws;" namely, to the
rule connecting the mean distances of the planets
from the sun with the times of their revolutions.
This rule is expressed in mathematical terms by say-
ing 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

^ L. U. K. Kepler, 6.

INDUCTIVE EPOCH OF KEPLER. 417

of the " Mysterium," Kepler had said, " In the year
15^5, I brooded with the whole energy of my mind
on the subject* of the Copemican system. There
were three things in particular of which I pertina-
ciously 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 suc-
cess in this respect he was not himself completely
satisfied. But in the fifth book of the ^' Harmonice
Mundi," published in 1619, he says, " What I pro-
phesied two-and-twenty years ago as soon as I had
discovered the five solids among the heavenly bodies ;
—-what I firmly believed biefore 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 recognised its truth
beyond my most sanguine expectations."

The rule thus referred to is stated in the third
chapter of this fifth book. " It is," he says, " a
most certain and exact thing that the proportion
which exists between the periodic times of any

VOL. I. 2 E

418 FOBHAL HISTORY OF AGTrBONOMT.

two planets is precisely the sesquiplicate of the pro-
portion 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 proportimi, that 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 I ; and
the cube root of 30 is greater than 8, and therefore
the square of it is greater than fi. And Saturn at
his mean distance from the sun is at a little more
than 9 thnes the mean distance of the earth.''

When we now look back at the time and exer-
tions which the establishment of this law cost
Kepler, we are tempted to imagine that he was
strangely blind in not seeing it sooner. His object,
we might reason, was to discover a law connecting
the distances and the periodic times. What law of
connexion could be more simple and obvious, we
might say, than that one of these quantities should
vary as some power of the other, or as some root, or
as some combination of the two, which in a more
general sense, may still be called a power? And if
the problem had been viewed in this way, the ques*
tion must have occurred, to what power of the
periodic times are the distances proportional ? And
the answer must have been, that they are propor-
tional to the square of the cube root. This ea^posi-
facto obviousness of discoveries is a delusion to

INDUOTIVB EPOCH OP KEPLER. 419

which we are liable wittf 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 5 and that in Kepler's time, algebra
had not taken the place of geometry, as the most
usual vehicle of mathematical reasoning. It may be
added, also, that Kepler always sought his formal
laws by means of physical reasonings ; and these,
though vague or erroneous, determined the nature
of tie mathematical connexion which he assumed.
Thus in the « Mysterium" he had been led by his
notions of moving virtue of the sun to this conjec-
ture, 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 Har-
monics of the Universe consists in attempts to ex-
plain various relations among the distances, times,
and eccentricities of the planets, by means of the
ratios which belong to certain concords and discords.
This portion of the work is so complex and labo-
rious, that probably few modem readers have had
courage to go through it. Delambre* acknowledges

* A. M. i. 358.

2 E 2

420 HISTORY OF FORMAL ASTRONOMY.

that his patience often foiled him during the task ;
and subscribes to the judgment of Bailly ; "After this
sublime eflTort, Kepler replunges himself in the rela^
tions of music to the motions, the distance, and the
eccentricities of the planets. In all these harmonic
ratios there is not one true relation ; iii a crowd of
ideas there is not one truth : he becomes a- man
after being a spirit of light." Certainly these spe-
culations 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 colours and the notes of the gamut*
The numerical relations of concords are so peculiar,
that we can easily suppose them to have other bear-
ings than those which first oiflfer 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
deduced from it, and which are foimd in the " Epi-
tome Astronomise Copemicande," published 1622.
In that work also (p. 554), he extended this law,
though in a loose manner, to the satellites of Jupiter.
These physical speculations were only a vague and
distant prelude to Newton's discoveries; and the
law, as 9^ 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.

* Optics, b. 2. p. iy. obs. 5.

INDUCTIVE EPOCH OF KEPLER. 421

Sect, 3. — Kepler's Discovery of his First and Second
Laws. Elliptical Themy 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 by
lines drawn from the sun to the planet are propor-
tional 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 hypo-
thesis of eccentrics and epicycles ; the event of it was
the complete overthrow of that hypothesis, and the
establishment, in its stead, of the elliptical theory of
the planets. Astronomy was now ripe for such a
change. As soon as Copernicus had taught men
that the orbits of the planets were to be referred to
the sun, it obviously became a question, what was the
true form of these orbits, and the rule of the motion
of each planet in its own orbit. Copernicus repre-
sented the motions in longitude by means of eccen-
tries and epicycles, a« we have already said ; and the
motions in latitude by certain librations, or alternate
elevations and depressions of epicycles. If a mathe-
matician could have 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 refe-
rence to the sun as well as to the earth ; but this
was not possible, for though the geocentric position,
or the direction in which the planet was seen, could

422 HISTORY OF FORMAL ASTRONOMY.

be observed, its distance from the earth was not
known. Hence, when Kepler attempted to deter-
mine the orbit of a planet, he combined the observed
geocentric places with successive modifications of
the theory of epicycles, till at last he was led, by
one step after another, to change the epicyclical into
the elliptical theory. We may observe, moreover,
that at every step he endeavoured to support his
new suppositions by what he called, in his fitnciful.
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
hjrpotheses 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 endeavour to connect remote
points of their knowledge, not those who stop cau-
tiously 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 then he also
entered upon that train of researches which he
published in 1609 in his extraordinary work " On
the Motion 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 suppo-
sitions which he had made, the notions by which he
had been led to invent or to entertain them, tha

INDUCTIVE EPOCH OF KEPLEB. 423

processes by which he had proved their falsehood,
and the alternations of hope and sorrow, of vexation
and triumph, through which he had gone. It will
not be convenient however for us to cite many pas-
sages of these kinds, curious and amusing as they are.
Oiie of the most important truths contained in
the "Motion 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 eccen-
tric hypothesis introduced ; and that, when so con-
sidered) it has none of the librations which Ptolemy
and Copernicus had attributed to it. The fourteenth
chapter of the second part asserts, " Plana eccentri-
dorum esse irdXavTaf that the planes are urdi-
bratingi retaining always the same inclination to the
ecliptic, and the same line of nodes. With this step
Kepler appears to have been justly delighted. His
reflections on it are very philosophical. " Coper-
nicus," he says, " not knowing the value of what he
possessed (his system), undertook to represent
Ptolemy rather than nature, to which, however, he
had approached more nearly than any other person.
For being rejoiced that the quantity of the latitude
was increased by the approach of the earth to the
stars, according to his theory, he did not venture to
reject the rest of Ptolemy's increase of latitude, but
in order to express it, devised librations of the
planes of the eccentric, depending not upon its own
eccentric, but (most improbably) upon the orbit of

424 HISTORY OF FORMAL ASTRONOMT.

the earth, which has nothing to do with it. I always
fought against this impertinent tying together of two
orbits, even before I saw the observations of Tycho;
and I therefore rejoice much, that in this, as in
others of my preconceived opinions, the observations
were found to be on my side." Kepler established
his point by a fair and laborious calculation of the
results of observations of Mars, made by himself
and Tycho Brahe ; and had a right to exult, when
the result of these calculations confirmed his views
of the symmetry and simplicity of nature.

We may judge of the difficulty of casting off the
theory of eccentrics and epicycles, by recollecting
that Copernicus did not do it at all, and that Kepler
did it only after repeated struggles, the history of
which occupies thirty-nine chapters of his book. At
the end of them he says, " This prolix disputation
was necessary, in order to prepare the way to the
natural form of the equations, of which I am now to
treat*. 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, in proportion as it was
supported by the authority of all philosophers, and
apparently agreeable to metaphysics." But before
he attempts to correct this erroneous part of his
hypothesis, he sets about discovering the law ac-
cording to which the different parts of the orbit are
described in the case of the earth, in which case the

• iii. 40.

INDUCTIVE EPOCH OF KEPLER. 425

ecGentricity is so small that the effect of the oval
form is insensible. The result of this inquiry was',
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 to the extremities of
the arc. It is to be observed that this rule, at first,
though it had the recommendation of being selected
after the unavoidable abandonment of many, which
were suggested by the notions of those times, was far
from being adopted upon any very rigid or cautious
grounds. A rule had been proved to hold at the ap-»
sides of the orbit, by calculation from observations,
and had then been extended by conjecture to other
parts of the orbit ; and the rule of the areas was only
an approximate and inaccurate mode of representing
this rule, employed for the purpose of brevity and
convenience, in consequence of the difficulty of
applying, geometrically, that which Kepler then
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";
and the deviation from exactness in the result was
attributed to the inaccuracy of those approximate pro-

' p. 194. « iv. c. 47.

426 HISTORY OP FORMAL ASTRONOMY.

cesses. The supposition of the oval had ahreadj 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*.

It may serve to show the kind of labour by which
Kepler was led to his result, if we here enumerate,
as he does in his fortynseventh chapter ^% six hypo-
theses^ on which he calculated the longitudes of
Mars, in order to see which best agreed with obser-
yation.

1. The simple eccentricity.

2. The bisection of the eccentricity, and the dupli-
cation of the superior part of the equation.

3. The bisection of the eccentricity and a stationary
point of equations, after the manner of Ptolemy.

4. The vicarious hypothesis by a free section of
the eccentricity made to agree as nearly as possible
with the truth.

5. The physical hypothesis on the supposition of
a perfect circle.

6. The physical hypothesis on the supposition of
a perfect ellipse.

By the physical hypothesis, he meant the doctrine
that the time of a planet's describing any part of its
orbit is proportional to the distance of the planet
from the sun, for which supposition, as we have

• L. U. K. Kepler, p. 30. '' p. 228.

INDUCTIVE EPOCH OF KEPLER. 427

8aid| 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'* that he might take
another ellipsis, exactly intermediate between the
former one and the circle, and that this must give
the path and the motion of the planet. Making this
assumption, and taking the areas to represent the
times, he now saw'* 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 whcSn I had communicated my
hypothesis of cap. 45, was able, by his observations,
to show that it erred in making the distances too
short at mean longitudes ; of which he informed me
by letter while I was labouring, by repeated eiforts,
to discover the true hypothesis. So nearly did he get
the start of me in detecting the truth." But this was
less easy than it might seem. When Kepler's first
hypothesis was enveloped in the complex construction
which was 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

»» c. 58. " p. 235.

428 HISTORY OP FORMAL ASTRONOMY.

the coincidences of certain numbers, which, as he
says, raised him as if from sleep, and gave him a new
light. We may observe, also, that he was perplexed
to reconcile this new view, according to which the
planet described an exact ellipse, with his former
opinion, which represented the motion by means of
libration in an epicycle. ** This,'* he says, " was my
greatest trouble, that, though I considered and re-
flected till I was almost mad, I could not find why
the planet, to which, with so much probability, and
with such an exact accordance of the distances, the
libration in the diameter of the epicycle was attri-
buted, should, according to the indication of the
equations, go in an elliptical path. What an ab-
surdity 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 sdlving, 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 solu-
tion. As, however, the calculation can be performed,
and, indeed, was performed by Kepler himself, with
a sufficient degree of accuracy to show that the
elliptical hypothesis is true, the insolubility of this
problem is a mere mathematical difficulty in the
deductive process, to which Kepler's inductions
gave rise.

INDUCTIVE EPOCH OP KEPLER. 429

Of Kepler's physical reasonings we shall speak
more at length on another occasion. His numerous
and fanciful hypotheses had discharged their office,
when they had suggested to him his many lines of
laborious calculation, and encouraged him under the
exertions and disappointments to which these led.
The result of this work was, the formal laws of the
motion of Mars, established by a clear induction,
since they represented, with sufficient accuracy, the
best observations. And we may allow that Kepler
was entitled to the praise which he claims in the
motto on his first leaf. Ramus had said that if any
one would construct an astronomy without hypothesis,
he would be ready to. resign to him his professorship
in the University of Paris. Kepler quotes this pas-
sage, and adds, " it is well, Rsimus, that you have
run from this pledge, by quitting life and your pro-
fessorship*'; if you held it still, I should, with justice,
claim it." This was not saying too much, since he
had entirely overturned the hypothesis of eccentrics
and epicycles, and had obtained a theory which was
a mere representation of the motions and distances
as they were observed.

18

Ramus perished in the Massacre of St. Bartholomew*

430

CHAPTER y.

Sequel to the Epoch op Keplbm. RECEPnoif,
Verification, and Extension of the Elliptical
Theoby.

Sect. 1. — ApplicatioH of the Elliptical Theory to the

Planets.

The extension, to the other planets, of Keplei^s dis-
coveries concerning the orbit of Mars, obviously
offered itself as a strong probability, and was con-
firmed by trial. This was made in the first place
upon the orbit of Mercury ; which planet, in conse-
quence of the largeness of its eccentricity, exhibits
more clearly than the others the circumstances of the
elliptical motion. These and various other supple-
mentary portions of the views to which Kepler^s
discoveries had led, appeared in the latter part of his
** Epitome Astronomiae CopemicanaB," published in
1622.

The real verification of the new doctrine concern-
ing the orbits and motions of the heavenly bodies
was, of course, to be found in the construction of
tables of those motions, and in the continued com-
parison of such tables with observation. Kepler's
discoveries had been founded, as we have seen, prin-

SEQUEL TO THE EPOCH OF KEPLER. 431

cipally on Tyoho's observations. Longomontanus (so
ealled as being a native of Langberg in Denmark,)
published, in 1621, in his •* Astronomia Danica,'*
tables founded upon the theories as well as the ob*
servations of his countryman. Kepler^ in 1627
published his tables of the planets, which he called
^* Budolphine Tables," the result and application of
his own theory. In 1683, Lansberg, a Belgian, pub-
lished also ** Tabulae Perpetuee ;" 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 astronomer, who lived in the same
part of Lancashire. By him Horrox was warned
that Lansberg was not to be depended on ; that his
hypotheses were vicious, and his observations falsi-
fied or forced into agreement with his theories. He
then read the works and adopted the opinions of
Kepler ; and after some hesitation which he felt at

^ Rheticus, Narratio, p. 98,

432 HISTORY OF FORMAL ASTRONOMY.

the thought of attacking the object of his former
idolatry, he wrote a dissertation on the points of di&
ference between them. It appears that» at one
time, he intended to have offered himself as the
timpire who was to adjudge the prize of excellence
among the three rival theories, of Longomontanus,
Kepler and Lansberg ; and, in allusion to the story
of ancient mythology, his work was to have been
called " Paris Astronomicus ;" we easily see that he
would have given the golden apple to the Keplerian
goddess. Succeeding observations confirmed his judg-
ment : and the ^^ Budolphine 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 to rule of the motions of the moon
was a harder task than the formation of planetary
tables, if accuracy was required ; for the moon's
motion is affected by an incredible nmnber of diffe-
rent and complex inequalities, which, till their law
is detected, appear to defy a^l theory. Still, how-
ever, 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 evectiouy which Ptolemy had discovered)

INDUCTIVE EPOCH OF KEPLER. 438

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
€mnual eqtmtion.

These steps concerned the longitude of the moon ;
Tycho also made important advances in the know-
ledge of the latitude. The inclination of the orbit
had hitherto been assumed to be the same at all
times ; and the motion of the node had been sup-
posed uniform. He found that the inclination in-
creased snd diminished by twenty minutes, according
to the position of the line of nodes ; and that the
nodes, though they regress upon the whole, some-
times go forwards and sometimes go backwards.

Tycho's discoveries concerning the moon are given
in his " Progynmasmata," which was published in
1603, two years after the author's death. He repre-
sents 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 impos-

» We have seen (Book III, p. 228), that Aboul-Wefa, in the
tenth century, had already noticed this inequality ; but his dis-
covery had been entirely forgotten long before the time of
Tycho, and has only recently been brought again into notice.

VOL. I. 2 F

4d4 HISTORY OF FORMAL ASTRONOMY.

sifole not to think of extending the elliptical theory
to the moon. Horrox succeeded in doing this ; and
in 1638 sent his essay to his fiiend Crabtree. It
was published in 1673, with the'numerical elements
i^uisite for its application added by Flamsteed.
Flamsteed had also (in 1671 and 2) compared ibis
theory with observation, and found that it agreed
fiir more nearly than the " Philolaic Tables" oF
BolUaldus, or the '' Carolinian Tables" of Street
(Epilogus and Tabulas.) Halley, by making ihe
centre of the ellipse revolve in an epicycle, gaTe mn
explanation of the evection, as well as of > the
equation of the centre.

Modem astronomers, by calculating the effoete^Rf
the perturbing forces of the solar system, and cooh
paring their calculations with observafaon, .jiavd
added many new corrections or equations to tbosd
known at the time of Horrox ; and since ihe m^
tions of the heavenly bodies were even tib^i aflfeot^
by these variations as yet undetected, it is clear, itmlk
the tables of that time must have shown some errors
when compared with observation. These errors
much perplexed astronomers, and naturally gave rise
to the question, whether the motions of the heav^f
bodies really were exactly regular, or whether they
were not affected by accidents as little reducible to
rule as wind and weather. Kepler had held the
opinion of the casualty of such errors ; but Horrox,
far more philosophically, argues against this opinion,
though he allows that he is much embarrassed by

INDUCTIVE EPOCH OF KKPLEB. 43&

the deviations. His arguments show a singukrly-
olear and strong apprehension of the features of the
oase» and their real import. He saysS '^ these errors
of .the tables are alternately in excess and defect ;
bow could this constant compensation happen, if they
wetie casual ? Moreover, the alternation from excess
to defect is most rapid in the moon, most slow in
Jupiter and Saturn, in which planets the error con-
tinues 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
ineqimlities are of long period, while those of the
Bfeoon aafe numerous, and rapidly changing." It would
be impossible, at the present moment, to reason
better on this subject ; and the doctrine, that all the
a^pparent irregularities of the celestial motions are
teally regular, was one of great consequence to
establish at this period of the science.

Sect. ^. -^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 Copemican theory, led
inevitably, after some vagueness and perplexity, to a

' Astron. Kepler. Proleg. p. 17*

2 F 2

436 HifirroRY of formal astronomy.

sound science of mechanics ; and this science in time
gave a new fece to astronomy. But in the mean
time, while medbanical mathematicians were gene-
ralising from the astronojny already established,
astronomers were accumulating new fiacts, which
pointed the way to new theories and new generalisa-
tions. Copernicus, while he bad established the per-
manent length of the year, had confirmed the motion
of the sun's apogee, and had shown that the eccen-
tricity of the earth's orbit, and the obliquity of the
ecliptic, were gradually, though slowly, diminishing.
Tycho had accumulated a store of excellent observa-
tions. These, as well as the laws of the motions of
the moon and planets already explained, were mate-
rials 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 c<m-
firming the Copemican doctrine by the phases of
Venus, and the analogical examples of Jupiter and
Saturn, which appeared like models of the solar sys-
tem ; but disclosing unexpected objects, as the ring
of Saturn, and the spots of the sun. The art of ob-
serving made rapid advances, both by the use of the
telescope, and by the sounder notions of the con-
struction of instruments which Tycho introduced.
Copernicus had laughed at Rheticus, when he was
disturbed about single minutes ; and declared that if
he could be sure to ten minutes of space, he should
be as much delighted as Pythagoras was when he

INDUCTIVE EPOCH OF KEPLER. 437

discovered the property of the right angle. But
Kepler founded the revolution which he introduced
on a quantity less than this. " Since," he says*,
" the divine goodness . has given us in Tycho an
observer so exact that this error of eight minutes is
impossible, we must be thankful to God for this,
and turn it to account. And these eight minutes,
which we must not neglect, will, of themselves,
enable us to reconstruct the whole of astronomy."
In addition to other improvements, the art of nume-
rical calculation made an inestimable advance by
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 unsys-
tematised facts. The science was, therefore, forced
along by a strong impulse on all sides. We now
proceed to speak of the new path into which this
pressure forced it, and first we must trace the rise
and progress of the science of mechajiics.

* De Mot. Mart. 19.

END OF THE FIRST VOLUME.

Errata.

. ..c bed

ERRATA IN VOL. I.

Page 42, line 16, /or inscribed, read invented.
126,. line 1, &c., read

Chorus op Clouds.

The Moon by us to you her greeting sends.
But bids lis say that she*8 an ill-used moon.
And takes it much amiss that you should still
Shuffle her days and turn them topsy-turvey ;
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.

ATo^tf.— This passage is supposed by the commentators to be intended as a
satire upon those who had introduced the cycle of Meton at Athens, which
had been done a few years before ^' The Clouds** was acted.

Page 146, note ^* Acronieai, read Aeronyeai (joKpowKiog, happening at the
extremity of the night).
181, bottom line, for somewhat, read somehow.

245, note, line 7? /or audentes, read rudentes.

246, line 11, read of Caius.

271, note, line 2, for essus, read fessus.

273, line 3 from bottom, /or compounds, read compends.

274, line 5 from bottom, /or Padiymeus read Pachymerus*
291, line 11, /or rerpaxrifv, read rrrpcutrxiv.

301, line 1, for astronom. read Astroninu
413, line 7; for Male ne, read lialo me.

London:

JOHN W. PARKER,
Wbst Stband.